Stress analysis of elastic bi-materials by using the localized method of fundamental solutions

Juan Wang; Wenzhen Qu; Xiao Wang; Rui-Ping Xu; Juan Wang; Wenzhen Qu; Xiao Wang; Rui-Ping Xu

doi:10.3934/math.2022074

AIMS Mathematics

2022, Volume 7, Issue 1: 1257-1272. doi: 10.3934/math.2022074

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Research article

Stress analysis of elastic bi-materials by using the localized method of fundamental solutions

1.
School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
2.
Institute of Mechanics for Multifunctional Materials and Structures, Qingdao University, Qingdao 266071, China

Received: 20 May 2021 Accepted: 18 October 2021 Published: 22 October 2021
MSC : 35E20, 65N22

The localized method of fundamental solutions belongs to the family of meshless collocation methods and now has been successfully tried for many kinds of engineering problems. In the method, the whole computational domain is divided into a set of overlapping local subdomains where the classical method of fundamental solutions and the moving least square method are applied. The method produces sparse and banded stiffness matrix which makes it possible to perform large-scale simulations on a desktop computer. In this paper, we document the first attempt to apply the method for the stress analysis of two-dimensional elastic bi-materials. The multi-domain technique is employed to handle the non-homogeneity of the bi-materials. Along the interface of the bi-material, the displacement continuity and traction equilibrium conditions are applied. Several representative numerical examples are presented and discussed to illustrate the accuracy and efficiency of the present approach.
- meshless method,
- localized method of fundamental solutions,
- domain decomposition technique,
- multi-layered elastic materials,
- stress analysis
Citation: Juan Wang, Wenzhen Qu, Xiao Wang, Rui-Ping Xu. Stress analysis of elastic bi-materials by using the localized method of fundamental solutions[J]. AIMS Mathematics, 2022, 7(1): 1257-1272. doi: 10.3934/math.2022074

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Abstract

The localized method of fundamental solutions belongs to the family of meshless collocation methods and now has been successfully tried for many kinds of engineering problems. In the method, the whole computational domain is divided into a set of overlapping local subdomains where the classical method of fundamental solutions and the moving least square method are applied. The method produces sparse and banded stiffness matrix which makes it possible to perform large-scale simulations on a desktop computer. In this paper, we document the first attempt to apply the method for the stress analysis of two-dimensional elastic bi-materials. The multi-domain technique is employed to handle the non-homogeneity of the bi-materials. Along the interface of the bi-material, the displacement continuity and traction equilibrium conditions are applied. Several representative numerical examples are presented and discussed to illustrate the accuracy and efficiency of the present approach.

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