Variational consistent one-point integration with Taylor's expansion-based stabilization in the second-order meshfree Galerkin method for strain gradient elasticity

被引：0

作者：

Wang, Bingbing ^{[1
,2
]}

Wang, Ruoyu ^{[1
]}

Lu, Chunsheng ^{[3
]}

Zhao, Minghao ^{[1
,2
,4
]}

Zhang, Jianwei ^{[1
,2
]}

机构：

[1] Zhengzhou Univ, Sch Mech & Safety Engn, Zhengzhou 450001, Henan, Peoples R China

[2] Henan Prov Ind Sci & Technol Inst Antifatigue Mfg, Zhengzhou 450016, Henan, Peoples R China

[3] Curtin Univ, Sch Civil & Mech Engn, Perth, WA 6845, Australia

[4] Zhengzhou Univ, Sch Mech & Power Engn, Zhengzhou 450001, Henan, Peoples R China

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2024年 / 431卷

基金：

中国国家自然科学基金;

关键词：

Meshfree; Strain gradient; Numerical integration; Variational principle; Variational consistency; Taylor's expansion; FINITE-ELEMENT FORMULATIONS; BOUNDARY-VALUE-PROBLEMS; NODAL INTEGRATION; QUADRATIC EXACTNESS;

D O I：

10.1016/j.cma.2024.117305

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A generalized variational principle with five independent variables is proposed for strain gradient elasticity, including displacement, strain, strain gradient, stress, and double stress. Based on the principle, a one-point integration scheme is designed for the second order meshfree Galerkin method through nodal smoothed derivatives and their high order derivatives by Taylor's expansion. Since the proposed integration scheme meets the orthogonality conditions, it is variational consistent. The weak form expanded with Taylor's polynomials can be well evaluated by nodal smoothed derivatives and their high order derivatives on one quadrature point. Numerical one- and two-dimensional case studies show that the proposed integration scheme performs better than the standard Gaussian integration method in terms of accuracy, convergence, efficiency, and stability.

引用

页数：23