功能梯度材料板壳结构的耦合问题研究
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摘要
功能梯度材料(Functionally graded material,简写FGM)是一种特殊的非均匀材料。自从1984年日本科学家首次提出其设计概念以来,FGM在制造、设计和应用方面引起了广大学者的极大关注。虽然提出FGM的最初设想是作为热隔栅应用于航空航天领域,但目前发现它在电子、化学、核能、光学、声学、生物医学及土木工程等诸多领域,都有十分广阔的应用前景。对FGM结构力学行为的研究,既有丰富非均匀材料力学的需要,也有实际工程应用的需要。
FGM的不均匀性,给FGM结构的理论分析增加了难度。目前对FGM结构的力学研究有很大一部分利用了建立在均匀材料基础上的假定和理论,这种做法的合理性值得商讨。本文首先利用状态空间法结合三角级数展开技术,对简支的FGM梁、板、圆柱壳结构进行了弹性理论分析。FGM的不均匀性,使得状态方程具有变系数的特性,为此文中引入层合模型进行分层近似处理。由于状态方程直接从弹性力学基本方程导得,没有引入任何有关应力和位移的假定,因此所得结果可以作为其它各种简化理论和数值方法的检验标准。通过分析发现,改变FGM的不均匀程度,可以明显改变FGM结构的静力和动力响应。因此工程设计中可以通过调整FGM的梯度指标(反映FGM材料常数分布情况的量),达到设计目的。
压电FGM结构是一种新型的智能结构,其应用越来越广泛。由于制造时存在的缺陷,或服役时出现的损坏,或人为特意的设置,压电层与FGM之间的粘结面有时会变得非完美。本文采用线性弹簧模型,引入界面传递矩阵,对此进行了分析,讨论了界面特性对智能结构响应的影响。
本文还采用了Soldatos提出的层合板简化理论,对各种边界条件下单跨和多跨FGM板的柱形弯曲进行分析。与传统简化理论预先给定厚度向位移分布函数不同,Soldatos理论用一个位移分布形函数来描述位移沿厚度向的变化,通过求解三维平衡方程来确定这个形函数,可以反映材料不均匀性对厚度向位移分布的影响。其中形函数的确定、单跨平衡方程的求解以及多跨FGM板的传递都采用了状态空间法,提高了计算效率。通过对比发现,传统的经典薄板理论、一阶剪切变形理论和Rdddy的三阶剪切变形理论,在分析FGM结构时,都会由于材料的不均匀性而使计算精度降低。
在上述工作中,本文考虑了多个耦合因素,包括结构与弹性介质的耦合、圆柱壳与流体的耦合;力场与温度场的耦合、力场与电场的耦合。这些耦合因素同样会影响FGlM结构的静力和动力响应,对FGM结构的服役设计具有重要的指导意义。
As nonhomogeneous materials, functionally graded materials (FGMs) were first introduced by a group of Japanese scientists to address the needs of aggressive environment of thermal shock. Since then, FGMs have received more and more attention. Nowadays, FGMs have extended their first applications in aerospace to electronics, chemistry, optics, biomedicine, acoustics, nuclear engineering, civil engineering and the like. Research on the behavior of FGM structures not only benefits the development of mechanics of nonhomogeneous materials, but also satisfies the needs of practice.The inhomogeneity of FGM makes it very difficult to analyze the FGM structures. Most of the present works on FGM structures employed kinds of assumptions or theories derived for the homogeneous materials, which may become doubtful for FGM structures. So, we employ an elasticity method, i.e. state space method, to analyze the simply-supported FGM beams, plates and cylindrical shells. For FGM, the coefficient matrix of the state equation is not constant and is very difficult to solve directly. The FGM plates/shells are then approximated by a laminate model. Since no assumptions are introduced on the deformations or stress fields in the analysis, the presented results can serve as benchmarks for clarifying the reliability of various approximate theories or numerical methods. We find that the inhomogeneity of FGM will affect the response of FGM structures effectively, which will be crucial to the design in the practice.As new smart structures, piezoelectric FGM structures have gained much interest recently. The interface between the piezoelectric actuator or sensor layers and the FGM layers, however, may become debonding during the service time. In some cases, weak bonding is particularly introduced to achieve some particular aims. A linear spring-layer model is adopted in this paper to simulate the weakness of bonding and the effect of bonding is discussed.Finally, a generalized refined theory suggested by Soldatos is employed to analyze the cylindrical bending of single- or multi-span FGM plates under various boundary conditions. Since the shape function of displacements is determined by the elasticity equations of equilibrium, it can be self-adjusted with the gradient index, which makes this theory more suitable for analyzing FGM structures. To improve the efficiency of calculations, the state space method is adopted to derive the shape function and solve the equations governing the FGM plate deformation. The numerical comparisons between several theories show that the inhomogeneity of FGM will decline the accuracy of the classical thin plate theory, the first-order shear
