高性能整体—局部高阶理论及高阶层合板单元
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摘要
本文旨在客观地评价位移基层合板理论，并且提出应用范围广范且准确高效的层合板理论。基于这一目的，本文用解析解对十几种有代表性的层合板理论进行数值比较。结果表明：对于层数较少的层合板，整体-局部1，2-3高阶理论GLHT-30(3表示整体面内位移沿板厚度方向展开三次多项式，0表示横向位移沿厚向为常数)能够通过本构方程直接准确计算横向剪切应力不需要任何后处理。基于整体-局部1，2-3高阶理论，本文建立了几种层合板单元并分析了层合板弯曲、动力和屈曲问题。进一步研究表明，整体-局部1，2-3高阶理论不能处理多层板弯曲，面内和任意温度分布载荷作用的层合板问题。从提高效率和扩展应用范围考虑，本文基于整体-局部1，2-3高阶理论建立了几种增强整体-局部高阶理论并系统地研究了复合材料层合板有限元方法。具体工作为：
1．建立几种整体-局部高阶理论。
●为了提高计算效率，本文建立了Reddy型整体-局部高阶理论。Reddy型整体-局部理论能够预先满足面内位移和横向剪切应力层间连续，而且独立变量个数比整体-局部1，2-3高阶理论少了4个。此理论已被用于分析层数较少层合板和功能梯度板弯曲问题。
●通过提高整体-局部1，2-3高阶理论整体面内位移沿板厚度方向展开多项式的阶数，本文提出整体-局部高阶理论GLHT-m0(m为整体面内位移沿厚度方向展开多项式的阶数，m取不同的值可以得到不同的理论)，基于此理论研究了高阶剪切变形对多于五层层合板弯曲、动力及屈曲响应的影响，并且给出结论即对于多于五层层合板问题应采用五阶整体-局部理论(m=5)。
●对于热膨胀问题，横法向应变扮演重要角色。为了处理热膨胀问题，本文把整体-局部1，2-3高阶理论的横向位移w沿厚向展开二次多项式建立了考虑横法向应变的整体-局部高阶理论GLHT-32(3表示整体面内位移沿厚度方向展开三次多项式，2表示横向位移沿厚向展开二次多项式)。数值试验表明，GLHT-32确实能够处理热膨胀问题。
●本文进一步提出了能够处理在任意温度载荷作用下任意铺设层合板问题的整体-局部高阶理论GLHT-52。此工作把整体-局部高阶理论应用范围扩展到任意温度载荷问题和角铺设层合板问题。
●复合材料层合板自由边问题是典型三维问题，现有等效单层板理论不能处理此类问题，不得不采用三维有限元和Layerwise理论(效率低)。通过提高整体面内位移和横向位移沿厚度方向展开多项式的阶数，本文建立了增强型整体-局部高阶理论GLHT-mn(m，n分别表示整体面内位移和横向位移沿厚度方向展开多项式的阶数，m，n取不同的值可以得到不同的理论)并应用此理论分析了层合板自由边问题。数值试验表明，GLHT-99能够准确分析多种自由边问题。本文增强型整体-局部高阶理论属于等效单层板理论但可以准确分析自由边问题，直接验证了等效单层板理论有能力分析层合板自由边问题。
●本文建立了整体-局部高阶层合壳理论GLHST-52并给出了简单解析解。当前的层合壳理论特点是未知变量个数独立于层合壳层数，并且应用本构方程可以直接准确地计算横向剪切应力。数值比较表明，当前理论计算的结果精度明显高于同类层合壳理论。
2．基于建立的整体-局部高阶理论，本文系统地研究了复合材料层合板有限元方法。
●应用精化元法分别提出了精化四边形单元RQLP13和精化三角形单元RTLP23；基于满足单元间C~1连续的离散Kirchhoff薄板单元，建立了三角形层合板单元TLP13和四边形单元QLP19。整体-局部高阶理论的应变项中出现了横向位移w的一阶导数和二阶导数，构造有限元时应使用同时满足C~0和C~1连续的横向位移函数，被称为C~(0-1)连续，是一种新提法。为此，本文用同样节点参数分别构造满足C~0和C~1连续的两套横向位移函数。本文有限元法列式简单，便于实施，计算过程中无须特殊的数值技巧，求解各种算例效果很好，在规则和不规则网格下，它们都能保持良好的性态。
●基于整体-局部1，2-3高阶理论推导了动力及稳定问题的有限元，把修改几何刚度阵的方法推广到复合材料层合板稳定问题。用本文方法分析了软核夹层板和变厚度层合板动力及屈曲问题，结果表明：一阶理论甚至整体型高阶理论不适于预测软核夹层板和变厚度层合板静动力及屈曲响应，本文有限元能够给出准确结果。
●组合整体-局部1，2-3高阶理论和Layerwise理论，本文建立了混合模型并应用此模型分析压电层合板问题，研究沿厚度方向电位移选取对结果的影响。在混合模型中整体-局部1，2-3高阶理论模拟压电板的结构变形，Layerwise理论模拟电位移沿厚度方向的变化。该模型突破了以往用位移基高阶理论求解层合压电板必需使用后处理方法计算横向剪切应力的限制。
●基于整体-局部1，2-3理论推导了几何非线性有限元并且分析了层合板几何非线性问题。结果表明：对于层合板几何非线性分析，面内位移的二次项对横向剪切应力确实影响较大。
Aim of this thesis is to propose more accurate and efficient laminated plate theories afterobjectively estimating previous the displacement-based laminated plate theories. To pursuethis goal, this thesis firstly compared several theories by using analytical methods. Numericalresults show that 1,2-3 global-local higher-order theory is able to accurately predict transverseshear stresses without any smoothing methods as the number of layers of laminated plates isless than five. Based on this theory, several laminated plate elements have been constructed.Moreover, these elements were used to analyze bending, vibration and buckling of laminatedplates. By further research on 1,2-3 global-local higher-order theory, it is found that thistheory will encounter some accuracy difficulties to analyze bending of multilayered plates andthermal expansion of laminated plates. In view of computational efficiency and range ofapplicability, this thesis proposes several enhanced global-local higher-order theories andstudies detailedly laminated plate elements. Main work includes the following aspect:
1. Proposed several global-local higher-order theories.
●To improve computional efficiency, Reddy-type global-local higher-order theory ispresented. This theory can a priori satisfy continuity of in-plane displacements andtransverse shear stresses at interfaces. Moreover, compared to 1,2-3 global-localhigher-order theory, number of independent variables is reduced to 7. This theory hasbeen used to analyze bending of lamianted plates with few layers and functionally gradedplates.
●By increasing the number of orders of the global in-plane displacement component in1,2-3 global-local higher-order theory, the global-local higher-order theory GLHT-m0 ispresented. Using this theory, effects of higher-order global-local shear deformations onbending, vibration and buckling of multilayered plates have been studied and thecorresponding conclusions are drawn: considering computational efficiency and accuracyof the results, the fifth-order global-local theory (m=5) should be applied to predict thestatic, the dynamic and the buckling response of multilayered plates.
●For thermal expansion problems of laminated plates, transverse normal strain plays animportant role. To analyze such problems, global-local higher-order theory GLHT-32 isproposed by considering transverse normal strain of 1,2-3 global-local higher-ordertheory. Numerical results show that GLHT-32 is suitable for predicting thermal responseof laminated plates under uniform temperature.
●This thesis further developes the global-local higher-order theory GLHT-52 which canaccuratelly predict thermal response of angle-ply laminated plates subjected to arbitrarytemperature loads. This work extends the range of applicability of the global-localhigher-order theory.
●It is well known that the free-edge problem is a typical three-dimensional problem.Three-dimensional finite elements and layerwise theories have to be used to analyzefree-edge effects because previous equivalent single layer plate theories can not analyzeso complicated problem. By increasing the number of order of in-plane and transversedisplacements, an enhanced global-local higher-order theory GLHT-mn has beendeveloped to analyze free-edge problems. Numerical results show that GLHT-99 which isa typical equivalent single layer plate theory is able to predict accurately static responseof the free-edge effects. Thereby, this work directly proves that equivalent single layerplate theory can analyze free-edge problems of laminated plates.
●Global-local higher-order laminated shell theory GLHST-52 as well as correspondinganalytical results have been given in this thesis. Unknown variables of this theory areindependent of number of layers and transverse shear stresses can be directly computedfrom constitutive equations. Numerical results show that present shell theory is moreaccurate than other shell models.
2. Based on global-local higher-order theory, this thesis detailedly studies laminatedplate elements.
●Based on the refined nonconforming element method, a refined four-node quadrilateralplate element RQLP13 and a refined three-node triangular element RTLP23 are presented.Subsequently, a triangular plate element TLP13 and a quadrilateral plate element QLP19are also proposed by using the discrete Kirchhoff thin plate bending element satisfying C~1continuity on the element boundary. Global-local higher-order theory possesses first andsecond derivatives of transverse displacement w in the strain components. Thustransverse displacement function satisfying C~0 as well as C~1 continuity on the elementboundary, which is named as C~(0-1) continuity, should be employed. This thesiscircumvents the requirement of C~(0-1) continuity by using C~0 continuity displacementfunction and C~1 continuity displacement function, respectively. Finite element modelsconstructed in this thesis are simple and are convenient to use, which are suitable for allkinds of cases without any numerical technique. Moreover, they exhibit goodperformance for both regular and irregular meshes.
●Based on 1,2-3 global-local higher order theory, laminated plate elements for vibration and buckling analysis are given. Furthermore, the modified geometric stiffness matrixmethod is extended to buckling problems of laminated composite plate. By using ourapproaches, dynamic and buckling problems on soft-core sandwich plates as well aslaminated composite plates with different thickness and materials at each ply have beenanalyzed. Numerical results show that first order theories even global higher-ordertheories are inadequate to predict dynamic and buckling response of so special structureswhereas 1,2-3 global-local higher order theory is still suitable for analyzing dynamic andbuckling problems of laminated composite plates with variational thickness and materialsat each layer and soft-core sandwich plates.
●Combining 1,2-3 global-local higher order theory and layerwise theory, the mixed modelis developed in this thesis. This model is used to analyze bending problems of laminatedpiezoelectric plates. Moreover, effects of electric displacement on static response oflaminated piezoelectric plates are also studied. The concept of mixed model is that themechanical component is modeled by 1,2-3 global-local higher-order theory whereas theelectric field is modeled with layerwise theory. Present mixed model is able to accuratelypredict transverse shear stresses of laminated piezoelectric plate without any smoothingmethods.
●Geometrically nonlinear finite element based on 1,2-3 global-local higher-order theoryhas been constructed, which is used for geometrically nonlinear analysis of laminatedplates. Numerical results show that for geometrically nonlinear analysis, effect of thesecond-order components in in-plane displacement on transverse shear stresses is actuallysignificant.
