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The Use of the BE SBS Algorithm to Evaluate Boundary and Interface Stresses in 3D Solids

F.C. de Araújo1,2, C. R. da Silva Jr.1, M. J. Hillesheim1
Dept. of Civil Eng., UFOP, Ouro Preto, MG, Brazil.
Corresponding author. Email:

Computer Modeling in Engineering & Sciences 2013, 96(3), 185-198.


In this paper, the BE SBS (subregion-by-subregion) algorithm, a generic substructuring technique for the BEM, is applied to evaluate stresses at boundary and interfacial points of general 3D composites and solids. At inner points, regular boundary integration schemes may be employed. For boundary or interfacial points, the Hooke’s law along with global-to-local axis-rotation transformations is directly applied. In fact, in thin-walled domain parts, only boundary stresses are needed. As the SBS algorithm allows the consideration of a generic number of subregions, the technique applies to the stress analysis in any composite and solid, including the microstructural (grain-by-grain) modeling of materials. The independent assembly and algebraic manipulation of the BE matrices for the many substructures involved in the model, makes the formulation very suitable for dealing with large-order models, as it typically happens in the 3D microstructural analysis of general composites. For that, Krylov solvers were incorporated into the SBS algorithm. To show the performance of the technique, stresses are calculated in beams, and 3D representative volume elements (RVEs) of carbon-nanotube (CNT).


3D boundary-element models, subregion-by-subregion algorithm, general composites, stress analysis, Krylov solvers.

Cite This Article

Araújo, F. D., R., C., Hillesheim, M. J. (2013). The Use of the BE SBS Algorithm to Evaluate Boundary and Interface Stresses in 3D Solids. CMES-Computer Modeling in Engineering & Sciences, 96(3), 185–198.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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