平面热应力问题的组合杂交有限元方法

利用组合变分原理可以增强杂交元方法解的稳定性,建立了平面热应力问题的基于区域分解的组合变分原理.与弹性力学问题相比,右端项改变;并且提出组合杂交元来离散新的变分原理、形成刚度矩阵;进而引入能量协调条件,不仅简化了变分原理及其相应的刚度矩阵,而且减少有限元解的误差.数值结果表明,能量协调的4节点组合杂交元数值性能最佳:实现粗网格高精度,对网格畸变不敏感且可以克服闭锁现象.

Combined Hybrid Finite Element Method Applied in Plane Thermal Stress Problem

In view of combinative stability,combinative variational principle based on domain decomposition for plane elastic thermal stress problem is constructed.Compared with the principle of elasticity problem,new load items from thermal are involved.In addition,combined hybrid finite element is proposed to discretize the new principle and to formulate element stiffness matrix.Energy compatibility is introduced not only to simplify the variational principle and the corresponding element stiffness matrix but also to reduce the error of finite element solutions.The numerical results indicate that the energy compatible combined hybrid element with 4 nodes possesses the best numerical performance: can achievehigh accuracy under coarse mesh,is not sensitive to mesh distortion and can circumvent Poisson-locking phenomenon.