功能梯度平板的二维热弹性分析  

Two-dimensional Thermoelastic Analysis of a Functionally Graded Plate

作　　者：刘五祥[1] 仲政[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2008年第1期40-47,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金重点项目(10432030)

摘　　要：本文研究正交各向异性功能梯度平板的二维热弹性问题。该平板在y方向无限长,x方向对边简支且温度恒定。从热弹性力学的基本方程出发,假设材料参数沿板厚方向(z方向)按同一函数规律变化,基于状态空间法,在板的上下表面作用机械荷载和热荷载的情况下,获得了功能梯度平板二维热弹性问题的Peano-Baker级数解。通过算例,验证了Peano-Baker级数解的正确性;同时也分析了材料参数沿板厚方向不同的幂函数分布对平板响应的影响。Two-dimensional thermoelastic anaylsis is presented for an orthotropic functionally graded plate, which is infinitely long along y-direction, simply supported and isothermal at two opposite edges in x-direction. From the basic equations of thermoelasticity, assuming that material properties have the same variations along the plate-thickness direction, Peano-Baker series solution is obtained for the thermoelastic fields of the functionally graded plate subjected to mechanical and thermal loads on its upper and lower surfaces by means of state space method. The correctness of the obtained series solution is validated through numerical examples. The influence of different material properties distribution on the structural response of the plate is also studied when material properties have different power function dependence on the thickness-coordinate.

关 键 词：功能梯度板 Peano-Baker级数 热弹性分析 状态空间法 

分 类 号：O345[理学—固体力学]