功能梯度矩形厚板的三维热弹性分析

直接从三维热弹性力学基本方程出发，通过引入两个位移函数和两个应力函数，导出了一个二阶的齐次状态方程和一个四阶的非齐次状态方程。分析中采用了层合近似模型，即将板划分成厚度足够小的若干薄层，从面可将每一层内的材料常数近似为常数。给出了任意厚度的四边简支横观各向同性功能梯度矩形板的热弹性分析，特别当板较薄时，与薄板理论进行了数值对比，发现两者结果吻合很好。最后研究了材料梯度指标对热弹性场的影响，结果显示梯度指标对热应力和位移都有着显著的作用：在不同的区间，梯度指标对它们有不同的影响；并且在同一区间，梯度指标对两者的影响程度也有所不同。

Three-dimensional Thermoelastic Analysis of Functionally Graded Rectangular Thick Plates

Based on the three-dimensional equations for thermoelasticity and by the introduction of two displacement functions and two stress functions, a second-order homogeneous state equation and a fourth-order inhomogeneous state equation were derived. A laminate approximation model, for which the plate is divided into a certain number of sufficiently thin layers, was employed. Thus the material constants in any layer can be approximately taken as constant. The thermoelastic analysis of a simply supported transversely isotropic functionally graded rectangular plate of arbitrary thickness was analyzed. For a thin plate, compared with the thin plate theory, the good agreement is acquired. The effect of material gradient index on the thermoelastic field was finally discussed. It is found that the effect is different in different intervals of the material gradient index, and the effect on thermal stress is also different from that on displacement even in the same interval of the material gradient index.