FGM的不均匀性,给FGM结构的理论分析增加了难度。目前对FGM结构的力学研究有很大一部分利用了建立在均匀材料基础上的假定和理论,这种做法的合理性值得商讨。本文首先利用状态空间法结合三角级数展开技术,对简支的FGM梁、板、圆柱壳结构进行了弹性理论分析。FGM的不均匀性,使得状态方程具有变系数的特性,为此文中引入层合模型进行分层近似处理。由于状态方程直接从弹性力学基本方程导得,没有引入任何有关应力和位移的假定,因此所得结果可以作为其它各种简化理论和数值方法的检验标准。通过分析发现,改变FGM的不均匀程度,可以明显改变FGM结构的静力和动力响应。因此工程设计中可以通过调整FGM的梯度指标(反映FGM材料常数分布情况的量),达到设计目的。
压电FGM结构是一种新型的智能结构,其应用越来越广泛。由于制造时存在的缺陷,或服役时出现的损坏,或人为特意的设置,压电层与FGM之间的粘结面有时会变得非完美。本文采用线性弹簧模型,引入界面传递矩阵,对此进行了分析,讨论了界面特性对智能结构响应的影响。
本文还采用了Soldatos提出的层合板简化理论,对各种边界条件下单跨和多跨FGM板的柱形弯曲进行分析。与传统简化理论预先给定厚度向位移分布函数不同,Soldatos理论用一个位移分布形函数来描述位移沿厚度向的变化,通过求解三维平衡方程来确定这个形函数,可以反映材料不均匀性对厚度向位移分布的影响。其中形函数的确定、单跨平衡方程的求解以及多跨FGM板的传递都采用了状态空间法,提高了计算效率。通过对比发现,传统的经典薄板理论、一阶剪切变形理论和Rdddy的三阶剪切变形理论,在分析FGM结构时,都会由于材料的不均匀性而使计算精度降低。
在上述工作中,本文考虑了多个耦合因素,包括结构与弹性介质的耦合、圆柱壳与流体的耦合;力场与温度场的耦合、力场与电场的耦合。这些耦合因素同样会影响FGlM结构的静力和动力响应,对FGM结构的服役设计具有重要的指导意义。
As nonhomogeneous materials, functionally graded materials (FGMs) were first introduced by a group of Japanese scientists to address the needs of aggressive environment of thermal shock. Since then, FGMs have received more and more attention. Nowadays, FGMs have extended their first applications in aerospace to electronics, chemistry, optics, biomedicine, acoustics, nuclear engineering, civil engineering and the like. Research on the behavior of FGM structures not only benefits the development of mechanics of nonhomogeneous materials, but also satisfies the needs of practice.The inhomogeneity of FGM makes it very difficult to analyze the FGM structures. Most of the present works on FGM structures employed kinds of assumptions or theories derived for the homogeneous materials, which may become doubtful for FGM structures. So, we employ an elasticity method, i.e. state space method, to analyze the simply-supported FGM beams, plates and cylindrical shells. For FGM, the coefficient matrix of the state equation is not constant and is very difficult to solve directly. The FGM plates/shells are then approximated by a laminate model. Since no assumptions are introduced on the deformations or stress fields in the analysis, the presented results can serve as benchmarks for clarifying the reliability of various approximate theories or numerical methods. We find that the inhomogeneity of FGM will affect the response of FGM structures effectively, which will be crucial to the design in the practice.As new smart structures, piezoelectric FGM structures have gained much interest recently. The interface between the piezoelectric actuator or sensor layers and the FGM layers, however, may become debonding during the service time. In some cases, weak bonding is particularly introduced to achieve some particular aims. A linear spring-layer model is adopted in this paper to simulate the weakness of bonding and the effect of bonding is discussed.Finally, a generalized refined theory suggested by Soldatos is employed to analyze the cylindrical bending of single- or multi-span FGM plates under various boundary conditions. Since the shape function of displacements is determined by the elasticity equations of equilibrium, it can be self-adjusted with the gradient index, which makes this theory more suitable for analyzing FGM structures. To improve the efficiency of calculations, the state space method is adopted to derive the shape function and solve the equations governing the FGM plate deformation. The numerical comparisons between several theories show that the inhomogeneity of FGM will decline the accuracy of the classical thin plate theory, the first-order shear
引文
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