复合材料层合板壳的三维退化热壳元分析

根据壳元的几何形状规定, 推导了壳元几何关系公式; 假设温度沿壳元厚度是二次多项式分布, 在给定边界条件下, 推导了壳元温度函数表达式; 根据传热定理和有限元离散原理, 推导了复合材料热传导系数从材料坐标系到有限元分析的等参元正则坐标系的变换关系, 建立了各向异性复合材料层合板的有限元热分析列式; 通过积分变换, 推导了三维退化热壳元公式。在此工作基础上, 编制了有限元计算程序, 将计算结果和ANSYS 计算结果进行了比较, 结果吻合较好。经证明, 三维退化热壳元可以节省内存和提高计算效率。 

3D-DEGENERATED THERMAL SHELL ELEMENTANALYSIS IN COMPOSITE LAMINATES

According to the geometric form of a shell element, geometric formulations of the shell element are deduced. This paper supposes that temperature has quadratic variation through layers of the shell element, and gives the expression of temperature functions in given boundary conditions. In this paper, the orthotropic feature of material property is considered; heat conductivity can be transformed from material coordinates into element coordinates and then the formulations of thermal analysis are deduced. Finite element formulations are established using 3D-degenerated shell element and then thermal shell formulations are gotten. Thus this method can change 3D problems into 2D problems. Then a program is designed to test this theory. It not only has the same precision with isoparametric element, but also improves the efficiency of analysis. It also can save memory of computer and running time. The numerical results are compared with ANSYS results and are satisfactory.