【作者】 杨杰；

【导师】 沈惠申；

【作者基本信息】 上海交通大学 ， 固体力学， 2001， 博士

【摘要】 功能梯度材料通常是由陶瓷和金属复合而成的一种新型先进非均匀复合材料,在航空航天、核工业、动力机械、汽车工程等领域内有着极为广阔的应用前景。关于该类材料结构在复杂的机械载荷和热载荷作用下的宏观力学响应分析具有重要的理论与应用价值。本文研究工作包括三部分的内容:(1) 提出了基于一维DQ 近似原理的半解析数值方法;(2) 从理论和数值分析两方面对功能梯度复合材料板结构的几何非线性问题及其动力特性进行了全面系统的研究;(3) 分析讨论了层合软夹芯板在局部载荷作用下的线性与非线性局部变形问题,得到了新的有益的结果。首先基于一维DQ 逼近原理,提出了在多维域问题求解中利用解析解和Galerkin 技术使原问题降维的半解析DQ 法。在此基础上,进一步提出了结合运用摄动技术和半解析DQ 法求解非线性问题的半解析摄动DQ 法,为本文研究工作提供了高效可靠的数值分析手段。本文重点对功能梯度复合材料矩形薄板、剪切板和圆柱曲板在不同边界约束条件与复杂热/机械载荷作用下的非线性力学行为和动力特性问题进行了全面系统的研究,分析中考虑了材料组分沿厚度方向依幂律变化及材料物性参数随环境温度改变的特性,同时为便于处理面内载荷和边界约束条件,采用了以位移分量和应力函数表示的基本控制方程。对于功能梯度复合材料薄板结构,推导出基于经典板理论的无量纲几何非线性动力方程,运用半解析数值方法对不同边界约束条件的功能梯度复合材料矩形薄板在面内与横向载荷共同作用下的线性弯曲、自由振动、瞬态动力响应、大挠度弯曲以及后屈曲问题进行了详尽的研究,并通过大量的参数分析讨论了功能梯度复合材料薄板宏观力学响应的特点。对于功能梯度复合材料中厚板,采用Reddy 高阶剪切板理论计入横向剪切应变和面内与转动惯性项的影响,建立了定常温度场中功能梯度复合材料剪切板在各种不同的热/机械载荷条件下几何非线性问题的无量纲动力方程。对于具有不同边界条件和中面位移约束的矩形板,运用半解析数值方法相继研究了温度均匀变化时矩形剪切板的热/机静力弯曲问题和考虑热/机预应力时的横向自由振动问题、并结合运用模态叠加法给出了其瞬态动力响应解;对于热/机非线性弯曲问题则联合运用多参数摄动技术与半解析DQ 法进行了研究。最后,对一般功能梯度复合材料矩形板的屈曲问题进行了探讨,分析了Feldman 与Aboudi 结果错误的原因,指出仅周边固支FGM 板存在分支点屈曲并给出了相应的临界屈曲载荷和临界温度。更多还原

【Abstract】 Functionally graded materials (FGMs), usually made from a mixture of metals and ceramics,have been regarded as one of the advanced inhomogeneous composite materials with greatapplication potential in many engineering sectors such as aerospace vehicles, nuclear reactors,power generators, automobile industries and so on. Investigations on the mechanical response ofFGM structures under various combinations of mechanical and thermal loading conditions havebeen, therefore, receiving considerably more attention in recent years due to their primeimportance in both theoretical and practical aspects.This paper consists of three parts: (1) development of semi-analytical approaches on the basisof one-dimensional DQ approximation; (2) comprehensive theoretical and numerical studies onthe geometrically nonlinear behavior and dynamics of functionally graded plate structures; (3)investigations of the local deformation of foam-filled sandwich plates induced by localizedtransverse patch loads.Based on the one-dimensional differential quadrature approximation rule, a semi-analyticalDQ method is proposed in the first place to reduce the order of the original system by taking theadvantages of existing analytical solutions and Galerkin procedure. A semi-analytical perturbationDQ approach, which makes use of the perturbation technique combined with the newly developedsemi-analytical DQ method, is then designed as an efficient and reliable way in the nonlinearanalysis of FGM structures.Present research is mainly focused on the nonlinear mechanical response and structuraldynamics of functionally graded rectangular thin plates, shear-deformable plates and cylindricalpanels under different boundary constraints and subjected to combined thermo-mechanical loading.Material properties are assumed to be both position and temperature dependent with materialcomposition varying along thickness direction according to a power law distribution. Theoreticalformulations are presented in terms of displacement components and stress function so that effectsof in-plane loads and boundary conditions can be handled easily. The geometrically nonlinear dynamic governing equations of functionally graded thin platesare derived in the framework of classical plate theory. By using the proposed semi-analyticalapproaches, linear bending, free vibration, transient response, large deflection and postbucklingbehavior of rectangular FGM thin plates under general boundary conditions and combinedtransverse and inplane loads have been investigated extensively. Extensive parametric studies havealso been carried out to reveal the effects of various factors on the mechanical response of theFGM thin plates. For functionally graded plates with moderate thickness, nonlinear dynamic governingequations and their dimensionless forms are derived by using the Reddy’s higher order sheardeformable plate theory to account for the parabolic distribution of the transverse shear strains andthe rotary inertia. Thermal effects due to a steady temperature distribution are taken intoconsideration in theoretical formulations. The present work covers a wide range of subjects for theFGM shear deformable rectangular plates with different boundary conditions and in-planeconstraints, and under uniform temperature change. Among those, static bending due tothermo-mechanical loads and free vibration of initially stressed FGM plates are analyzed by usingthe semi-analytical DQ method, the transient response due to impulsive loading is determined bythe mode superposition method, and the thermo-mechanical nonlinear bending solutions areobtained by means of multi-parameter perturbation technique together with the semi-analyticalDQ method. The conditions for the critical buckling to occur for a general functionally gradedplate are also discussed, and the buckling loads and critical temperatures are determined forclamped rectangular plates. Using the Donnell’s shell theory and Reddy’s higher order shear deformation theory, lineardynamic governing equations are established for the shear deformable functionally gradedcylindrical shell panels with moderate thickness and subjected to thermo-mechanical loading.After the vibrational characteristics of initially stressed FGM cylindrical panels being fullyinvestigated, attention is given to the parametric resonance of FGM cylindrical panels subjected toperiodic dynamic excitation force in the axial direction. Bolotin’s method is then employed todetermine the principal instability regions. In the nonlinear analysis of composite laminated thin plates with general boundary supportsand resting on elastic foundations, both large deflection and postbuckling behavior ofanti-symmetric angle-ply and symmetrically cross-ply laminated rectangular plates are examined更多还原