含脱层层合板分叉屈曲的宏微观失效机制分析
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摘要
根据板壳理论并考虑层合板脱层处的接触效应影响,推导了层合板的控制方程,借助量纲归一化分析建立了该问题的八次特征方程。通过对特征方程各参数进行定性分析,建立了求解八次方程根的解析表达式,发现了层合板的宏微观变形模态。利用MATLAB软件进行算例分析,获得了在不同脱层情况下层合板的屈曲模态参数和临界屈曲荷载。研究表明:层合板的屈曲模态包含整体一致的宏观变形和界面处的微观变形。研究结果与ABAQUS的有限元解进行了对比,结果表明:理论解与有限元分析的结果非常一致。论文从理论分析的角度研究了复合材料矩形层合板的屈曲问题,从理论上剖析了分层层合板的宏微观失效模态。
This paper presents theoretical analysis for the buckling problem of rectangular composite plates containing a buried delamination. The macro-micro failure mechanism of the layered laminated plate is analyzed. According to the theory of plates and shells, the governing equations of the laminates are deduced by considering the influence of the contact effect at the delamination of the laminates. An eight-order characteristic equation of the problem is established by means of dimensionless analysis. Based on the qualitative analysis of the coefficients of the characteristic equation, analytical expressions for the solutions of the eight-order equation are established from which the macro and the micro deformation modes of the laminated plate are identified. The buckling modal parameters and the critical buckling loads of the laminated plates are obtained for different delamination depth and delamination length by developing MATLAB code. The results show that the buckling modes of the laminates contain the macroscopic deformation and the microscopic deformation. The results are compared to ABAQUS finite element solutions. It shows that the theoretical solutions and finite element results are consistent with each other very well.
This paper presents theoretical analysis for the buckling problem of rectangular composite plates containing a buried delamination. The macro-micro failure mechanism of the layered laminated plate is analyzed. According to the theory of plates and shells, the governing equations of the laminates are deduced by considering the influence of the contact effect at the delamination of the laminates. An eight-order characteristic equation of the problem is established by means of dimensionless analysis. Based on the qualitative analysis of the coefficients of the characteristic equation, analytical expressions for the solutions of the eight-order equation are established from which the macro and the micro deformation modes of the laminated plate are identified. The buckling modal parameters and the critical buckling loads of the laminated plates are obtained for different delamination depth and delamination length by developing MATLAB code. The results show that the buckling modes of the laminates contain the macroscopic deformation and the microscopic deformation. The results are compared to ABAQUS finite element solutions. It shows that the theoretical solutions and finite element results are consistent with each other very well.
引文
[1]韩强.弹塑性系统的动力屈曲和分叉[M].北京:科学出版社,2000:1-33.(HAN Qiang.Dynamic buckling and bifurcation of elastoplasticity system[M].Beijing:Science Press,2000:1-33(in Chinese)).
[2]CHAI H,BABCOCK C D,KNAUSS W G.One dimensional modeling of failure in laminated plates by delamination buckling[J].International journal of solids and structures,1981,17(11):1069-1083.
[3]YANG J,SHEN H S.Non-linear analysis of functionally graded plates under transverse and in-plane loads[J].International journal of non-linear mechanics,2003,38(4):467-482.
[4]CHATTOPADHYAY A,GU H.Modeling of delamination buckling in composite cylindrical shells with a new higher-order theory[J].Composites science and technology,1995,54(2):223-232.
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[8]陈金龙,宫文然,李峰.含分层损伤复合材料层合结构在弯曲载荷作用下的屈曲问题研究[J].中国科学:技术科学,2015,45(5):464-470.(CHEN Jinlong,GONG Wenran,LI Feng.Buckling behavior of delaminated composite panels under four-point bending[J].Scientia sinica(technologica),2015,45(5):464-470(in Chinese)).
[9]张薇,王熙.压磁压电层合复合材料圆柱壳表面局部分层屈曲[J].上海交通大学学报,2013,47(2):198-202.(ZHANG Wei,WANGXi.Delaminated buckling near the surface of piezoelectricpiezomagnetic laminated shells[J].Journal of Shanghai Jiao Tong university,2013,47(2):198-202(in Chinese)).
