具有任意梯度分布函数的梯度板的三维热弹性

摘要

研究任意梯度分布函数的功能梯度板的三维热弹性问题.从正交各项异性功能梯度材料板热弹性力学的基本方程出发,假设材料参数沿板厚方向的梯度分布函数是任意的,基于状态空间法,获得了板在上下表面作用热/机荷载时的Peano-Baker级数解.通过数值算例,研究了级数解的收敛性以及不同的材料梯度分布对板位移、应力和温度场的影响.%A three-dimensional thermoelastic analysis on functionally graded plates with arbitrary graded distributions is conducted. From the basic equation of thermoelasticity for the orthotropic functionally graded material plates, assuming the distribution functions of the plate thickness are arbitrary, the Peano-Baker series solution is obtained when the plate is subject to thermal and mechanical loads on its top and bottom surface based on the state space method. Through numerical examples, the convergence of the present series solution is investigated; the effects of different material gradient distributions on displacement, stresse and temperature of the plate are also discussed in detail.