1．建立几种整体-局部高阶理论。
●为了提高计算效率，本文建立了Reddy型整体-局部高阶理论。Reddy型整体-局部理论能够预先满足面内位移和横向剪切应力层间连续，而且独立变量个数比整体-局部1，2-3高阶理论少了4个。此理论已被用于分析层数较少层合板和功能梯度板弯曲问题。
●通过提高整体-局部1，2-3高阶理论整体面内位移沿板厚度方向展开多项式的阶数，本文提出整体-局部高阶理论GLHT-m0(m为整体面内位移沿厚度方向展开多项式的阶数，m取不同的值可以得到不同的理论)，基于此理论研究了高阶剪切变形对多于五层层合板弯曲、动力及屈曲响应的影响，并且给出结论即对于多于五层层合板问题应采用五阶整体-局部理论(m=5)。
●对于热膨胀问题，横法向应变扮演重要角色。为了处理热膨胀问题，本文把整体-局部1，2-3高阶理论的横向位移w沿厚向展开二次多项式建立了考虑横法向应变的整体-局部高阶理论GLHT-32(3表示整体面内位移沿厚度方向展开三次多项式，2表示横向位移沿厚向展开二次多项式)。数值试验表明，GLHT-32确实能够处理热膨胀问题。
●本文进一步提出了能够处理在任意温度载荷作用下任意铺设层合板问题的整体-局部高阶理论GLHT-52。此工作把整体-局部高阶理论应用范围扩展到任意温度载荷问题和角铺设层合板问题。
●复合材料层合板自由边问题是典型三维问题，现有等效单层板理论不能处理此类问题，不得不采用三维有限元和Layerwise理论(效率低)。通过提高整体面内位移和横向位移沿厚度方向展开多项式的阶数，本文建立了增强型整体-局部高阶理论GLHT-mn(m，n分别表示整体面内位移和横向位移沿厚度方向展开多项式的阶数，m，n取不同的值可以得到不同的理论)并应用此理论分析了层合板自由边问题。数值试验表明，GLHT-99能够准确分析多种自由边问题。本文增强型整体-局部高阶理论属于等效单层板理论但可以准确分析自由边问题，直接验证了等效单层板理论有能力分析层合板自由边问题。
●本文建立了整体-局部高阶层合壳理论GLHST-52并给出了简单解析解。当前的层合壳理论特点是未知变量个数独立于层合壳层数，并且应用本构方程可以直接准确地计算横向剪切应力。数值比较表明，当前理论计算的结果精度明显高于同类层合壳理论。
2．基于建立的整体-局部高阶理论，本文系统地研究了复合材料层合板有限元方法。
●应用精化元法分别提出了精化四边形单元RQLP13和精化三角形单元RTLP23；基于满足单元间C~1连续的离散Kirchhoff薄板单元，建立了三角形层合板单元TLP13和四边形单元QLP19。整体-局部高阶理论的应变项中出现了横向位移w的一阶导数和二阶导数，构造有限元时应使用同时满足C~0和C~1连续的横向位移函数，被称为C~(0-1)连续，是一种新提法。为此，本文用同样节点参数分别构造满足C~0和C~1连续的两套横向位移函数。本文有限元法列式简单，便于实施，计算过程中无须特殊的数值技巧，求解各种算例效果很好，在规则和不规则网格下，它们都能保持良好的性态。
●基于整体-局部1，2-3高阶理论推导了动力及稳定问题的有限元，把修改几何刚度阵的方法推广到复合材料层合板稳定问题。用本文方法分析了软核夹层板和变厚度层合板动力及屈曲问题，结果表明：一阶理论甚至整体型高阶理论不适于预测软核夹层板和变厚度层合板静动力及屈曲响应，本文有限元能够给出准确结果。
●组合整体-局部1，2-3高阶理论和Layerwise理论，本文建立了混合模型并应用此模型分析压电层合板问题，研究沿厚度方向电位移选取对结果的影响。在混合模型中整体-局部1，2-3高阶理论模拟压电板的结构变形，Layerwise理论模拟电位移沿厚度方向的变化。该模型突破了以往用位移基高阶理论求解层合压电板必需使用后处理方法计算横向剪切应力的限制。
●基于整体-局部1，2-3理论推导了几何非线性有限元并且分析了层合板几何非线性问题。结果表明：对于层合板几何非线性分析，面内位移的二次项对横向剪切应力确实影响较大。
Aim of this thesis is to propose more accurate and efficient laminated plate theories afterobjectively estimating previous the displacement-based laminated plate theories. To pursuethis goal, this thesis firstly compared several theories by using analytical methods. Numericalresults show that 1,2-3 global-local higher-order theory is able to accurately predict transverseshear stresses without any smoothing methods as the number of layers of laminated plates isless than five. Based on this theory, several laminated plate elements have been constructed.Moreover, these elements were used to analyze bending, vibration and buckling of laminatedplates. By further research on 1,2-3 global-local higher-order theory, it is found that thistheory will encounter some accuracy difficulties to analyze bending of multilayered plates andthermal expansion of laminated plates. In view of computational efficiency and range ofapplicability, this thesis proposes several enhanced global-local higher-order theories andstudies detailedly laminated plate elements. Main work includes the following aspect:
1. Proposed several global-local higher-order theories.
●To improve computional efficiency, Reddy-type global-local higher-order theory ispresented. This theory can a priori satisfy continuity of in-plane displacements andtransverse shear stresses at interfaces. Moreover, compared to 1,2-3 global-localhigher-order theory, number of independent variables is reduced to 7. This theory hasbeen used to analyze bending of lamianted plates with few layers and functionally gradedplates.
●By increasing the number of orders of the global in-plane displacement component in1,2-3 global-local higher-order theory, the global-local higher-order theory GLHT-m0 ispresented. Using this theory, effects of higher-order global-local shear deformations onbending, vibration and buckling of multilayered plates have been studied and thecorresponding conclusions are drawn: considering computational efficiency and accuracyof the results, the fifth-order global-local theory (m=5) should be applied to predict thestatic, the dynamic and the buckling response of multilayered plates.
●For thermal expansion problems of laminated plates, transverse normal strain plays animportant role. To analyze such problems, global-local higher-order theory GLHT-32 isproposed by considering transverse normal strain of 1,2-3 global-local higher-ordertheory. Numerical results show that GLHT-32 is suitable for predicting thermal responseof laminated plates under uniform temperature.
●This thesis further developes the global-local higher-order theory GLHT-52 which canaccuratelly predict thermal response of angle-ply laminated plates subjected to arbitrarytemperature loads. This work extends the range of applicability of the global-localhigher-order theory.
●It is well known that the free-edge problem is a typical three-dimensional problem.Three-dimensional finite elements and layerwise theories have to be used to analyzefree-edge effects because previous equivalent single layer plate theories can not analyzeso complicated problem. By increasing the number of order of in-plane and transversedisplacements, an enhanced global-local higher-order theory GLHT-mn has beendeveloped to analyze free-edge problems. Numerical results show that GLHT-99 which isa typical equivalent single layer plate theory is able to predict accurately static responseof the free-edge effects. Thereby, this work directly proves that equivalent single layerplate theory can analyze free-edge problems of laminated plates.
●Global-local higher-order laminated shell theory GLHST-52 as well as correspondinganalytical results have been given in this thesis. Unknown variables of this theory areindependent of number of layers and transverse shear stresses can be directly computedfrom constitutive equations. Numerical results show that present shell theory is moreaccurate than other shell models.
2. Based on global-local higher-order theory, this thesis detailedly studies laminatedplate elements.
●Based on the refined nonconforming element method, a refined four-node quadrilateralplate element RQLP13 and a refined three-node triangular element RTLP23 are presented.Subsequently, a triangular plate element TLP13 and a quadrilateral plate element QLP19are also proposed by using the discrete Kirchhoff thin plate bending element satisfying C~1continuity on the element boundary. Global-local higher-order theory possesses first andsecond derivatives of transverse displacement w in the strain components. Thustransverse displacement function satisfying C~0 as well as C~1 continuity on the elementboundary, which is named as C~(0-1) continuity, should be employed. This thesiscircumvents the requirement of C~(0-1) continuity by using C~0 continuity displacementfunction and C~1 continuity displacement function, respectively. Finite element modelsconstructed in this thesis are simple and are convenient to use, which are suitable for allkinds of cases without any numerical technique. Moreover, they exhibit goodperformance for both regular and irregular meshes.
●Based on 1,2-3 global-local higher order theory, laminated plate elements for vibration and buckling analysis are given. Furthermore, the modified geometric stiffness matrixmethod is extended to buckling problems of laminated composite plate. By using ourapproaches, dynamic and buckling problems on soft-core sandwich plates as well aslaminated composite plates with different thickness and materials at each ply have beenanalyzed. Numerical results show that first order theories even global higher-ordertheories are inadequate to predict dynamic and buckling response of so special structureswhereas 1,2-3 global-local higher order theory is still suitable for analyzing dynamic andbuckling problems of laminated composite plates with variational thickness and materialsat each layer and soft-core sandwich plates.
●Combining 1,2-3 global-local higher order theory and layerwise theory, the mixed modelis developed in this thesis. This model is used to analyze bending problems of laminatedpiezoelectric plates. Moreover, effects of electric displacement on static response oflaminated piezoelectric plates are also studied. The concept of mixed model is that themechanical component is modeled by 1,2-3 global-local higher-order theory whereas theelectric field is modeled with layerwise theory. Present mixed model is able to accuratelypredict transverse shear stresses of laminated piezoelectric plate without any smoothingmethods.
●Geometrically nonlinear finite element based on 1,2-3 global-local higher-order theoryhas been constructed, which is used for geometrically nonlinear analysis of laminatedplates. Numerical results show that for geometrically nonlinear analysis, effect of thesecond-order components in in-plane displacement on transverse shear stresses is actuallysignificant.
引文
[1] 刘人怀．复合材料层合板壳理论探索．广州：暨南大学出版社．2006．
[2] 杨乃宾，章怡宁．复合材料飞机结构设计．北京：航空工业出版社．2002．
[3] 沈观林，胡更开．复合材料力学．北京：清华大学出版社．2006．
[4] Grigolyuk E. I., Kogan F. A. The present status of the theory of multilayerd shells. Prikl Mekh, 1972, 8: 3-17.
[5] Leissa A. W. A review of laminated composite plate buckling. Appl Mech Rev, 1987, 40(5): 575-591.
[6] Grigolyuk E. I., Kulikov G. M. General directions of the development of theory of shells. Mekhanica Kompozitnykh Materialov, 1988, 24: 287-298.
[7] Kapania R. K., Raciti S. Recent advances in analysis of laminated beams and plates. AIAA J, 1989, 27(7): 923-946.
[8] Kapania R. K. A review on the analysis of laminated shells. ASME J Pressure Vessel Technol, 1989, 111 (2): 88-96.
[9] Noor A. K., Burton W. S. Assessment of computational models for multilayered composite shells. Appl Mech Rev, 1990, 43(4): 67-97.
[10] Jemleli ta G. On kinematical assumptions of refined theories of plates: A survey. J Appl Mech, 1990, 57: 1080-1091.
[11] Reddy J. N., Robbins D. H. Theories and computational models for composite laminates. Appl Mech Rev, 1994, 47(6): 147-165.
[12] Noor A. K., Burton W. S., Bert C. W. Computational models for sandwich panels and shells. Appl Mech Rev, 1996, 49(3): 155-199.
[13] Grigorenko Y. M. Approaches to numerical solution of linear and nonlinear problems in shell theory in classical and refined formulations. Int Appl Mech, 1996, 32: 409-422.
[14] Grigorenko Y. M., Vasilenko A. T. Solution of problems and analysis of the stress strain state of non-uniform anisotropic shells. Int Appl Mech, 1997, 33: 851-880.
[15] Reddy J. N. Mechanics of laminated composite plates theory and analysis: CRC press. 1997.
[16] Altenbach H. Theories for laminated and sandwich plates. A review. Mech Compos Mater, 1998, 34: 243-252.
[17] Kant T., Swaminathan K. Estimation of transverse/interlaminar stresses in laminated composites-a selective review and survey of current developments. Compos Struct, 2000, 49: 65-75.
[18] Carrera E. Developments, ideas, and evaluations based upon Reissner's Mixed Variational Theorem in the modeling of multilayered plates and shells. Appl Mech Rev, 2001, 54(4): 301-329.
[19] Ambartsumian S. A. Nontraditional theories of shell and plates. Appl Mech Rev, 2002, 55(5): 35-44.
[20] Mohamad S. Q. Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells. Appl Mech Rev, 2002, 55(4): 325-350.
[21] Carrera E. Historical review of Zig-Zag theories for multilayered plates and shells. Appl Mech Rev, 2003, 56(3): 287-308.
[22] Berthelot J. M. Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: static and fatigue loading. Appl Mech Rev, 2003, 56(1): 111-147.
[23] Reddy J. N., Arciniega R. A. Shear deformation plate and shell theories: From Stavsky to Present. Mech Advanced Mater Struct, 2004, 11: 535-582.
[24] Mittelstedt C., Becker W. Interlaminar stress concentrations in layered structures: Part Ⅱ-closed-form analysis of stresses at laminated rectangular wedges with arbitrary non-orthotropic layup. J Compos Mater, 2004, 38(12): 1063-1090.
