变分一致型伽辽金无网格法的最优积分域数量OA

The variationally consistent Galerkin meshfree methods satisfy the integration constraint,effectively addressing the issues related to integration instability and low efficiency.To further enhance efficiency,this paper determines the optimal numbers of integration domains for the consistent Galerkin meshfree methods based on Hellinger-Reissner mixed formulation framework.A minimum number of integration domains is established by ensuring the coercivity of the weak form,guaranteeing the convergence of the Galerkin method.Additionally,by considering both accuracy and efficiency,another minimum number of integration domains with optimal accuracy is derived from the relationship between the smoothed shape function derivatives'consistency condition and their degrees of freedom.Therefore,the optimal integration domain scheme involves using the minimum number of integration domains for better efficiency.For a balance between accuracy and efficiency,the minimum number of integration domains that ensures optimal accuracy should be employed.The proposed scheme improves the efficiency of variationally consistent Galerkin meshfree methods.Finally,a set of potential and elasticity problems is used to verify the effectiveness of the proposed method.