杂交宏元方法的收敛性分析

A convergence analysis for a hybrid macro-element

对一个4-节点的低阶杂交应力四边形宏元方法进行了理论分析.该宏元采用连续分片线性位移插值逼近和分片独立设计的5参数自平衡应力模式.分析表明,单元上采用连续分片线性位移与采用等参双线性位移具有等价性,从而证明了有限元解的存在唯一性,并导出相应的误差估计.

A theoretical analysis is done for a 4-node hybrid stress quadrilateral macro-element, which adopts continuous linear displacement approximations and piecewise-independent 5-parameter self-equilibrium stress mode. Some equivalence is shown between the linear displacement mode and the isoparametric bilinear displacement mode. By virtue of this, the existence and uniqueness of the finite element solution is proved and an error estimate is obtained.