[25] Mittelstedt C., Becker W. Interlaminar stress concentrations in layered structures: Part Ⅰ-A selective literature survey on the free-edge effect since 1967. J Compos Mater, 2004, 38(12): 1037-1062.
[26] Carrera E. C_z~0 requirements-models for the two dimensional analysis of multilayered structures. Compos Struct, 1997, 37: 373-383.
[27] Di Sciuva M. Multilayered anisotropic plate models with continuous interlaminar stresses. Compos Struct, 1992, 22: 149-167.
[28] Cho M., Parmerter R. R. An efficient higher-order plate theory for laminated composites. Compos Struct, 1992, 20: 113-123.
[29] Cho M., Kim J. S. Improved Mindlin plate stress analysis for laminated composites in finite element method. A/AA J, 1996, 35(3): 587-590.
[30] Icardi U., Di Sciuva M. Large-deflection and stress analysis of multilayered plates with induced-strain actuators. Smart Mater Struct, 1996, 5: 140-164.
[31] Li X. Y., Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Methods Eng, 1997, 40: 1197-1212.
[32] Sze K. Y., Chen. R. G., Cheung Y. K. Finite element model with continuous transverse shear stress for composite laminates in cylindrical bending. Finite Element in Analysis and Design, 1998, 31: 153-164.
[33] 陈荣庚，陈万吉．基于整体．局部位移假设的高阶理论及其三角形板单元．复合材料学报，2000，17(3)：96-102．
[34] 何录武，李乐．复合材料层合板的高阶理论．兰州大学学报，2001，37(3)：26-33．
[35] 李乐，何录武，闵国林．复合材料层合梁的横向剪应力分析．兰州大学学报，2001，37(5)：15-22．
[36] 何录武，李乐．复合材料层合板的应力分析．兰州大学学报，2002，38(1)：36-43．
[37] Pagano N. J. Exact solutions for composite laminates in cylindrical bending. J Compos Mater, 1969, 3: 398-411.
[38] Chia C. Y. Nonlinear analysis of plates. New York: McGraw-Hill. 1980.
[39] Whitney J. M., Pagano N. J. Shear deformation in heterogeneous anisotropic plates. J Appl Mech, 1970, 37: 1031-1036.
[40] Noor A. K., Burton W. S. Stress and free vibration analysis of multilayered composite plates. Compos Struct, 1989, 11: 183-204.
[41] Rolfes R., Noor A. K., Sparr H. Evaluation of transverse thermal stresses in composite plates based on first-order shear deformation theory. Comput Methods Appl Mech Engrg, 1998, 167: 355-368.
[42] Noor A. K., Malik M. An assessment of five modeling approaches for thermo-mechanical stress analysis of laminated composite panels. Comput Mech, 2000, 25: 43-58.
[43] Sze K. Y., He L. W., Cheung Y. K. Predictor-corrector procedures for analysis of laminated plates using standard Mindlin finite element methods. Compos Struct, 2000, 51: 171-192.
[44] 何录武，冯春．复合材料层合壳有限元分析的预测-校正法．力学季刊，2004，25(3)：317-321．
[45] 冯跃中，何录武．复合材料层合板的热应力分析．兰州大学学报，2005，41(6)：94-99．
[46] Fares M. E. Non-linear bending analysis of composite laminated plates using a refined first-order theory. Compos Struct, 1999, 46: 257-266.
[47] Fares M. E., Zenkour A. M., El-Marghany M. K. Non-linear thermal effects on the bending response of cross-ply laminated plates using refined first-order theory. Compos Struct, 2000, 49: 257-267.
[48] Kim J. S., Cho M. Enhanced first-order theory based on mixed formulation and transverse normal effect. Int J Solids Struct, 2007, 44: 1256-1276.
[49] Whitney J. M. The effect of transverse shear deformation on the bending of laminated plates. J Compos Mater, 1969,3:534-547.
[50] Sun C. T, Whitney J. M. Theories for the dynamic response of laminated plates. AIAA J, 1973, 11:178-183.
[51]Liew K. M., Peng L. X., Kitipornchai S. Buckling of folded plate structures subjected to partial in-plane edge loads by the FSDT meshfree Galerkin method. Int J Numer Methods Eng, 2006,65:1495-1526.
[52] Hu X. X., Sakiyama T., Lim C. W, Xiong Y., Matsuda H., Morita C. Vibration of angle-ply laminated plates with twist by Rayleigh-Ritz procedure. Comput Meth Appl Mech Eng, 2004,193:805-823.
[53] Bert C. W, Chen T. L. C. Effect of shear deformation on vibration of antisymmetric angle ply laminated rectangular plates Int J Solids Struct, 1978, 14:465-473.
[54] 杨加明．复合材料板的非线性弯曲．北京：国防工业出版社．2006．
[55]Whitney J. M., Sun C. T. A higher order theory for extensional motion of laminated composites. J Sound Vib, 1973,30:85-89.
[56] Nelson R. B., Lorch D. R. A refined theory for laminated orthotropic plates. J Appl Mech, 1974,41:177-183.
[57] Lo K. H., Christensen R. M., Wu E. M. A higher order theory of plate deformation, Part 1: Homogeneous plates. J Appl Mech, 1977,44(4):663-668.
[58] Lo K. H., Christensen R. M., Wu E. M. A higher order theory of plate deformation, Part 2: Laminated plates. J Appl Mech, 1977, 44(4):669-676.
[59] Kant T. Numerical analysis of thick plates. Comput Meth Appl Mech Eng, 1982, 31:1-18.
[60]Pandya B. N., Kant T. A consistent refined theory for flexure of a symmetric laminate Mech Res Commun, 1987, 14:107-113.
[61]Pandya B. N., Kant T. Higher order shear deformation theories for flexure of sandwich plates-finite element evaluations. Int J Solids Struct, 1988,24(12): 1267-1286.
[62] Kant T., Swaminathan K. Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order theory. Compos Struct, 2001, 53:73-85.
[63] Kant T., Swaminathan K. Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos Struct, 2002, 56:329-344.
[64] Kant T., Swaminathan K. Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories. J Sound Vib, 2001,241:319-327.
[65]Reddy J. N. A simple higher-order theory for laminated composite plates. J Appl Mech, 1984, 51(12):745-752.
[66] Reddy J. N. A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct, 1984, 20:881-896.
[67] Reddy J. N., Phan N. D. Stability and vibration of isotropic and laminated plates according to higher order shear deformation theory. J Sound Vib, 1985, 98:157-170.
[68] Reddy J. N. Analysis of functionally graded plates. Int J Numer Methods Eng, 2000, 47:663-684.
[69]Matsunaga H. Effects of higher-order deformations on in-plane vibration and stability of thick circular rings. Acta Mechanica, 1997, 124:47-61.
[70]Matsunaga H. Vibration and buckling of multilayered composite beam according to higher order deformation theories. J Sound Vib, 2001,246(1):47-62.
[71]Matsunaga H. Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses. Int J Mech Sci, 2001,43:1925-1944.
[72] Matsunaga H. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos Struct, 2000, 48:231-244.
[73] Matsunaga H. Vibration of cross-ply laminated composite plates subjected to initial in-plane stresses. Thin-Walled Struct, 2002,40:557-571.
[74] Matsunaga H. Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading. Compos Struct, 2007, (77):249-262.
[75] Matsunaga H. Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory Compos Struct, 2006, 72:177-192
[76] Matsunaga H. Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory. Compos Struct, 2005,68:439-454.
[77] Matsunaga H. Interlaminar stress analysis of laminated composite and sandwich circular arches subjected to thermal/mechanical loading. Compos Struct, 2003, 60:345-358.
[78]Matsunaga H. Interlaminar stress analysis of laminated composite beams according to global higher-order deformation theories. Compos Struct, 2002,55:105-114.
[79] Matsunaga H. Assessment of a global higher-order deformation theory for laminated composite and sandwich plates. Compos Struct, 2002, 56:279-291.
[80] Matsunaga H. A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings. Compos Struct, 2004, 64:161-177.
[81]Pagano N. J. Exact solutions for rectangular bidirectional composites. J Compos Mater, 1970,4:20-34.
[82] Murakami H. Laminated composite plate theory with improved in-plane response. J Appl Mech, 1986, 53:661-666.
[83]Toledano A., Murakami H. A high-order laminated plate theory with improved in-plane responses. Int J Solids Struct, 1987,23:111-131.
[84] Carrera E. On the use of the Murakami's zig-zag function in the modeling of layered plates and shells. Comput Struct, 2004, 82:541-554.
[85] Tessler A., Saether E. A computationally viable higher-order theory for laminated composite plates. Int J Numer Methods Eng, 1991, 1069-1086.
[86]Reddy J. N. A general non-linear third-order theory of plates with moderate thickness. Int J Nonlinear Mech, 1990,25(6):677-686.
[87] Reddy J. N. On refined theories of composite laminates. Meccanica, 1990,25(4):230-238.
[88]Bhimaraddi A., Stevens L. K. A higher order theory for free vibration of orthotropic, homogeneous and laminated rectangular plates. JAppl Mech, 1984,51:195-198.
[89] Di Sciuva M. A refined transverse shear deformation theory for multilayered anisotropic plates. Atti Accademia Scienze Torino, 1984, 118:279-295.
[90] Di Sciuva M. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model. J Sound Vib, 1986, 105:425-442.
[91] Di Sciuva M. An improved shear deformation theory for moderately thick multilayered anisotropic shells and plates. J Appl Mech, 1987, 54:589-596.
[92] Di Sciuva M. Further refinement in the transverse shear deformation theory for multilayered composite plates. Atti Accademia Scienze Torino, 1990, 124:248-267.
[93] Lee K., Lee S. W. A postprocessing approach to determine transverse stress in geometrically nonlinear composite and sandwich structures. J Compos Mater, 2003, 37(24):2207-2224.
[94]Icardi U. Cylindrical bending of laminated cylindrical shells using a modified zig-zag theory. Struct Eng Mech, 1998, 6(5):497-516.
[95] Di Sciuva M., Icardi U., Librescu L. Effects of interfacial damage on the global and local static response of cross-ply laminates. Int J Fracture, 1999, 96: 17-35.
[96] Icardi U., Ruotolo R. Laminated shell model with second-order expansion of the reciprocals of Lame coefficients H_a, H_B and interlayer continuities fulfilment. Compos Struct, 2002, 56: 293-313.
[97] Di Sciuva M., Gherlone M. A global/local third-order Hermitian displacement field with damaged interfaces and transverse extensibility: analytical formulation. Compos Struct, 2003, 59: 419-431.
[98] Cho M., Klm K. O., Kim M. H. Efficient higher-order shell theory for laminated composites. Compos Struct, 1996, 34: 197-212.
[99] Cho M., Kim M. H. A postprocess method using a displacement field of higher-order shell theory. Compos Struct, 1996, 34: 185-196.
[100] Cho M., Kim J. S. Higher-order zig-zag theory for laminated composite with multiple delaminations. J Appl Mech, 2001, 68: 869-877.
[101] Cho M., Oh J. Higher order zig-zag plate theory under thermo-electric-mechanical loads combined. Composites: Part B, 2003, 34: 67-82.
[102] Cho M., Oh J. Higher order zig-zag theory for fully coupledthermo-electric-mechanical smart composite plates. Int J Solids Struct, 2004, 41: 1331-1356.
[103] Oh J., Cho M. Higher order zig-zag theory for smart composite shells under mechanical-thermo-electric loading. Int J Solids Struct, 2007, 44: 100-127.
[104] Oh J., Cho M., Kim J. S. Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory. Int J Solids Struct, 2005, 42: 6122-6140.
[105] Kim J. S., Cho M. Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory. Int J Numer Methods Eng, 2002, 55: 1323-1343.
[106] Cho M., Choi Y. J. A new postprocessing method for laminated composites of general lamination configurations. Compos Struct, 2001, 54: 397-406.
[107] Kapuria S., Dumir P. C., Ahmed A. An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading. Int J Solids Struct, 2003, 40: 6613-6631.
[108] Kapuria S., Achary G. G. S. An efficient higher order zigzag theory for laminated plates subjected to thermal loading. Int J Solids Struct, 2004, 41: 4661-4684.
