The coupling of the direct boundary element method with the finite element displacement technique in elastostatics

Abstract

This work is concerned with the formation of an 'equivalent' stiffness matrix for a body, using a Direct Boundary Element method approach, which only requires a surface discretisation. This 'equivalent' stiffness matrix may then be treated in the same way as a Finite Element, and coupled into a global Finite Element formulation. 

The thus derived, equivalent stiffness matrix is not found to exhibit the inherent symmetry properties generally expected of a stiffness formulation, and this problem is examined in depth. A simple symmetrisation process is adopted, the validity and accuracy of which is also examined in the context of the overall symmetry considerations. 

The difficulties arising due to surface geometry discontinuities are also examined, and a technique is proposed for their solution. This is implemented for 2-Dimensional problems, but may readily be extended to 3-Dimensions. 

3-Dimensional problems involving finite and semi-infinite regions are treated using constant Boundary Elements, and both constant and linear element formulations are presented for the 2-D case. Finally an explicit formulation is presented for a 2-D half-space, loaded at the free surface, using constant, linear or quadratic elements, which does away with the necessity of numerical integration.

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