多域组合非耦合热弹性问题的虚边界元法

Virtual Boundary Element Method for Solving Uncoupled Thermoelastic Problems with Multidomain Combinations

摘要:

采用边界元法求解热弹性力学问题通常涉及到关于温度作用的域内体积分，使其在求解此类问题时失去了可降维的优点.为此，应用虚边界元法思想分别考虑热传导问题和与之对应的弹性力学问题的数值格式，并将两者的求解思路结合起来，从而形成解多域组合非耦合热弹性问题时无需计算域内体积分的虚边界元法思想.该方法具有一般性，既适用于二维问题又适用于三维问题，而且可将多域求解思想蜕化到单域问题.按单域定义的方板、厚壁圆筒热应力的计算和按多域定义的含圆形夹杂方板有效热膨胀系数的数值模拟结果已充分表明该方法具有较好的计算效率和较高的计算精度.

Abstract:

The volume integrals caused by temperature has to be dealt with while the boundary element method is employed to solve thermoelastic mechanics problems,as a result,the advantages of reducing dimensions are extinguished.This paper presents,a numerical approach for solving uncoupled thermoelastic problems with multidomain combinations without calculating volume integral,which is the formation of the numerical formats established for solving heat conduction and corresponding elasticity in accordance with virtual boundary element method (VBEM),respectively,and two ideas are combined,too.The method is available for both 2D and 3D problem,and can also degenerates singledomain problem solving.The method can also be applied to thermoelastic problems of composite materials containing holes or inclusions,arbitrary combinations with different material properties and contact problems.In the end,several numerical examples are given to illustrate the performance of the method,and the results validate the high accuracy and efficiency of the method.