功能梯度材料圆板的三维弹性分析  

THREE-DIMENSIONAL ELASTIC ANALYSIS OF A FUNCTIONALLY GRADED CIRCULAR PLATE

作　　者：周凤玺[1] 李世荣[2] 

机构地区：[1]兰州理工大学土木工程学院,兰州730050 [2]兰州理工大学理学院,兰州730050

出　　处：《振动与冲击》2008年第1期115-118,130,共5页Journal of Vibration and Shock

基　　金：国家自然基金资助项目(10472039)

摘　　要：基于线弹性理论的基本方程,选用两个位移分量和两个应力分量作为状态变量,利用状态空间法建立了功能梯度材料轴对称圆板的三维状态方程。根据微分求积法,将状态方程在径向进行离散,考虑周边固支的边界条件,采用打靶法数值求解了材料常数沿板厚按幂率变化的轴对称弯曲问题和自由振动问题,为求解功能梯度材料三维弹性响应提供了一种方法。并且给出了功能梯度材料三维圆板的静动态响应受组分材料分布以及板厚径比变化的影响规律。The state equation of a functionally graded axisymmetric circular plate are established based on the three-dimensional linear elasticity theory using state space approach,in which two displacement components and two stress components are chosen as state variables.By discretizing the state space formulations along the radial direction using the technique of differential quadrature,new state equations at discrete points are established.Giving clamped boundary conditions,assuming that the mechanical properties of the materials have an exponential law distributing along the thickness direction,the static bending and free vibration problems of a three-dimensional functionally graded circular plate are solved using the shooting method.Effects of volume fraction distributions of constituent materials and thickness-to-radius ratio of the plate on its dynamical and static responses are studied.

关 键 词：功能梯度材料 三维分析 状态空间法 微分求积法 打靶法 静力弯曲 自由振动 

分 类 号：O343[理学—固体力学]