[10]王爱军,王鑫伟,陆浦.圆柱壳板非线性屈曲的分叉解[J].南京航空航天大学学报,2008,40(5):637-640.(WANG Aijun,WANGXinwei,LU Pu.Nonlinear bifurcation buckling solution of circular cylindrical shell panel[J].Journal of Nanjing university of aeronautics&astronautics,2008,40(5):637-640(in Chinese)).
[11]龚良贵,侯瑾,李情.面内载荷作用下复合材料层合板非线性屈曲[J].南昌大学学报:工科版,2011,33(3):252-256.(GONGLianggui,HOU Jin,LI Qing.Nonlinear buckling of composite laminated plates subjected to in-plane loading[J].Journal of Nanchang university(engineering&technology),2011,33(3):252-256(in Chinese)).
[12]刘述伦,薛江红,王璠,等.含脱层纤维增强复合材料层合板在湿热环境下的屈曲分析[J].工程力学,2015,32(3):1-8.(LIUShulun,XUE Jianghong,WANG Fan,et al.Buckling analysis of fiber-reinforced laminated composite plate with delamination under hygrothermal environments[J].Engineering mechanics,2015,32(3):1-8(in Chinese)).
[13]XUE J,YUAN L Z H,LIU R,et al.Contact analysis for fiber reinforced,delaminated laminates with kinematic nonlinearity[J].Acta mechanica solida sinica,2013,26(4):388-402.
[14]XUE J H,LUO Q Z,HAN F,et al.Two dimensional analyses of delamination buckling of symmetrically cross-ply,rectangular laminates[J].Applied mathematics and mechanics(english edition),2013,34(5):597-612.
[15]TANG M Q,XUE J H,YUAN H,et al.Macro-micro analysis for anti-penetrating postbuckling of T300/QY8911 carbon fiber reinforced,deboned laminates with contact effects[J].International journal of applied mechanics,2014,6(4):1-24.
[16]ZHANG X Q,HAN Q.Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion[J].Thin-walled structures,2007,45(12):1035-1043.
[17]CHEN H,WANG M,BAI R.The effect of nonlinear contact upon natural frequency of delaminated stiffened composite plate[J].Composite structures,2006,76(1/2):28-33.
[18]BRUNO D,GRECO F,LONETTI P.A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites[J].International journal of solids and structures,2003,40(26):7245-7268.
[19]KARIHALOO B L,STANG H.Buckling-driven delamination growth in composite laminates:guidelines for assessing the threat posed by interlaminar matrix delamination[J].Composites part Bengineering,2008,39(2):386-395.
[20]沈观林,胡更开.复合材料力学[M].第2版.北京:清华大学出版社,2006:143-153.(SHEN Guanlin,HU Gengkai.Mechanics of composite materials[M].2nd ed.Beijing:Tsinghua University Press,2006:143-153(in Chinese)).
[21]刘人怀.板壳力学[M].北京:机械工业出版社,1990:75-80.(LIURenhuai.Theory of plates and shells[M].Beijing:Machinery Industry Press,1990:75-80(in Chinese)).
[2]CHAI H,BABCOCK C D,KNAUSS W G.One dimensional modeling of failure in laminated plates by delamination buckling[J].International journal of solids and structures,1981,17(11):1069-1083.
[3]YANG J,SHEN H S.Non-linear analysis of functionally graded plates under transverse and in-plane loads[J].International journal of non-linear mechanics,2003,38(4):467-482.
[4]CHATTOPADHYAY A,GU H.Modeling of delamination buckling in composite cylindrical shells with a new higher-order theory[J].Composites science and technology,1995,54(2):223-232.
[5]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].Journal of sound and vibration,2005,286(4/5):763-780.
[6]NIKRAD S F,KEYPOURSANGSARI S,ASADI H,et al.Computational study on compressive instability of composite plates with off-center delaminations[J].Computer methods in applied mechanics and engineering,2016,310:429-459.
