非稳定温度场的三维p型有限元方法研究

非稳定温度场的边界往往是温度梯度较大的区域，需要划分较密的网格。但在三维温度应力的计算中太密的网格往往使得计算成本很高。将p型阶谱有限元方法引入温度场的计算，则可以开拓一条解决这类问题的有效途径。研究了p型有限元中的温度边界条件和初值，编制了有关程序，对同一个算例，采用不同网格密度的常规有限元法和p型有限元法进行了温度场计算分析和对比。研究结果表明，用p型有限元进行非稳定温度场计算，在网格稀疏的条件下能够达到较高的精度。

Research on 3D p-version hierarchical FEM for unsteady temperature field

The boundary of unsteady temperature field is always a large grade area where a dense mesh is necessary. But too many nodes will cost much time in the three dimensional thermal stresses computation. An effective way to solve the problem is introducing p-version hierarchical finite element method to temperature field. The temperature boundary condition and initial value in p-version finite element method are researched and corresponding program is compiled. For a same example, several meshes with different density are computed by traditional finite element method and a sparse mesh is computed by p-version finite element method. The results show that the p-version hierarchical finite element method brings better precision with a coarse grid in unsteady temperature field analysis.