The classical way to consider domains in contact with the BEM, as described in reference [1], is based on imposing equilibrium and compatibility along the interfaces, what may cause inaccuracies. However, in the alternative technique described in reference [2], one region is elected as a reference and all regions displacement fundamental solutions are related. This allows taking into account all domains contribution for each equation written for a boundary point. Thus, the multi-region solid is considered as a unique domain and better accuracy is obtained.

The objective of this work is to employ this alternative BEM technique in three-dimensional non-homogeneous infinite domain problems. In the first example a three-dimensional solid with four regions is simulated employing three different numerical models. The first one is with the commercial program ANSYS 10.0, using a fine mesh of three-dimensional finite elements. The second is the classical non-homogeneous BEM formulation and the last is the alternative BEM technique. The accurate results obtained with the alternative technique proved that it guarantees good continuity between domains. In addition to that, the classical formulation presented significant inaccuracies.

An infinite non-homogeneous half space, composed of two layers with different physical characteristics, is analyzed in the second example. A vertical circular uniform load is applied to the top layer surface and the vertical displacement at the central point of the loaded area is calculated using another author solution, the alternative multi-region technique and the classical one. The three values obtained were very close, therefore the numerical simulations may be considered accurate for this example.

Analyzing the results, it may be concluded that both techniques were accurate at the second example. However, in the first one, only the alternative technique presented satisfactory results. It may be concluded that the alternative formulation is more accurate than the classical one, which may become unreliable in complex non-homogeneous simulations. Nevertheless, one disadvantage of the alternative technique is that it can not be used in problems in which the domains have different Poisson's ratios.

1

C.A. Brebbia and J. Dominguez, "Boundary Elements: An Introductory Course", Computational Mechanics Publications, London, 1992.

2

D.B. Ribeiro and J.B. Paiva, "An alternative static boundary element formulation for 3D zoned solids", In: Proceedings of the 6th Conference on Boundary Integral Methods, Durham, England, Durham University, 2007.

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