稳定节点积分伽辽金无网格法的应力计算方法研究

应力计算是基于稳定节点积分的伽辽金无网格法的重要组成部分.该文着重研究稳定节点积分伽辽金无网格法的应力计算方法,对稳定节点积分方法的变分一致条件进行了讨论.证明当节点代表域内的应变采用非局郎光滑应变时,相应的应力在节点代表域内为常数,稳定节点积分伽辽金无网格离散方程是变分一致的.文中提出了三种节点应力计算方法,研究表明,基于位移梯度的节点应力计算方法不满足变分一致性要求,而采用光滑应变的节点应力计算方法和一致形心应力计算方法满足变分一致性要求.典型数值算例的误差分析表明,满足变分一致性不一定确保得到更为精确的结果.而基于光滑应变的一致形心应力计算方法总是较其它两种方法更为精确.

ON STRESS EVALUATION IN GALERKIN MESHFREE METHODS WITH STABILIZED CONFORMING NODAL INTEGRATION

Accurate stress computation is an essential step of the efficient Galerkin meshfree formulation with the stabilized conforming nodal integration (SCND. In this work particular emphasis is placed on the stress computations of SCNI-based Galerkin meshfree methods. The requirement for variational consistency of the SCNI formulation is discussed. It is shown that the discrete SCNI formulation is consistent in the variational sense if a constant stress field based on the smoothing strain is employed in the nodal representative or smoothing domain. Subsequently three stress computation approaches, i. e. , direct nodal stress evaluation (DNS), consistent nodal stress evaluation (CNS), and consistent centroid stress evaluation (CCS), are presented. It turns out that both CNS and CCS satisfy the condition of variational consistence whereas DNS does not. A comprehensive numerical comparison of nodal strain energy error reveals that the variational consistence does not necessarily lead to more accurate results, while the proposed CCS approach is uniformly confirmed to yield the most favorable results.