【作者】 杨雷；

【导师】 戴宏亮；

【作者基本信息】 湖南大学 ， 固体力学， 2012， 硕士

【摘要】 功能梯度材料(FGM)是一种由两种或两种以上的材料复合而成，材料参数沿着一定方向连续变化的复合材料。功能梯度材料满足了人们对材料梯度功能的要求，避免了层合材料出现的应力集中和脱层等问题。功能梯度材料已经被广泛应用在航空航天、核反应堆、内燃机和其他领域。功能梯度材料结构常常被用于恶劣的环境中，并在不同的环境中将呈现不同的性质。本文以功能梯度圆板结构为研究对象，假设功能梯度圆板的材料性质沿着板厚连续变化，并考虑温度场、电场和几何非线性的影响。首先，应用Hamilton原理或最小势能原理建立功能梯度圆板的运动控制方程；其次，基于一阶剪切变形原理和Kirchhoff理论，将功能梯度圆板的运动控制方程表达成为位移形式；然后利用有限差分法、正交配置法、Galerkin法和Newmark法在空间上和时间上对位移变量进行离散；最后整个问题通过迭代求解。通过以上方法，求解了刚性球低速冲击作用下，功能梯度圆板的非线性动态响应问题；功能梯度粘弹性圆板的弯曲和非线性动力响应问题，热环境下功能梯度圆板的非线性动态响应和机电荷载作用下上下表面含压电层的功能梯度圆板的非线性动态响应。在数值算例中讨论了功能梯度材料成分，功能梯度圆板的几何参数和外界环境和荷载对功能梯度圆板的非线性动态响应的影响，得到了很多重要的结论。本论文的研究工作将丰富和发展智能材料与结构力学、非线性动力学和热力学耦合理论，同时为功能梯度板状结构的可靠性评定和优化设计提供了一定的理论依据，并具有一定的工程应用价值。更多还原

【Abstract】 Functionally graded materials(FGM) composed of two or more materials and thematerial parameters change continuously along a certain direction. FGMs achievedthe purpose of optimizing the structure and avoid the stress concentration,delamination and so on. FGM is widely used in aerospace, nuclear reactors, internalcombustion engines and other fields. However, these FGM structures, often undersevere conditions, would exhibit the different property within the different conditions.In this paper, as the research of the functionally graded circular plates, assumingthe material properties of FGM circular plates vary through the thickness, consideringthe effect of the temperature field, electric field and geometry nonlinear factors. Atfirstly, applying the theory of Hamilton or minmum total energy states establishedfunctionally graded circular plate’s motion control equations; Secondly, based on theFirst-order shear deformation Mindlin plate theory or Kirchhoff theory, functionallygraded circular plate’s motion control equations could be rewritten for displacement;Then utilizing the the finite difference method, the orthotropic collocation pointmethod, the Galerkin method and Newmark method to discretize the variablefunctions in space domain and time domain, respectively; Lastly, the whole problemis solved by the iterative method. Through the above method, solved the impactingnonlinear dynamic response of functionally graded material circular plates, nonlineardynamic response of the viscoelastic functionally graded circular plates, the nonlineardynamic response of functionally graded circular plates in the thermal environmentand nonlinear dynamic response of piezoelectric functionally graded circular plates.In the numerical examples, discussed the effects of the material composition, thegeometrical parameters and the outside environment on the nonlinear dynamicresponse of the functionally graded material circular plates.This paper will enrich and develop smart materials and structural mechanics,nonlinear dynamic mechanics and thermomechanical coupling, supplys the theoreticalbasis for security assessment and optimum design, and is important to engineeringapplications.更多还原