[109] Kapuria S., Dumir P. C., Jain N. K. Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams. Compos Struct, 2004, 64: 317-327.
[110] 何陵辉，刘人怀．一种考虑层间位移和横向剪应力连续条件的层合板理论．固体力学学报，1994，15(4)：319-325．
[111] 舒小平．满足板面载荷和横向剪应力连续的层板理论．复合材料学报，1994，11(4)：61-68．
[112] Shu X. P. An improved simple higher-order theory for laminated composite shells. Comput Struct, 1996, 60(3): 343-350.
[113] Shu X. P. A refined theory of laminated shells with higher-order transverse shear deformation. Int J Solids Struct, 1997, 34(6): 673-683.
[114] 舒小平．层间滑移对复合材料层合板自由振动的影响．淮海工学院学报，2000，9(3)：9-11．
[115] 舒小平．层间弱粘贴复合材料层板的热弹性脱层．工程力学，2002，19(3)：153-158．
[116] Shu X. P., Soldatos K. P. An accurate de-lamination model for weakly bonded laminates subjected to different sets of edge boundary conditions. Int J Mech Sci, 2001, 43: 935-959.
[117] Shu X. P., Soldatos K. P. Cylindrical bending of angle-ply laminates subjected to different sets of edge boundary conditions. Int J Solids Struct, 2000, 37: 4289-4307.
[118] Shu X. P. Vibration and bending of antisymmetrically angle-ply laminated plates with perfectly and weakly bonded layers. Compos Struct, 2001, 53:245-255.
[119] Liu D., Li X. Y. An overall view of laminated theories based on displacement hypothesis. J Compos Mater, 1996,30:1539-1561.
[120] Li X. Y., Liu D. A laminate theory based on global-local superposition. Commun Numer Meth Engng, 1995,11:633-641.
[121] Reddy J. N. On refined computational models of composite laminates. Int J Numer Methods Eng, 1989, 27:361-382.
[122] Reddy J. N. A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct, 1987,20:881-896.
[123] Tahani M., Noiser A. Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading. Compos Struct, 2003,60:91-103.
[124] Tahani M., Noiser A. Three-dimensional interlaminar stress analysis at free edges of general cross-ply composite laminates. Materials and Design, 2003,24:121-130.
[125] Tahani M., Noiser A. Edge effects of uniformly loaded cross-ply composite laminates. Materials and Design, 2003,24:647-658.
[126] Tahani M., Noiser A. Accurate determination of interlaminar stresses in general cross-ply laminates. Mech Advanced Mater Struct, 2004, 11:67-92.
[127] Noiser A., Bahrami A. Free-edge stresses in antisymmetric angle-ply laminates in extension and torsion. Int J Solids Struct, 2006,43:6800-6816.
[128] Noiser A., Bahrami A. Interlaminar stresses in antisymmetric angle-ply laminates. Compos Struct, 2007, 78:18-33.
[129] Mittelstedt C, Becker W. Fast and reliable analysis of free-edge stress fields in a thermally loaded composite strip by a layerwise laminate theory. Int J Numer Methods Eng, 2006,67(6):747-770.
[130] Toledano A., Murakami H. A composite plate theory for arbitrary laminated configurations. J Appl Mech, 1987,54:181-189.
[131] Carrera E. Mixed layer-wise models for multilayered plates analysis. Compos Struct, 1998, 43:57-70.
[132] Carrera E. A study of transverse normal stress effect on vibration of multilayered plates and shells. J Sound Vib, 1999,225(5):803-829.
[133] Carrera E. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos Struct, 2000, 50:183-198.
[134] Carrera E. An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates. J thermal Stresses, 2000,23:797-831.
[135] Carrera E., Ciuffreda A. Closed-form solutions to assess multilayered-plate theories for various thermal stress problems. J thermal Stresses, 2004,27:1001-1031.
[136] Carrera E., Ciuffreda A. A unified formulation to assess theories of multilayered plates for various bending problems. compos Struct, 2005, 69:271-293.
[137] Dafedar J. B., Desai Y. M. Thermomechanical buckling of laminated composite plates using mixed, higher-order analytical formulation. J Appl Mech, 2002, 69:790-799.
[138] Dafedar J. B., Desai Y. M., Mufti A. A. Stability of sandwich plates by mixed, higher-order analytical formulation. Int J Solids Struct, 2003,40:4501-4517.
[139] Rao M. K., Desai Y. M. Analytical solutions for vibrations of laminated and sandwich plates using mixed theory. Compos Struct, 2004, 63:361-373.
[140] Rao M. K., Scherbatiuk K., Desai Y. M., Shah A. H. Natural vibrations of laminated and sandwich plates. J Eng Mech, 2004, 130: 1268-1278.
[141] Ren J. G. Exact solutions for laminated cylindrical shells in cylindrical bending. Compos Sci Technol, 1987, 29: 169-187.
[142] Varadan T. K., Bhaskar K. Bending of laminated orthotropic cylindrical shells-An elasticity approach. Compos Struct, 1991, 17: 141-156.
[143] Wang Y. M., Tarn J. Q., Hsu C. K. State space approach for stress decay in laminates. Int J Solids Struct, 2000, 37: 3535-3553.
[144] Ding H. J., Chen W. Q., Xu R. Q. On the bending, vibration and stability of laminated rectangular plates with transversely isotropic layers. Appl Math Mech, 2001, 22(1): 17-24.
[145] Chen W. Q., Bian Z. G., Ding H. J. Three-dimensional analysis of a thick FGM rectangular plate in thermal environment. J Zhejiang University, 2003, 4(1): 1-7.
[146] Chen W. Q., Lee K. Y. Three-dimensional exact analysis of angle-ply laminates in cylindrical bending with interracial damage via state-space method. Compos Struct, 2004, 64: 275-283.
[147] Chen W. Q., Lee K. Y. Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections. Compos Struct, 2004, 65: 329-337.
[148] Chen W. Q., Ying J., Cai J. B., Ye G. R. Benchmark solution of imperfect angle-ply laminated rectangular plates in cylindrical bending with surface piezoelectric layers as actuator and sensor. Comput Struct, 2004, 82: 1773-1784.
[149] Ge Z. J., Chen W. J. A refined discrete triangular Mindlin element for laminated composite plates. Struct Eng Mech, 2002, 14(5): 575-593.
[150] Cen S., Long Y. Q., Yao Z. H. A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates. Comput Struct, 2002, 80: 819-833.
[151] Cen S., Soh A. K., Long Y. Q., Yao Z. H. A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates. Compos Struct, 2002, 58: 583-599.
[152] Zhang Y. X., Kim K. S. Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements. Compos Struct, 2006, 72: 301-310.
[153] Reddy J. N. A penalty plate-bending element for the analysis of laminated anisotropic composite plates. Int J Numer Methods Eng, 1980, 15: 1187-1206.
[154] Hughes T. J. R., Tezduyar T. E. Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J Appl Mech, 1981, 48(3): 587-596.
[155] Belytschko T., Tsay C. S., Liu W. K. Stabilization matrix for the bilinear Mindlin plate element. Comput Meth Appl Mech Eng, 1981, 29: 313-327.
[156] Bathe K. J., Dvorkin E. N. A four-node plate bending element based on Mindlin/Reissner plate theory and mixed interpolation. Int J Numer Methods Eng, 1985, 21: 367-383.
[157] 朱菊芬，牛海英．含多个分层复合材料层合板后屈曲性态研究．计算力学学报，2004，21(6)：711-717．
[158] 牛海英，朱菊芬．含单个分层复合材料层合板后屈曲性态研究．大连理工大学学报，2004，44(5)：634-639．
[159] 白瑞祥，张志峰，陈浩然．含面＼芯开裂损伤复合材料夹层板的自由振动．吉林大学学报，2005，35(2)：199-204．
[160] 白瑞祥，陈浩然．含面芯开裂损伤复合材料夹层板考虑几何非线性的能量释放率数值分析．复合材料学报，2003，20(3)：1-6．
[161] Kant T., Owen D. R. J., Zienkiewicz O. C. A refined higher order C0 plate bending element. Comput Struct, 1982, 15:177-183.
[162] Kant T., Manjunatha B. S. An unsymmetric FRC laminate C0 finite element model with 12 degrees of freedom per node. Eng Comput, 1988, 5(3):300-308.
[163] Pandya B. N., Kant T. Finite element stress analysis of laminated composite plates using higher order displacement model. Compos Sci Technol, 1988, 32:137-155.
[164] Pandya B. N., Kant T. Flexure analysis of laminated composites using refined higher order C0 plate bending elements. Comput Meth Appl Mech Eng, 1988,66:173-198.
[165] Kant T., Kommineni J. K. C0 finite element geometrically non-linear analysis of fibre reinforced composite and sandwich laminates based on a higher-order theory. Comput Struct, 1992,45(3):511-520.
[166] Kant T., Khare R. A higher-order facet quadrilateral composite shell element. Int J Numer Methods Eng, 1997,40:44774499.
[167] Khare R., Kant T., Garg A. K. Free vibration of composite and sandwich laminates with a higher-order facet shell element. Compos Struct, 2004,65:405-418.
[168] Nayak A. K., Moy S. S. J., Shenoi R. A. Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory. Composites: Part B, 2002,33:505-519.
[169] Nayak A. K., Moy S. S. J., Shenoi R. A. A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates. J Sound Vib, 2005, 286:763-780.
[170] Sheikh A. H., Chakrabarti A. A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates. Finite Element in Analysis and Design, 2003,39:883-903.
[171] Chakrabarti A., Sheikh A. H. Buckling of laminated composite plates by a new element based on higher order shear deformation theory. Mech Advanced Mater Struct, 2003, 10:303-317.
[172] Cho M., Parmerter R. R. Finite element for composite plate bending on efficient higher order theory. AIAA J, 1994, 32: 2241-2248.
[173] Oh J., Cho M. A finite element based on cubic zig-zag plate theory for the prediction of thermo-electric-mechanical behaviors. Int J Solids Struct, 2004,41:1357-1375.
[174] Chakrabarti A., Sheikh A. H. A new triangular element to model inter-laminar shear stress continuous plate theory. Int J Numer Methods Eng, 2004, 60:1237-1257.
[175] Di Sciuva M. A third-order triangular multilayered plate finite element with continuous interlaminar stresses. Int J Numer Methods Eng, 1995,38:1-26.
[176] Carrera E. C0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. Int J Numer Methods Eng, 1996, 39:1797-1820.
[177] Saravanos D. A,, Heyliger P. R., Hopkins D. A. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates Int J Solids Struct, 1997, 34(3):359-378.
[178] Kimpara I., Kageyama K., Suzuki K. Finite element stress analysis of interlayer based on selective layerwise higher-order theory, composites: Part A, 1998,29:1049-1056.
[179] Gaudenzi P., Mannini A., Carbonaro R. Multi-layer higher-order finite elements for the analysis of free-edge stresses in composite laminates. Int J Numer Methods Eng, 1998,41:851-873.
[180] Ramtekkar G S., Desai Y. M., Shah A. H. Mixed finite-element model for thick composite laminated plates. Mech Advanced Mater Struct, 2002,9:133-156.
[181] Carrera E., Demasi L. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices. Int J Numer Methods Eng, 2002, 55:191-231.
[182] Carrera E., Demasi L. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations. Int J Numer Methods Eng, 2002, 55: 253-291.
[183] Desai Y. M., Ramtekkar G. S., Shah A. H. Dynamic analysis of laminated composite plates using a layer-wise mixed finite element model. Compos Struct, 2003, 59: 237-249.
[184] Ramtekkar G. S., Desai Y. M., Shah A. H. Application of a three-dimensional mixed finite element model to the flexure of sandwich plate. Comput Struct, 2003, 81: 2183-2198.
[185] Semedo J. E., Mota Soares C. M., Mota Soares C. A., Reddy J. N. Analysis of laminated adaptive plate structures using layerwise finite element models. Comput Struct, 2004, 82: 1939-1959.
