复合材料广义热弹性问题格点型有限体积法研究

基于Lord-Shulman(L-S理论)、Green-Lindsay(G-L理论)及经典热弹性耦合理论(T-C理论),本文发展了一种适用于二维复合材料广义热弹性问题的格点型有限体积法(CV-FVM).运用交错网格技术，待解变量存储在单元节点，物性参数存储在单元中心，控制方程空间项采用双线性四边形单元进行离散，时间项采用欧拉隐式进行离散.针对均质无限大方板热冲击问题，本文对CV-FVM进行了数值验证，计算结果表明，本文发展的数值方法可以很好地捕捉热波波前和弹性波前的温度阶跃特性及热弹耦合特征.本文采用CV-FVM进一步研究了不同梯度系数p下钛合金/氮化硅复合板的热冲击问题，发现L-S理论复合板p=1时预测的功能梯度界面应力最小；T-C、G-L理论下，复合板p=10时预测的功能梯度界面应力最小，不同耦合理论选系数p对界面热弹性行为影响规律并不相同，并非材料线性分布(p=1)时界面应力幅值最小.本文发展的CV-FVM可作为复合材料热波问题和广义热弹性问题求解的一种备用工具.

Vertex-center finite element method for generalized thermoelastic analysis of composite materials

To analyze the generalized thermoelastic problem in two-dimensional composite material, a new two-dimensional vertex-center finite volume method (CV-FVM) has been developed based on Lord-Shulman (L-S), Green-Lindsay (G-L) and traditional coupled theories. Using the staggered grid technique, the unknown variable is defined at the cell vertex, while the material property is defined at the cell center. The space terms of governing equations are discretized by bilinear quadrilateral element, and the time terms are discretized by Euler implicit formula. Thermal shock problem in infinite plate with homogeneous material is studied by CV-FVM. The results show that the present method can effectively capture the temperature jump and thermoelastic coupling characteristics at the front of the thermal wave and elastic wave. Then, the developed CV-FVM was used to study the thermal shock problem in composite with Ti-6Al-4V/ZrO2 with different material constant p, the results show that the value p=1 minimizes the maximum (tensile) stress applied at the middle of the functionally graded layer under L-S theory, and the value p=10 minimizes the maximum (tensile) stress under G-L and T-C theories. The effects of p on interfacial thermoelastic response is different under different coupling theories, one cannot conclude that a linear variation of the properties minimizes the maximum stress. The developed method can be used as an alternative tool for solving thermal wave and generalized thermoelastic problems.