计算力学学报2026，Vol.43Issue(1)：132-138,156,8.DOI:10.7511/jslx20241006001
变分一致型伽辽金无网格法的最优积分域数量
Optimal integration domain number for variationally consistent Galerkin meshfree methods
摘要
Abstract
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.关键词
伽辽金无网格法/变分一致性/数值积分域/赫林格-赖斯纳混合离散/再生光滑梯度Key words
Galerkin meshfree methods/variational consistency/numerical integration domain/Hellinger-Reissner mixed-formulation/Reproducing kernel smoothed gradient分类
数理科学引用本文复制引用
吴俊超,徐洋涛,王崇志,赵珧冰..变分一致型伽辽金无网格法的最优积分域数量[J].计算力学学报,2026,43(1):132-138,156,8.基金项目
国家自然科学基金(12272139) （12272139）
福建省自然科学基金(2023J01108 （）
2022J01290) （）
福厦泉国家自主创新示范区协同创新平台项目(3502ZCQXT2022002)资助. （3502ZCQXT2022002）