[186] Lage R. G., Mota Soares C. M., Mota Soares C. A., Reddy J. N. Analysis of adaptive plate structures by mixed layerwise finite elements. Compos Struct, 2004, 66: 269-276.
[187] Lage R. G., Mota Soares C. M., Mota Soares C. A., Reddy J. N. Modeling of piezolaminated plates using layerwise mixed finite elements. Comput Struct, 2004, 82: 1849-1863.
[188] Ye J. Q., Sheng H. Y., Qin Q. H. A state space finite element for laminated composites with free edges and subjected to transverse and in-plane loads. Comput Struct, 2004, 82: 1131-1141.
[189] Robaldo A. Finite element analysis of the influence of temperature profile on thermoelasticity of multilayered plates. Comput Struct, 2006, 84: 1236-1246.
[190] Carrera E. A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates. Compos Struct, 2000, 48: 245-260.
[191] Wu Z., Chen W. J. A study of global-local higher-order theory for laminated composite plates. Compos Struct, 2007, 79: 44-54.
[192] Chen W. J., Cheung Y. K. Refined quadrilateral element based on Mindlin/Reissner plate theory. Int J Numer Methods Eng, 2000, 47: 605-627.
[193] Chen W. J., Cheung Y. K. Refined triangular discrete Kirchhoff plate element for thin plate bending, vibration and buckling analysis. Int J Numer Methods Eng, 1998, 41: 1507-1525.
[194] 陈万吉．精化直接刚度法及九参数三角形薄板单元．大连理工大学学报，1993，33(3)：289-296．
[195] 龙驭球，辛克贵．广义协调元．土木工程学报，1987，20(1)：1-14．
[196] 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社．1997．
[197] Chen W. J., Cheung Y. K. Ref'med nonconforming quadrilateral thin plate bending element. Int J Numer Methods Eng, 1997, 41: 3915-3935.
[198] Bazeley G. P., Cheung Y. K., Irons B. M., Zienkiewiz O. C. Triangular elements in bending conforming and non-conforming solution. Proc Conf Matrix Meth Struct Mech Wright-Patterson AF Base, Ohio: Air Force Ins Tech, 1965: 547-576.
[199] Stricklin J. A., Haisler W. E., Tisdale P. R., Gunderson R. A rapidly converging triangular plate element. AIAA J, 1969, 7(1): 180-181.
[200] Batoz J. L., Bathe K. J., Ho L. W. A study of three-node triangular plate bending element. Int J Numer Methods Eng, 1980, 15: 1771-1812.
[201] Batoz J. L., Tahar M. B. Evaluation of a new quadrilateral thin plate bending element. Int J Numer Methods Eng, 1982, 18: 1655-1677.
[202] Wu Z., Chen W. J. Refined global-local higher-order theory and finite element for laminated plates. Int J Numer Methods Eng, 2007, 69: 1627-1670.
[203] Wu Z., Chen R. G., Chen W. J. Refined laminated composite plate element based on global-local higher-order shear deformation theory. Compos Struct, 2005, 70: 135-152.
[204] Wu Z., Chen W. J. A quadrilateral element based on refined global-local higher-order theory for thermal/mechanical analysis of laminated plates. Int J Solids Struct, 2007, 44: 3187-3217.
[205] Chen W. J., Wu Z. A new higher-order shear deformation theory and refined beam element of composite laminates. Acta Mechanica Sinica, 2005,21: 65-69.
[206] Tungikar V. B., Rao K. M. Three dimensional exact solution of thermal stresses in rectangular composite laminates. Compos Struct, 1994,27:419-427.
[207] Bogdanovich A. E., Yushanov S. P. Three-dimensional variational analysis of Pagano's problems for laminated composite plates. Compos Sci Technol, 2000, 60:2407-2425.
[208] Dafedar J. B., Desai Y. M. Stability of composite and sandwich struts by mixed formulation. J Eng Mech, 2004, 130(7):762-770.
[209] Wu Z., Chen W. J. Free vibration of laminated composite and sandwich plates using global-local higher-order theory. J Sound Vib, 2006, 298:333-349.
[210] Noor A. K. Free vibrations of multilayered composite plates. AIAA J, 1973, 11(7):1038-1039.
[211] Noor A. K., Burton W. S. Three-dimensional solutions for antisymmetrically laminated anisotropic plates. J Appl Mech, 1990, 57(3): 182-188.
[212] Son A. K., Chen L. Alternative approach to modify a discrete Kirchhoff triangular element. J Eng Mech, 2001, 127:791-799.
[213] Cheung Y. K., Zhang Y. X., Chen W. J. The application of a refined non-conforming quadrilateral plate bending element in thin plate vibration and stability analysis. Finite Element in Analysis and Design, 2000, 34:175-191.
[214] Noor A. K. Stability of multilayered composite plates. Fibre Sci Tech, 1975, 8:81-89.
[215] Kant T., Patil H. S. Buckling loads of sandwich columns with a higher-order theory. J Reinf Plast Compos, 1991, 10:102-107.
[216] Kant T., Swaminathan K. Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates. Struct Eng Mech, 2000,10(4): 337-357.
[217] Lee J. Thermally induced buckling of laminated composites by a layerwise theory. Comput Struct, 1997, 65(6):917-922.
[218] Noor A. K., Fellow, Burton W. S. Three-dimensional solutions for thermal buckling of multilayered anisotropic plates. J Eng Mech, 1992,118(4):683-701.
[219] Babu C. S., Kant T. Refined higher order finite element models for thermal buckling of laminated composite and sandwich plates. J thermal Stresses, 2000,23:111-130.
[220] Wu Z., Cheung Y. K., Lo S. H., Chen W. J. Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates. Compos Struct, on line.
[221] Sheikh A. H., Topdar P., Haider S. An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates. Compos Struct, 2001, 51:401-409.
[222] Jonnalagadda K. D., Blandford G E., Tauchert T. R. Piezo-thermoelastic composite plate analysis using a first-order shear theory. Compos Struct, 1994, 51(1):79-89.
[223] Huang J. H., Wu T. L. Analysis of hybrid multilayered piezoelectric plates. Int J Eng Sci, 1995, 34(2):171-181.
[224] Ha S. K., Keilers C, Chang F. Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA J, 1992, 30(3):772-780.
[225] Saravanos D. A., Heyliger P. R., Hopkins D. A. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int J Solids Struct, 1997, 34(3):359-378.
[226] Heyliger P., Ramirez G, Saravanos D. A. Coupled discrete-layer finite element for laminated piezoelectric plates. Commun Numer Meth Engng, 1994, 10:971-981.
[227] Sze K. Y., Yang X. M., Fan H. Electric assumptions for piezoelectric laminate analysis. Int J Solids Struct, 2004,41:2363-2382.
[228] Topdar P., Chakrabarti A., Sheikh A. H. An efficient hybrid plate model for analysis and control of smart sandwich laminates. Comput Meth Appl Mech Eng, 2004,193:4591-4610.
[229] Ray M. C, Bhattacharya R., Samanta B. Exact solutions for static analysis of intelligent structures. AIAA J, 1993,31:1684-1691.
[230] Erdogan F. Fracture mechanics of functionally graded materials. Compos Eng, 1995,5:753-770.
[231] Pan E. Exact solution for functionally graded anisotropic elastic composite laminates. J Compos Mater, 2003,37:1903-1920.
[232] Kashtalyan M. Three-dimensional elasticity solution for bending of functionally graded rectangular plates. Eur J Mech A/Solids, 2004, 23(5):853-864.
[233] Koizumi M. The concept of FGM. Ceramic Transactions, 1993, 34:3-10.
[234] Vel S. S., Batra R. C. Exact solution for thermoelastic deformation of functionally graded thick rectangular plates. AIAA J, 2002, 40:1421-1433.
[235] Reddy J. N., Wang C. M., Kitipornchai S. Axisymmetric bending of functionally graded circular and annular plates. Eur J Mech A/Solids, 1999, 18(2): 185-199.
[236] Aoudi J., Pindera M. J., Arnold S. M. Higher-order theory for functionally graded materials. Composites: Part B, 1999, 30(8):777-832.
[237] Reddy J. N., Cheng Z. Q. Three-dimensional solutions of smart functionally graded plates. J Appl Mech, 2001,68:234-241.
[238] Yang J., Kitipornchai S., Liew K. M. Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates. Comput Meth Appl Mech Eng, 2003, 192:3861-3885.
[239] Carrera E., Kroplin B. Zigzag and interlaminar equilibria effects in large-deflection and postbuckling analysis of multilayered plates. Mech Compos Mater Struct, 1997,4:69-94.
[240] Lo S. H., Wu Z., Cheung Y. K., Chen W. J. An enhanced global-local higher-order theory for the free edge effect in laminates. Compos Struct, on line.
[241] Wang A. S. D., Crossman F. W. Some new results on edge effect in symmetric composite laminates. J Compos Mater, 1977,11:92-106.
[242] Becker W. Closed-form solution for the free-edge effect in cross-ply laminates. Compos Struct, 1993, 26:39-45.
[243] Raghuram P. V., Murty A. V. K. A high precision coupled bending-extension triangular finite element for laminated plates. Comput Struct, 1999,72:763-777.
[244] Kim T., Atluri S. N. Analysis of edge stresses in composite laminates under combined thermo-mechanical loading, using a complementary energy approach. Comput Mech, 1995,16:83-87.
[245] Yin W. L. The effect of temperature gradient on the free-edge interlaminar stresses in multi-layered structures. J Compos Mater, 1997,31:2460-2477.
[246] Dong S. B., Tso F. K. W. On a laminated orthotropic shell theory including transverse shear deformation. J Appl Mech, 1972, 29:969-975.
[247] Reddy J. N., Liu C. F. A higher-order shear deformation theory of laminated elastic shell. Int J Eng Sci, 1985,23:319-330.
[248] Barbero E. J., Reddy J. N. General two-dimensional theory of laminated cylindrical shells. AIAA J, 1990, 28:5544-5553.
[249] Qatu M. S. Research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells. Appl Mech Rev, 2002, 55:325-350.
[250] 监凯维奇(Zienkiewicz，O．C．)，泰勒(Taylor，R．L．)著；庄茁，岑松译．有限元方法．第2卷，固体力学—5版．北京：清华大学出版社．2006．
[2] 杨乃宾，章怡宁．复合材料飞机结构设计．北京：航空工业出版社．2002．
[3] 沈观林，胡更开．复合材料力学．北京：清华大学出版社．2006．
[4] Grigolyuk E. I., Kogan F. A. The present status of the theory of multilayerd shells. Prikl Mekh, 1972, 8: 3-17.
[5] Leissa A. W. A review of laminated composite plate buckling. Appl Mech Rev, 1987, 40(5): 575-591.
[6] Grigolyuk E. I., Kulikov G. M. General directions of the development of theory of shells. Mekhanica Kompozitnykh Materialov, 1988, 24: 287-298.
[7] Kapania R. K., Raciti S. Recent advances in analysis of laminated beams and plates. AIAA J, 1989, 27(7): 923-946.
[8] Kapania R. K. A review on the analysis of laminated shells. ASME J Pressure Vessel Technol, 1989, 111 (2): 88-96.
[9] Noor A. K., Burton W. S. Assessment of computational models for multilayered composite shells. Appl Mech Rev, 1990, 43(4): 67-97.
[10] Jemleli ta G. On kinematical assumptions of refined theories of plates: A survey. J Appl Mech, 1990, 57: 1080-1091.
[11] Reddy J. N., Robbins D. H. Theories and computational models for composite laminates. Appl Mech Rev, 1994, 47(6): 147-165.
[12] Noor A. K., Burton W. S., Bert C. W. Computational models for sandwich panels and shells. Appl Mech Rev, 1996, 49(3): 155-199.
[13] Grigorenko Y. M. Approaches to numerical solution of linear and nonlinear problems in shell theory in classical and refined formulations. Int Appl Mech, 1996, 32: 409-422.
[14] Grigorenko Y. M., Vasilenko A. T. Solution of problems and analysis of the stress strain state of non-uniform anisotropic shells. Int Appl Mech, 1997, 33: 851-880.
