一般壳体温度场的有限元分析

构造了一种适用于壳体温度场分析的壳体温度单元。此种单元可以假设温度沿壳体厚度方向为线性变化或二次函数变化。通过引入壳体内外表面的边界条件，最终只保留壳体中面节点温度为未知自由度；用罚函数法实现了壳体温度单元与实体温度单元的联接。由此建立的有限元表达格式在数据准备和计算机运算时间上都比现行算法节省很多。

Finite Element Analysis of Temperature Field in General Shells

A kind of finite elements for the temperature field analysis in shells is presented in this paper. The temperature variation in the direction of thickness is assumed to be linear or quadratic. After introducing the boundary conditions of inner and outer surfaces, the only unknown degree of freedom left is the node temperature of middle surface. The temperature variation in middle surface is expressed by two-dimensional interpolation functions. The joining between shell temperature elements and three- dimensional temperature elements is accomplished by the penalty function method. Compared with the methods commonly used, the finite element formulation in this paper considerably decreases the amount of input data and computing time. The examples indicates that the precision is well satisfactory.