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Coupling BEM and the Local Point Interpolation for the Solution of Anisotropic Elastic Nonlinear, Multi-Physics and Multi-Fields Problems

Richard Kouitat Njiwa

http://orcid.org/0000-0001-6264-7879

Institut Jean Lamour, CNRS UMR 7198, Université de Lorraine, 2 Allée André Guinier, BP 50840, 54011 Nancy Cedex, France

E-mail Address: Richard.kouitat@univ-lorraine.fr

Corresponding author.

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Gael Pierson

Institut Jean Lamour, CNRS UMR 7198, Université de Lorraine, 2 Allée André Guinier, BP 50840, 54011 Nancy Cedex, France

E-mail Address: gael.pierson@univ-lorraine.fr

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, and

Arnaud Voignier

Institut Jean Lamour, CNRS UMR 7198, Université de Lorraine, 2 Allée André Guinier, BP 50840, 54011 Nancy Cedex, France

E-mail Address: arnaud.voignier@univ-lorraine.fr

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https://doi.org/10.1142/S0219876219500671Cited by:4 (Source: Crossref)

Abstract

The pure boundary element method (BEM) is effective for the solution of a large class of problems. The main appeal of this BEM (reduction of the problem dimension by one) is tarnished to some extent when a fundamental solution to the governing equations does not exist as in the case of nonlinear problems. The easy to implement local point interpolation method applied to the strong form of differential equations is an attractive numerical approach. Its accuracy deteriorates in the presence of Neumann-type boundary conditions which are practically inevitable in solid mechanics. The main appeal of the BEM can be maintained by a judicious coupling of the pure BEM with the local point interpolation method. The resulting approach, named the LPI-BEM, seems versatile and effective. This is demonstrated by considering some linear and nonlinear elasticity problems including multi-physics and multi-field problems.

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