[15] Reddy J. N. Mechanics of laminated composite plates theory and analysis: CRC press. 1997.
[16] Altenbach H. Theories for laminated and sandwich plates. A review. Mech Compos Mater, 1998, 34: 243-252.
[17] Kant T., Swaminathan K. Estimation of transverse/interlaminar stresses in laminated composites-a selective review and survey of current developments. Compos Struct, 2000, 49: 65-75.
[18] Carrera E. Developments, ideas, and evaluations based upon Reissner's Mixed Variational Theorem in the modeling of multilayered plates and shells. Appl Mech Rev, 2001, 54(4): 301-329.
[19] Ambartsumian S. A. Nontraditional theories of shell and plates. Appl Mech Rev, 2002, 55(5): 35-44.
[20] Mohamad S. Q. Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells. Appl Mech Rev, 2002, 55(4): 325-350.
[21] Carrera E. Historical review of Zig-Zag theories for multilayered plates and shells. Appl Mech Rev, 2003, 56(3): 287-308.
[22] Berthelot J. M. Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: static and fatigue loading. Appl Mech Rev, 2003, 56(1): 111-147.
[23] Reddy J. N., Arciniega R. A. Shear deformation plate and shell theories: From Stavsky to Present. Mech Advanced Mater Struct, 2004, 11: 535-582.
[24] Mittelstedt C., Becker W. Interlaminar stress concentrations in layered structures: Part Ⅱ-closed-form analysis of stresses at laminated rectangular wedges with arbitrary non-orthotropic layup. J Compos Mater, 2004, 38(12): 1063-1090.
[25] Mittelstedt C., Becker W. Interlaminar stress concentrations in layered structures: Part Ⅰ-A selective literature survey on the free-edge effect since 1967. J Compos Mater, 2004, 38(12): 1037-1062.
[26] Carrera E. C_z~0 requirements-models for the two dimensional analysis of multilayered structures. Compos Struct, 1997, 37: 373-383.
[27] Di Sciuva M. Multilayered anisotropic plate models with continuous interlaminar stresses. Compos Struct, 1992, 22: 149-167.
[28] Cho M., Parmerter R. R. An efficient higher-order plate theory for laminated composites. Compos Struct, 1992, 20: 113-123.
[29] Cho M., Kim J. S. Improved Mindlin plate stress analysis for laminated composites in finite element method. A/AA J, 1996, 35(3): 587-590.
[30] Icardi U., Di Sciuva M. Large-deflection and stress analysis of multilayered plates with induced-strain actuators. Smart Mater Struct, 1996, 5: 140-164.
[31] Li X. Y., Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Methods Eng, 1997, 40: 1197-1212.
[32] Sze K. Y., Chen. R. G., Cheung Y. K. Finite element model with continuous transverse shear stress for composite laminates in cylindrical bending. Finite Element in Analysis and Design, 1998, 31: 153-164.
[33] 陈荣庚，陈万吉．基于整体．局部位移假设的高阶理论及其三角形板单元．复合材料学报，2000，17(3)：96-102．
[34] 何录武，李乐．复合材料层合板的高阶理论．兰州大学学报，2001，37(3)：26-33．
[35] 李乐，何录武，闵国林．复合材料层合梁的横向剪应力分析．兰州大学学报，2001，37(5)：15-22．
[36] 何录武，李乐．复合材料层合板的应力分析．兰州大学学报，2002，38(1)：36-43．
[37] Pagano N. J. Exact solutions for composite laminates in cylindrical bending. J Compos Mater, 1969, 3: 398-411.
[38] Chia C. Y. Nonlinear analysis of plates. New York: McGraw-Hill. 1980.
[39] Whitney J. M., Pagano N. J. Shear deformation in heterogeneous anisotropic plates. J Appl Mech, 1970, 37: 1031-1036.
[40] Noor A. K., Burton W. S. Stress and free vibration analysis of multilayered composite plates. Compos Struct, 1989, 11: 183-204.
[41] Rolfes R., Noor A. K., Sparr H. Evaluation of transverse thermal stresses in composite plates based on first-order shear deformation theory. Comput Methods Appl Mech Engrg, 1998, 167: 355-368.
[42] Noor A. K., Malik M. An assessment of five modeling approaches for thermo-mechanical stress analysis of laminated composite panels. Comput Mech, 2000, 25: 43-58.
[43] Sze K. Y., He L. W., Cheung Y. K. Predictor-corrector procedures for analysis of laminated plates using standard Mindlin finite element methods. Compos Struct, 2000, 51: 171-192.
[44] 何录武，冯春．复合材料层合壳有限元分析的预测-校正法．力学季刊，2004，25(3)：317-321．
[45] 冯跃中，何录武．复合材料层合板的热应力分析．兰州大学学报，2005，41(6)：94-99．
[46] Fares M. E. Non-linear bending analysis of composite laminated plates using a refined first-order theory. Compos Struct, 1999, 46: 257-266.
[47] Fares M. E., Zenkour A. M., El-Marghany M. K. Non-linear thermal effects on the bending response of cross-ply laminated plates using refined first-order theory. Compos Struct, 2000, 49: 257-267.
[48] Kim J. S., Cho M. Enhanced first-order theory based on mixed formulation and transverse normal effect. Int J Solids Struct, 2007, 44: 1256-1276.
[49] Whitney J. M. The effect of transverse shear deformation on the bending of laminated plates. J Compos Mater, 1969,3:534-547.
[50] Sun C. T, Whitney J. M. Theories for the dynamic response of laminated plates. AIAA J, 1973, 11:178-183.
[51]Liew K. M., Peng L. X., Kitipornchai S. Buckling of folded plate structures subjected to partial in-plane edge loads by the FSDT meshfree Galerkin method. Int J Numer Methods Eng, 2006,65:1495-1526.
[52] Hu X. X., Sakiyama T., Lim C. W, Xiong Y., Matsuda H., Morita C. Vibration of angle-ply laminated plates with twist by Rayleigh-Ritz procedure. Comput Meth Appl Mech Eng, 2004,193:805-823.
[53] Bert C. W, Chen T. L. C. Effect of shear deformation on vibration of antisymmetric angle ply laminated rectangular plates Int J Solids Struct, 1978, 14:465-473.
[54] 杨加明．复合材料板的非线性弯曲．北京：国防工业出版社．2006．
[55]Whitney J. M., Sun C. T. A higher order theory for extensional motion of laminated composites. J Sound Vib, 1973,30:85-89.
[56] Nelson R. B., Lorch D. R. A refined theory for laminated orthotropic plates. J Appl Mech, 1974,41:177-183.
[57] Lo K. H., Christensen R. M., Wu E. M. A higher order theory of plate deformation, Part 1: Homogeneous plates. J Appl Mech, 1977,44(4):663-668.
[58] Lo K. H., Christensen R. M., Wu E. M. A higher order theory of plate deformation, Part 2: Laminated plates. J Appl Mech, 1977, 44(4):669-676.
[59] Kant T. Numerical analysis of thick plates. Comput Meth Appl Mech Eng, 1982, 31:1-18.
[60]Pandya B. N., Kant T. A consistent refined theory for flexure of a symmetric laminate Mech Res Commun, 1987, 14:107-113.
[61]Pandya B. N., Kant T. Higher order shear deformation theories for flexure of sandwich plates-finite element evaluations. Int J Solids Struct, 1988,24(12): 1267-1286.
[62] Kant T., Swaminathan K. Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order theory. Compos Struct, 2001, 53:73-85.
[63] Kant T., Swaminathan K. Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos Struct, 2002, 56:329-344.
[64] Kant T., Swaminathan K. Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories. J Sound Vib, 2001,241:319-327.
[65]Reddy J. N. A simple higher-order theory for laminated composite plates. J Appl Mech, 1984, 51(12):745-752.
[66] Reddy J. N. A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct, 1984, 20:881-896.
[67] Reddy J. N., Phan N. D. Stability and vibration of isotropic and laminated plates according to higher order shear deformation theory. J Sound Vib, 1985, 98:157-170.
[68] Reddy J. N. Analysis of functionally graded plates. Int J Numer Methods Eng, 2000, 47:663-684.
[69]Matsunaga H. Effects of higher-order deformations on in-plane vibration and stability of thick circular rings. Acta Mechanica, 1997, 124:47-61.
[70]Matsunaga H. Vibration and buckling of multilayered composite beam according to higher order deformation theories. J Sound Vib, 2001,246(1):47-62.
[71]Matsunaga H. Vibration and stability of angle-ply laminated composite plates subjected to in-plane stresses. Int J Mech Sci, 2001,43:1925-1944.
[72] Matsunaga H. Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory. Compos Struct, 2000, 48:231-244.
[73] Matsunaga H. Vibration of cross-ply laminated composite plates subjected to initial in-plane stresses. Thin-Walled Struct, 2002,40:557-571.
[74] Matsunaga H. Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading. Compos Struct, 2007, (77):249-262.
[75] Matsunaga H. Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory Compos Struct, 2006, 72:177-192
[76] Matsunaga H. Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory. Compos Struct, 2005,68:439-454.
[77] Matsunaga H. Interlaminar stress analysis of laminated composite and sandwich circular arches subjected to thermal/mechanical loading. Compos Struct, 2003, 60:345-358.
[78]Matsunaga H. Interlaminar stress analysis of laminated composite beams according to global higher-order deformation theories. Compos Struct, 2002,55:105-114.
[79] Matsunaga H. Assessment of a global higher-order deformation theory for laminated composite and sandwich plates. Compos Struct, 2002, 56:279-291.
[80] Matsunaga H. A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings. Compos Struct, 2004, 64:161-177.
[81]Pagano N. J. Exact solutions for rectangular bidirectional composites. J Compos Mater, 1970,4:20-34.
[82] Murakami H. Laminated composite plate theory with improved in-plane response. J Appl Mech, 1986, 53:661-666.
[83]Toledano A., Murakami H. A high-order laminated plate theory with improved in-plane responses. Int J Solids Struct, 1987,23:111-131.
[84] Carrera E. On the use of the Murakami's zig-zag function in the modeling of layered plates and shells. Comput Struct, 2004, 82:541-554.
[85] Tessler A., Saether E. A computationally viable higher-order theory for laminated composite plates. Int J Numer Methods Eng, 1991, 1069-1086.
[86]Reddy J. N. A general non-linear third-order theory of plates with moderate thickness. Int J Nonlinear Mech, 1990,25(6):677-686.
[87] Reddy J. N. On refined theories of composite laminates. Meccanica, 1990,25(4):230-238.
[88]Bhimaraddi A., Stevens L. K. A higher order theory for free vibration of orthotropic, homogeneous and laminated rectangular plates. JAppl Mech, 1984,51:195-198.
[89] Di Sciuva M. A refined transverse shear deformation theory for multilayered anisotropic plates. Atti Accademia Scienze Torino, 1984, 118:279-295.
[90] Di Sciuva M. Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model. J Sound Vib, 1986, 105:425-442.
[91] Di Sciuva M. An improved shear deformation theory for moderately thick multilayered anisotropic shells and plates. J Appl Mech, 1987, 54:589-596.
[92] Di Sciuva M. Further refinement in the transverse shear deformation theory for multilayered composite plates. Atti Accademia Scienze Torino, 1990, 124:248-267.
[93] Lee K., Lee S. W. A postprocessing approach to determine transverse stress in geometrically nonlinear composite and sandwich structures. J Compos Mater, 2003, 37(24):2207-2224.
[94]Icardi U. Cylindrical bending of laminated cylindrical shells using a modified zig-zag theory. Struct Eng Mech, 1998, 6(5):497-516.
[95] Di Sciuva M., Icardi U., Librescu L. Effects of interfacial damage on the global and local static response of cross-ply laminates. Int J Fracture, 1999, 96: 17-35.
[96] Icardi U., Ruotolo R. Laminated shell model with second-order expansion of the reciprocals of Lame coefficients H_a, H_B and interlayer continuities fulfilment. Compos Struct, 2002, 56: 293-313.
[97] Di Sciuva M., Gherlone M. A global/local third-order Hermitian displacement field with damaged interfaces and transverse extensibility: analytical formulation. Compos Struct, 2003, 59: 419-431.
