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# Reinforced 2d Domain Analysis Using BEM and Regularized BEM/FEM Combination

Alexandre S. Botta1, Wilson S. Venturini2
São Carlos School of Engineering – University of São Paulo Av. Trabalhador São-Carlense, 400, 13566-970 – São Carlos, Brazil. alexbott@sc.usp.br
São Carlos School of Engineering – University of São Paulo, Av. Trabalhador São-Carlense, 400, 13566-970 – São Carlos, Brazil. venturin@sc.usp.br

Computer Modeling in Engineering & Sciences 2005, 8(1), 15-28. https://doi.org/10.3970/cmes.2005.008.015

### Abstract

In this work a regularized boundary-finite element combination is proposed to analyse 2D elastostatic solids reinforced by fibres. The boundary element is adopted to model the matrix behaviour, while finite elements model the embedded fibres. The debonding effects caused by the adherence loss between the two materials are also considered. A three-degree polynomial is adopted to approach the displacement field along the fibre elements, while linear approximations are used to represent the bonding forces between fibres and the matrix. The non-linear debonding model is governed by a loading function written in terms of the contact forces and the relative displacements. The BEM algebraic equations are combined with the fibre finite element relations to eliminate the displacement unknowns along the interface. Then, the resulting redundant algebraic equations are eliminated by applying the least square procedure. An implicit non-linear scheme was proposed to model the debonding effects. Examples dealing with reinforced concrete elements are presented to illustrate the capability of the proposed model.

### Keywords

Boundary elements, reinforcements, BEM/FEM combination

Botta, A. S., Venturini, W. S. (2005). Reinforced 2d Domain Analysis Using BEM and Regularized BEM/FEM Combination. CMES-Computer Modeling in Engineering & Sciences, 8(1), 15–28.

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