对偶变量块体混合元及其位移元的收敛性和精度分析

Abstract

The symplectic characteristics of the equivalent stiffness coefficient matrix for the Hamiltonian canonical equations of elasticity and the Hamiltonian mixed element were intuitive, and the symplectic characteristics of the equivalent stiffness coefficient matrix for the dual-variable brick mixed element (DVBME), which was derived based on the Hellinger-Reissner (H-R) variational principle and the symplectic-conservative theory of elasticity, were similarly intuitive. The governing equations of elasticity were established immediately through the DVBME formulation, and the solution of the governing equations was obtained with the mixed method. Meanwhile, the dual-variable brick displacement element (DVBDE) formulation was deduced from the DVBME formulation, which was only related to displacement variables. The solution of the governing equations based on the DVBDE formulation was got with the displacement method. The numerical examples show that the convergence rates of displacement and stress variables of the 8-node DVBDE with reduced integration are balanced and stable with high precision. The convergence rate of stress of the DVBDE is almost equal to that of the translational 20-node displacement element with reduced integration. The DVBDE is universal.