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An object-oriented approach to dual reciprocity boundary element method applied to 2D elastoplastic problems

Gilberto Gomes (Universidade de Brasilia, Brasilia, Brazil)
Alvaro Martins Delgado Neto (Universidade de Brasilia, Brasilia, Brazil)
Luciano Mendes Bezerra (Universidade de Brasilia, Brasilia, Brazil)
Ramon Silva (Universidade de Brasilia, Brasilia, Brazil)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 18 July 2019

Issue publication date: 8 August 2019

Abstract

Purpose

The purpose of this paper is to describe further developments on a novel formulation of the boundary element method (BEM) for inelastic problems using the dual reciprocity method (DRM) but using object-oriented programming (OOP). As the BEM formulation generates a domain integral due to the inelastic stresses, the DRM is employed in a modified form using polyharmonic spline approximating functions with polynomial augmentation. These approximating functions produced accurate results in BEM applications for a range of problems tested, and have been shown to converge linearly as the order of the function increases.

Design/methodology/approach

A programming class named DRMOOP, written in C++ language and based on OOP, was developed in this research. With such programming, general matrix equations can be easily established and applied to different inelastic problems. A vector that accounts for the influence of the inelastic strains on the displacements and boundary forces is obtained.

Findings

The C++ DRMOOP class has been implemented and tested with the BEM formulation applied to classical elastoplastic problem and the results are reported at the end of the paper.

Originality/value

An object-oriented technology and the C++ DRMOOP class applied to elastoplastic problems.

Keywords

Acknowledgements

The authors are grateful to the Brazilian National Research Council (CNPq) and to the Brazilian Coordination for the Improvement of Higher Education (CAPES) for the supporting funds for this research. The authors also thank the Graduate Program in Structural Engineering and Civil Construction in the Department of Civil and Environmental Engineering in the University of Brasilia (UnB).

Citation

Gomes, G., Delgado Neto, A.M., Bezerra, L.M. and Silva, R. (2019), "An object-oriented approach to dual reciprocity boundary element method applied to 2D elastoplastic problems", Multidiscipline Modeling in Materials and Structures, Vol. 15 No. 5, pp. 958-974. https://doi.org/10.1108/MMMS-05-2018-0095

Publisher

:

Emerald Publishing Limited

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