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A new element-free Galerkin method for 3D elasticity problems

Zhijuan Meng, Yanan Fang, Xiaofei Chi and Lidong Ma

Vol. 17 (2022), No. 5, 469–488
Abstract

A new element-free Galerkin (NEFG) method for three-dimensional (3D) elasticity problems is proposed, which reduces the dimension of the 3D elasticity problem along the splitting direction. The 3D problem domain is reduced to a set of two-dimensional (2D) domains by arbitrarily choosing one axis as the splitting direction. The equilibrium equations of two groups of 3D elastic problems are chosen arbitrarily and the corresponding boundary value conditions are combined to form a 2D boundary value problem. Then the improved interpolating element-free Galerkin (IIEFG) method is adopted to simulate the 2D problems. The finite difference method (FDM) is adopted in the splitting direction. The weight function chooses the nonsingular weight function. After that, the discrete system equations are obtained. Similarly, the system composed of the other two sets of equations can also be solved. Through comparing the numerical results of the NEFG method with those of the dimension splitting element-free Galerkin (DSEFG) method and the improved element-free Galerkin (IEFG) method, three numerical examples indicate the availability and benefit of the NEFG method.

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Keywords
improved interpolating moving least-squares method, dimension splitting method, finite difference method, nonsingular weight function, elasticity
Milestones
Received: 1 April 2022
Revised: 26 May 2022
Accepted: 3 June 2022
Published: 22 February 2023
Authors
Zhijuan Meng
School of Applied Science
Taiyuan University of Science and Technology
Taiyuan
China
Yanan Fang
School of Applied Science
Taiyuan University of Science and Technology
Taiyuan
China
Xiaofei Chi
School of Applied Science
Taiyuan University of Science and Technology
Taiyuan
China
Lidong Ma
School of Mechanical Engineering
Taiyuan University of Science and Technology
Taiyuan
China