[98] Cho M., Klm K. O., Kim M. H. Efficient higher-order shell theory for laminated composites. Compos Struct, 1996, 34: 197-212.
[99] Cho M., Kim M. H. A postprocess method using a displacement field of higher-order shell theory. Compos Struct, 1996, 34: 185-196.
[100] Cho M., Kim J. S. Higher-order zig-zag theory for laminated composite with multiple delaminations. J Appl Mech, 2001, 68: 869-877.
[101] Cho M., Oh J. Higher order zig-zag plate theory under thermo-electric-mechanical loads combined. Composites: Part B, 2003, 34: 67-82.
[102] Cho M., Oh J. Higher order zig-zag theory for fully coupledthermo-electric-mechanical smart composite plates. Int J Solids Struct, 2004, 41: 1331-1356.
[103] Oh J., Cho M. Higher order zig-zag theory for smart composite shells under mechanical-thermo-electric loading. Int J Solids Struct, 2007, 44: 100-127.
[104] Oh J., Cho M., Kim J. S. Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory. Int J Solids Struct, 2005, 42: 6122-6140.
[105] Kim J. S., Cho M. Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory. Int J Numer Methods Eng, 2002, 55: 1323-1343.
[106] Cho M., Choi Y. J. A new postprocessing method for laminated composites of general lamination configurations. Compos Struct, 2001, 54: 397-406.
[107] Kapuria S., Dumir P. C., Ahmed A. An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading. Int J Solids Struct, 2003, 40: 6613-6631.
[108] Kapuria S., Achary G. G. S. An efficient higher order zigzag theory for laminated plates subjected to thermal loading. Int J Solids Struct, 2004, 41: 4661-4684.
[109] Kapuria S., Dumir P. C., Jain N. K. Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams. Compos Struct, 2004, 64: 317-327.
[110] 何陵辉，刘人怀．一种考虑层间位移和横向剪应力连续条件的层合板理论．固体力学学报，1994，15(4)：319-325．
[111] 舒小平．满足板面载荷和横向剪应力连续的层板理论．复合材料学报，1994，11(4)：61-68．
[112] Shu X. P. An improved simple higher-order theory for laminated composite shells. Comput Struct, 1996, 60(3): 343-350.
[113] Shu X. P. A refined theory of laminated shells with higher-order transverse shear deformation. Int J Solids Struct, 1997, 34(6): 673-683.
[114] 舒小平．层间滑移对复合材料层合板自由振动的影响．淮海工学院学报，2000，9(3)：9-11．
[115] 舒小平．层间弱粘贴复合材料层板的热弹性脱层．工程力学，2002，19(3)：153-158．
[116] Shu X. P., Soldatos K. P. An accurate de-lamination model for weakly bonded laminates subjected to different sets of edge boundary conditions. Int J Mech Sci, 2001, 43: 935-959.
[117] Shu X. P., Soldatos K. P. Cylindrical bending of angle-ply laminates subjected to different sets of edge boundary conditions. Int J Solids Struct, 2000, 37: 4289-4307.
[118] Shu X. P. Vibration and bending of antisymmetrically angle-ply laminated plates with perfectly and weakly bonded layers. Compos Struct, 2001, 53:245-255.
[119] Liu D., Li X. Y. An overall view of laminated theories based on displacement hypothesis. J Compos Mater, 1996,30:1539-1561.
[120] Li X. Y., Liu D. A laminate theory based on global-local superposition. Commun Numer Meth Engng, 1995,11:633-641.
[121] Reddy J. N. On refined computational models of composite laminates. Int J Numer Methods Eng, 1989, 27:361-382.
[122] Reddy J. N. A refined nonlinear theory of plates with transverse shear deformation. Int J Solids Struct, 1987,20:881-896.
[123] Tahani M., Noiser A. Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading. Compos Struct, 2003,60:91-103.
[124] Tahani M., Noiser A. Three-dimensional interlaminar stress analysis at free edges of general cross-ply composite laminates. Materials and Design, 2003,24:121-130.
[125] Tahani M., Noiser A. Edge effects of uniformly loaded cross-ply composite laminates. Materials and Design, 2003,24:647-658.
[126] Tahani M., Noiser A. Accurate determination of interlaminar stresses in general cross-ply laminates. Mech Advanced Mater Struct, 2004, 11:67-92.
[127] Noiser A., Bahrami A. Free-edge stresses in antisymmetric angle-ply laminates in extension and torsion. Int J Solids Struct, 2006,43:6800-6816.
[128] Noiser A., Bahrami A. Interlaminar stresses in antisymmetric angle-ply laminates. Compos Struct, 2007, 78:18-33.
[129] Mittelstedt C, Becker W. Fast and reliable analysis of free-edge stress fields in a thermally loaded composite strip by a layerwise laminate theory. Int J Numer Methods Eng, 2006,67(6):747-770.
[130] Toledano A., Murakami H. A composite plate theory for arbitrary laminated configurations. J Appl Mech, 1987,54:181-189.
[131] Carrera E. Mixed layer-wise models for multilayered plates analysis. Compos Struct, 1998, 43:57-70.
[132] Carrera E. A study of transverse normal stress effect on vibration of multilayered plates and shells. J Sound Vib, 1999,225(5):803-829.
[133] Carrera E. An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates. Compos Struct, 2000, 50:183-198.
[134] Carrera E. An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates. J thermal Stresses, 2000,23:797-831.
[135] Carrera E., Ciuffreda A. Closed-form solutions to assess multilayered-plate theories for various thermal stress problems. J thermal Stresses, 2004,27:1001-1031.
[136] Carrera E., Ciuffreda A. A unified formulation to assess theories of multilayered plates for various bending problems. compos Struct, 2005, 69:271-293.
[137] Dafedar J. B., Desai Y. M. Thermomechanical buckling of laminated composite plates using mixed, higher-order analytical formulation. J Appl Mech, 2002, 69:790-799.
[138] Dafedar J. B., Desai Y. M., Mufti A. A. Stability of sandwich plates by mixed, higher-order analytical formulation. Int J Solids Struct, 2003,40:4501-4517.
[139] Rao M. K., Desai Y. M. Analytical solutions for vibrations of laminated and sandwich plates using mixed theory. Compos Struct, 2004, 63:361-373.
[140] Rao M. K., Scherbatiuk K., Desai Y. M., Shah A. H. Natural vibrations of laminated and sandwich plates. J Eng Mech, 2004, 130: 1268-1278.
[141] Ren J. G. Exact solutions for laminated cylindrical shells in cylindrical bending. Compos Sci Technol, 1987, 29: 169-187.
[142] Varadan T. K., Bhaskar K. Bending of laminated orthotropic cylindrical shells-An elasticity approach. Compos Struct, 1991, 17: 141-156.
[143] Wang Y. M., Tarn J. Q., Hsu C. K. State space approach for stress decay in laminates. Int J Solids Struct, 2000, 37: 3535-3553.
[144] Ding H. J., Chen W. Q., Xu R. Q. On the bending, vibration and stability of laminated rectangular plates with transversely isotropic layers. Appl Math Mech, 2001, 22(1): 17-24.
[145] Chen W. Q., Bian Z. G., Ding H. J. Three-dimensional analysis of a thick FGM rectangular plate in thermal environment. J Zhejiang University, 2003, 4(1): 1-7.
[146] Chen W. Q., Lee K. Y. Three-dimensional exact analysis of angle-ply laminates in cylindrical bending with interracial damage via state-space method. Compos Struct, 2004, 64: 275-283.
[147] Chen W. Q., Lee K. Y. Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections. Compos Struct, 2004, 65: 329-337.
[148] Chen W. Q., Ying J., Cai J. B., Ye G. R. Benchmark solution of imperfect angle-ply laminated rectangular plates in cylindrical bending with surface piezoelectric layers as actuator and sensor. Comput Struct, 2004, 82: 1773-1784.
[149] Ge Z. J., Chen W. J. A refined discrete triangular Mindlin element for laminated composite plates. Struct Eng Mech, 2002, 14(5): 575-593.
[150] Cen S., Long Y. Q., Yao Z. H. A new hybrid-enhanced displacement-based element for the analysis of laminated composite plates. Comput Struct, 2002, 80: 819-833.
[151] Cen S., Soh A. K., Long Y. Q., Yao Z. H. A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates. Compos Struct, 2002, 58: 583-599.
[152] Zhang Y. X., Kim K. S. Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements. Compos Struct, 2006, 72: 301-310.
[153] Reddy J. N. A penalty plate-bending element for the analysis of laminated anisotropic composite plates. Int J Numer Methods Eng, 1980, 15: 1187-1206.
[154] Hughes T. J. R., Tezduyar T. E. Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J Appl Mech, 1981, 48(3): 587-596.
[155] Belytschko T., Tsay C. S., Liu W. K. Stabilization matrix for the bilinear Mindlin plate element. Comput Meth Appl Mech Eng, 1981, 29: 313-327.
[156] Bathe K. J., Dvorkin E. N. A four-node plate bending element based on Mindlin/Reissner plate theory and mixed interpolation. Int J Numer Methods Eng, 1985, 21: 367-383.
[157] 朱菊芬，牛海英．含多个分层复合材料层合板后屈曲性态研究．计算力学学报，2004，21(6)：711-717．
[158] 牛海英，朱菊芬．含单个分层复合材料层合板后屈曲性态研究．大连理工大学学报，2004，44(5)：634-639．
[159] 白瑞祥，张志峰，陈浩然．含面＼芯开裂损伤复合材料夹层板的自由振动．吉林大学学报，2005，35(2)：199-204．
[160] 白瑞祥，陈浩然．含面芯开裂损伤复合材料夹层板考虑几何非线性的能量释放率数值分析．复合材料学报，2003，20(3)：1-6．
[161] Kant T., Owen D. R. J., Zienkiewicz O. C. A refined higher order C0 plate bending element. Comput Struct, 1982, 15:177-183.
[162] Kant T., Manjunatha B. S. An unsymmetric FRC laminate C0 finite element model with 12 degrees of freedom per node. Eng Comput, 1988, 5(3):300-308.
[163] Pandya B. N., Kant T. Finite element stress analysis of laminated composite plates using higher order displacement model. Compos Sci Technol, 1988, 32:137-155.
[164] Pandya B. N., Kant T. Flexure analysis of laminated composites using refined higher order C0 plate bending elements. Comput Meth Appl Mech Eng, 1988,66:173-198.
[165] Kant T., Kommineni J. K. C0 finite element geometrically non-linear analysis of fibre reinforced composite and sandwich laminates based on a higher-order theory. Comput Struct, 1992,45(3):511-520.
[166] Kant T., Khare R. A higher-order facet quadrilateral composite shell element. Int J Numer Methods Eng, 1997,40:44774499.
[167] Khare R., Kant T., Garg A. K. Free vibration of composite and sandwich laminates with a higher-order facet shell element. Compos Struct, 2004,65:405-418.
[168] Nayak A. K., Moy S. S. J., Shenoi R. A. Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory. Composites: Part B, 2002,33:505-519.
[169] Nayak A. K., Moy S. S. J., Shenoi R. A. A higher order finite element theory for buckling and vibration analysis of initially stressed composite sandwich plates. J Sound Vib, 2005, 286:763-780.
[170] Sheikh A. H., Chakrabarti A. A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates. Finite Element in Analysis and Design, 2003,39:883-903.
[171] Chakrabarti A., Sheikh A. H. Buckling of laminated composite plates by a new element based on higher order shear deformation theory. Mech Advanced Mater Struct, 2003, 10:303-317.
[172] Cho M., Parmerter R. R. Finite element for composite plate bending on efficient higher order theory. AIAA J, 1994, 32: 2241-2248.
[173] Oh J., Cho M. A finite element based on cubic zig-zag plate theory for the prediction of thermo-electric-mechanical behaviors. Int J Solids Struct, 2004,41:1357-1375.
[174] Chakrabarti A., Sheikh A. H. A new triangular element to model inter-laminar shear stress continuous plate theory. Int J Numer Methods Eng, 2004, 60:1237-1257.
