基于约束函数法的热力耦合有限元分析

Thermo-mechanical coupling analysis based on constraint function method

分析了滑移接触条件下热力耦合现象,建立了热力耦合的有限元分析连续模型,提出了系统动力学平衡方程和热力学平衡方程。对系统中物体间的接触条件进行了分析,得到了物体间接触条件的数学表达式,在此基础上,用约束函数表示接触约束条件。应用变分原理对约束函数进行变分,与系统平衡方程组成非线性方程组对热力耦合问题进行求解。实例表明,用约束函数法求解热力耦合问题,收敛性较好,算法稳定,计算结果能反映实际。

A thermo-mechanical coupling model was constituted for finite element analysis based on the thermo-mechanical phenomena. Dynamic equilibrium and thermodynamic equilibrium formulations of the system were brought forward. The conditions of contact were analyzed among the bodies in the system, and then these conditions were induced by mathematical formulas. The contact conditions were expressed by constraint functions. Applied the principle of variation, constraint through a resolution of a set of nonlinear equations including the variational and functions were carried equilibrium equations to solve the thermo-mechanical problems. Finally, a case is done to indicate the applied constraint function method to solve the thermo-mechanical problems. The results show good convergence, arithmetic stability and agreement with the experiment.