[7]蔡宇.复合材料层合板脱层损伤研究[D].天津:中国民航大学,2008.(CAI Yu.Study on delamination damage of laminated composite plates[D].Tianjin:Civil Aviation University of China,2008(in Chinese)).
[8]陈金龙,宫文然,李峰.含分层损伤复合材料层合结构在弯曲载荷作用下的屈曲问题研究[J].中国科学:技术科学,2015,45(5):464-470.(CHEN Jinlong,GONG Wenran,LI Feng.Buckling behavior of delaminated composite panels under four-point bending[J].Scientia sinica(technologica),2015,45(5):464-470(in Chinese)).
[9]张薇,王熙.压磁压电层合复合材料圆柱壳表面局部分层屈曲[J].上海交通大学学报,2013,47(2):198-202.(ZHANG Wei,WANGXi.Delaminated buckling near the surface of piezoelectricpiezomagnetic laminated shells[J].Journal of Shanghai Jiao Tong university,2013,47(2):198-202(in Chinese)).
[10]王爱军,王鑫伟,陆浦.圆柱壳板非线性屈曲的分叉解[J].南京航空航天大学学报,2008,40(5):637-640.(WANG Aijun,WANGXinwei,LU Pu.Nonlinear bifurcation buckling solution of circular cylindrical shell panel[J].Journal of Nanjing university of aeronautics&astronautics,2008,40(5):637-640(in Chinese)).
[11]龚良贵,侯瑾,李情.面内载荷作用下复合材料层合板非线性屈曲[J].南昌大学学报:工科版,2011,33(3):252-256.(GONGLianggui,HOU Jin,LI Qing.Nonlinear buckling of composite laminated plates subjected to in-plane loading[J].Journal of Nanchang university(engineering&technology),2011,33(3):252-256(in Chinese)).
[12]刘述伦,薛江红,王璠,等.含脱层纤维增强复合材料层合板在湿热环境下的屈曲分析[J].工程力学,2015,32(3):1-8.(LIUShulun,XUE Jianghong,WANG Fan,et al.Buckling analysis of fiber-reinforced laminated composite plate with delamination under hygrothermal environments[J].Engineering mechanics,2015,32(3):1-8(in Chinese)).
[13]XUE J,YUAN L Z H,LIU R,et al.Contact analysis for fiber reinforced,delaminated laminates with kinematic nonlinearity[J].Acta mechanica solida sinica,2013,26(4):388-402.
[14]XUE J H,LUO Q Z,HAN F,et al.Two dimensional analyses of delamination buckling of symmetrically cross-ply,rectangular laminates[J].Applied mathematics and mechanics(english edition),2013,34(5):597-612.
[15]TANG M Q,XUE J H,YUAN H,et al.Macro-micro analysis for anti-penetrating postbuckling of T300/QY8911 carbon fiber reinforced,deboned laminates with contact effects[J].International journal of applied mechanics,2014,6(4):1-24.
[16]ZHANG X Q,HAN Q.Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion[J].Thin-walled structures,2007,45(12):1035-1043.
[17]CHEN H,WANG M,BAI R.The effect of nonlinear contact upon natural frequency of delaminated stiffened composite plate[J].Composite structures,2006,76(1/2):28-33.
[18]BRUNO D,GRECO F,LONETTI P.A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites[J].International journal of solids and structures,2003,40(26):7245-7268.
[19]KARIHALOO B L,STANG H.Buckling-driven delamination growth in composite laminates:guidelines for assessing the threat posed by interlaminar matrix delamination[J].Composites part Bengineering,2008,39(2):386-395.
[20]沈观林,胡更开.复合材料力学[M].第2版.北京:清华大学出版社,2006:143-153.(SHEN Guanlin,HU Gengkai.Mechanics of composite materials[M].2nd ed.Beijing:Tsinghua University Press,2006:143-153(in Chinese)).
[21]刘人怀.板壳力学[M].北京:机械工业出版社,1990:75-80.(LIURenhuai.Theory of plates and shells[M].Beijing:Machinery Industry Press,1990:75-80(in Chinese)).