[175] Di Sciuva M. A third-order triangular multilayered plate finite element with continuous interlaminar stresses. Int J Numer Methods Eng, 1995,38:1-26.
[176] Carrera E. C0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. Int J Numer Methods Eng, 1996, 39:1797-1820.
[177] Saravanos D. A,, Heyliger P. R., Hopkins D. A. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates Int J Solids Struct, 1997, 34(3):359-378.
[178] Kimpara I., Kageyama K., Suzuki K. Finite element stress analysis of interlayer based on selective layerwise higher-order theory, composites: Part A, 1998,29:1049-1056.
[179] Gaudenzi P., Mannini A., Carbonaro R. Multi-layer higher-order finite elements for the analysis of free-edge stresses in composite laminates. Int J Numer Methods Eng, 1998,41:851-873.
[180] Ramtekkar G S., Desai Y. M., Shah A. H. Mixed finite-element model for thick composite laminated plates. Mech Advanced Mater Struct, 2002,9:133-156.
[181] Carrera E., Demasi L. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices. Int J Numer Methods Eng, 2002, 55:191-231.
[182] Carrera E., Demasi L. Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations. Int J Numer Methods Eng, 2002, 55: 253-291.
[183] Desai Y. M., Ramtekkar G. S., Shah A. H. Dynamic analysis of laminated composite plates using a layer-wise mixed finite element model. Compos Struct, 2003, 59: 237-249.
[184] Ramtekkar G. S., Desai Y. M., Shah A. H. Application of a three-dimensional mixed finite element model to the flexure of sandwich plate. Comput Struct, 2003, 81: 2183-2198.
[185] Semedo J. E., Mota Soares C. M., Mota Soares C. A., Reddy J. N. Analysis of laminated adaptive plate structures using layerwise finite element models. Comput Struct, 2004, 82: 1939-1959.
[186] Lage R. G., Mota Soares C. M., Mota Soares C. A., Reddy J. N. Analysis of adaptive plate structures by mixed layerwise finite elements. Compos Struct, 2004, 66: 269-276.
[187] Lage R. G., Mota Soares C. M., Mota Soares C. A., Reddy J. N. Modeling of piezolaminated plates using layerwise mixed finite elements. Comput Struct, 2004, 82: 1849-1863.
[188] Ye J. Q., Sheng H. Y., Qin Q. H. A state space finite element for laminated composites with free edges and subjected to transverse and in-plane loads. Comput Struct, 2004, 82: 1131-1141.
[189] Robaldo A. Finite element analysis of the influence of temperature profile on thermoelasticity of multilayered plates. Comput Struct, 2006, 84: 1236-1246.
[190] Carrera E. A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates. Compos Struct, 2000, 48: 245-260.
[191] Wu Z., Chen W. J. A study of global-local higher-order theory for laminated composite plates. Compos Struct, 2007, 79: 44-54.
[192] Chen W. J., Cheung Y. K. Refined quadrilateral element based on Mindlin/Reissner plate theory. Int J Numer Methods Eng, 2000, 47: 605-627.
[193] Chen W. J., Cheung Y. K. Refined triangular discrete Kirchhoff plate element for thin plate bending, vibration and buckling analysis. Int J Numer Methods Eng, 1998, 41: 1507-1525.
[194] 陈万吉．精化直接刚度法及九参数三角形薄板单元．大连理工大学学报，1993，33(3)：289-296．
[195] 龙驭球，辛克贵．广义协调元．土木工程学报，1987，20(1)：1-14．
[196] 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社．1997．
[197] Chen W. J., Cheung Y. K. Ref'med nonconforming quadrilateral thin plate bending element. Int J Numer Methods Eng, 1997, 41: 3915-3935.
[198] Bazeley G. P., Cheung Y. K., Irons B. M., Zienkiewiz O. C. Triangular elements in bending conforming and non-conforming solution. Proc Conf Matrix Meth Struct Mech Wright-Patterson AF Base, Ohio: Air Force Ins Tech, 1965: 547-576.
[199] Stricklin J. A., Haisler W. E., Tisdale P. R., Gunderson R. A rapidly converging triangular plate element. AIAA J, 1969, 7(1): 180-181.
[200] Batoz J. L., Bathe K. J., Ho L. W. A study of three-node triangular plate bending element. Int J Numer Methods Eng, 1980, 15: 1771-1812.
[201] Batoz J. L., Tahar M. B. Evaluation of a new quadrilateral thin plate bending element. Int J Numer Methods Eng, 1982, 18: 1655-1677.
[202] Wu Z., Chen W. J. Refined global-local higher-order theory and finite element for laminated plates. Int J Numer Methods Eng, 2007, 69: 1627-1670.
[203] Wu Z., Chen R. G., Chen W. J. Refined laminated composite plate element based on global-local higher-order shear deformation theory. Compos Struct, 2005, 70: 135-152.
[204] Wu Z., Chen W. J. A quadrilateral element based on refined global-local higher-order theory for thermal/mechanical analysis of laminated plates. Int J Solids Struct, 2007, 44: 3187-3217.
[205] Chen W. J., Wu Z. A new higher-order shear deformation theory and refined beam element of composite laminates. Acta Mechanica Sinica, 2005,21: 65-69.
[206] Tungikar V. B., Rao K. M. Three dimensional exact solution of thermal stresses in rectangular composite laminates. Compos Struct, 1994,27:419-427.
[207] Bogdanovich A. E., Yushanov S. P. Three-dimensional variational analysis of Pagano's problems for laminated composite plates. Compos Sci Technol, 2000, 60:2407-2425.
[208] Dafedar J. B., Desai Y. M. Stability of composite and sandwich struts by mixed formulation. J Eng Mech, 2004, 130(7):762-770.
[209] Wu Z., Chen W. J. Free vibration of laminated composite and sandwich plates using global-local higher-order theory. J Sound Vib, 2006, 298:333-349.
[210] Noor A. K. Free vibrations of multilayered composite plates. AIAA J, 1973, 11(7):1038-1039.
[211] Noor A. K., Burton W. S. Three-dimensional solutions for antisymmetrically laminated anisotropic plates. J Appl Mech, 1990, 57(3): 182-188.
[212] Son A. K., Chen L. Alternative approach to modify a discrete Kirchhoff triangular element. J Eng Mech, 2001, 127:791-799.
[213] Cheung Y. K., Zhang Y. X., Chen W. J. The application of a refined non-conforming quadrilateral plate bending element in thin plate vibration and stability analysis. Finite Element in Analysis and Design, 2000, 34:175-191.
[214] Noor A. K. Stability of multilayered composite plates. Fibre Sci Tech, 1975, 8:81-89.
[215] Kant T., Patil H. S. Buckling loads of sandwich columns with a higher-order theory. J Reinf Plast Compos, 1991, 10:102-107.
[216] Kant T., Swaminathan K. Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates. Struct Eng Mech, 2000,10(4): 337-357.
[217] Lee J. Thermally induced buckling of laminated composites by a layerwise theory. Comput Struct, 1997, 65(6):917-922.
[218] Noor A. K., Fellow, Burton W. S. Three-dimensional solutions for thermal buckling of multilayered anisotropic plates. J Eng Mech, 1992,118(4):683-701.
[219] Babu C. S., Kant T. Refined higher order finite element models for thermal buckling of laminated composite and sandwich plates. J thermal Stresses, 2000,23:111-130.
[220] Wu Z., Cheung Y. K., Lo S. H., Chen W. J. Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates. Compos Struct, on line.
[221] Sheikh A. H., Topdar P., Haider S. An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates. Compos Struct, 2001, 51:401-409.
[222] Jonnalagadda K. D., Blandford G E., Tauchert T. R. Piezo-thermoelastic composite plate analysis using a first-order shear theory. Compos Struct, 1994, 51(1):79-89.
[223] Huang J. H., Wu T. L. Analysis of hybrid multilayered piezoelectric plates. Int J Eng Sci, 1995, 34(2):171-181.
[224] Ha S. K., Keilers C, Chang F. Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA J, 1992, 30(3):772-780.
[225] Saravanos D. A., Heyliger P. R., Hopkins D. A. Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int J Solids Struct, 1997, 34(3):359-378.
[226] Heyliger P., Ramirez G, Saravanos D. A. Coupled discrete-layer finite element for laminated piezoelectric plates. Commun Numer Meth Engng, 1994, 10:971-981.
[227] Sze K. Y., Yang X. M., Fan H. Electric assumptions for piezoelectric laminate analysis. Int J Solids Struct, 2004,41:2363-2382.
[228] Topdar P., Chakrabarti A., Sheikh A. H. An efficient hybrid plate model for analysis and control of smart sandwich laminates. Comput Meth Appl Mech Eng, 2004,193:4591-4610.
[229] Ray M. C, Bhattacharya R., Samanta B. Exact solutions for static analysis of intelligent structures. AIAA J, 1993,31:1684-1691.
[230] Erdogan F. Fracture mechanics of functionally graded materials. Compos Eng, 1995,5:753-770.
[231] Pan E. Exact solution for functionally graded anisotropic elastic composite laminates. J Compos Mater, 2003,37:1903-1920.
[232] Kashtalyan M. Three-dimensional elasticity solution for bending of functionally graded rectangular plates. Eur J Mech A/Solids, 2004, 23(5):853-864.
[233] Koizumi M. The concept of FGM. Ceramic Transactions, 1993, 34:3-10.
[234] Vel S. S., Batra R. C. Exact solution for thermoelastic deformation of functionally graded thick rectangular plates. AIAA J, 2002, 40:1421-1433.
[235] Reddy J. N., Wang C. M., Kitipornchai S. Axisymmetric bending of functionally graded circular and annular plates. Eur J Mech A/Solids, 1999, 18(2): 185-199.
[236] Aoudi J., Pindera M. J., Arnold S. M. Higher-order theory for functionally graded materials. Composites: Part B, 1999, 30(8):777-832.
[237] Reddy J. N., Cheng Z. Q. Three-dimensional solutions of smart functionally graded plates. J Appl Mech, 2001,68:234-241.
[238] Yang J., Kitipornchai S., Liew K. M. Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates. Comput Meth Appl Mech Eng, 2003, 192:3861-3885.
[239] Carrera E., Kroplin B. Zigzag and interlaminar equilibria effects in large-deflection and postbuckling analysis of multilayered plates. Mech Compos Mater Struct, 1997,4:69-94.
[240] Lo S. H., Wu Z., Cheung Y. K., Chen W. J. An enhanced global-local higher-order theory for the free edge effect in laminates. Compos Struct, on line.
[241] Wang A. S. D., Crossman F. W. Some new results on edge effect in symmetric composite laminates. J Compos Mater, 1977,11:92-106.
[242] Becker W. Closed-form solution for the free-edge effect in cross-ply laminates. Compos Struct, 1993, 26:39-45.
[243] Raghuram P. V., Murty A. V. K. A high precision coupled bending-extension triangular finite element for laminated plates. Comput Struct, 1999,72:763-777.
[244] Kim T., Atluri S. N. Analysis of edge stresses in composite laminates under combined thermo-mechanical loading, using a complementary energy approach. Comput Mech, 1995,16:83-87.
[245] Yin W. L. The effect of temperature gradient on the free-edge interlaminar stresses in multi-layered structures. J Compos Mater, 1997,31:2460-2477.
[246] Dong S. B., Tso F. K. W. On a laminated orthotropic shell theory including transverse shear deformation. J Appl Mech, 1972, 29:969-975.
[247] Reddy J. N., Liu C. F. A higher-order shear deformation theory of laminated elastic shell. Int J Eng Sci, 1985,23:319-330.
[248] Barbero E. J., Reddy J. N. General two-dimensional theory of laminated cylindrical shells. AIAA J, 1990, 28:5544-5553.
[249] Qatu M. S. Research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells. Appl Mech Rev, 2002, 55:325-350.
[250] 监凯维奇(Zienkiewicz，O．C．)，泰勒(Taylor，R．L．)著；庄茁，岑松译．有限元方法．第2卷，固体力学—5版．北京：清华大学出版社．2006．