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A progressive cells activation algorithm for physically non-linear BEM analysis

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

A drawback of the boundary element method (BEM) to analyse solid non-linear problems is the necessity to discretize, not only the boundaries, but also the domain in internal cells. Such discretization is required to evaluate the domain integrals involving the inelastic (initial) fields and represents a loss of one of the most remarkable features of the BEM, which is the reduction of the problem’s dimension by one order. However, only regions where the dissipative effects take place need to be divided in cells, allowing optimization of the non-linear solution algorithms. In this paper, one of these optimization attempts is present in which the cells are progressively activated, augmenting the corresponding matrices, as the inelastic region develop and grow. In addition, the implicit formulation of the BEM with a unified constitutive modelling framework is used in order that different material behaviours may be addressed by a single numerical structure. Three numerical examples are presented: two involving ductile material behaviour, modelled with the elastoplastic von Mises associative constitutive model, and another to simulate quasi-brittle behaviour by an isotropic damage constitutive model.

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Acknowledgements

The authors gratefully acknowledge the financial support received from the following Brazilian agencies of research funding: CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Grant nos. 308785/2041-2 and 311109/2013-6) and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Grant nos. PPM-00669-15 and PPM-00307-13).

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Authors and Affiliations

  1. Departamento de Engenharia de Estruturas, Universidade Federal de Minas Gerais, Avenida Antônio Carlos, 6627, Pampulha, Belo Horizonte, Minas Gerais, CEP: 31270-901, Brazil

    Rodrigo G. Peixoto, Gabriel O. Ribeiro & Roque L. S. Pitangueira

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  1. Rodrigo G. Peixoto
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  2. Gabriel O. Ribeiro
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  3. Roque L. S. Pitangueira
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Correspondence to Rodrigo G. Peixoto.

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Technical Editor: Paulo de Tarso Rocha de Mendonça.

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Peixoto, R.G., Ribeiro, G.O. & Pitangueira, R.L.S. A progressive cells activation algorithm for physically non-linear BEM analysis. J Braz. Soc. Mech. Sci. Eng. 40, 112 (2018). https://doi.org/10.1007/s40430-017-0961-z

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