BEASY A Boundary Element Analysis System
Over the past decade the finite element method (FEM) has become established as a valuable tool in the solution of a wide variety of problems in engineering. The FEM may be seen as a method of solving boundary value problems where the phenomenon in the dom
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BEASY A Boundary Element Analysis System D.J. DANSON, C.A. BREBBIA & R.A. ADEY CM Consultants, Ashurst Lodge, Southampton, England
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INTRODUCTION
Over the past decade the finite element method (FEM) has become established as a valuable tool in the solution of a wide variety of problems in engineering. The FEM may be seen as a method of solving boundary value problems where the phenomenon in the domain being studied obeys known differential equations. In the FEM the domain is discretized into a number of elements in each of which the solution of the governing equation is approximated by some function which satisfies the boundary conditions. A set of equations is then set up which when solved forces the solution at various points in the domain, known as nodal points, to the best approximation allowed by the approximating functions and the boundary conditions. An alternative approach is to use functions which satisfy the differential equation in the domain but not the boundary conditions. The boundary may be divided into elements and the boundary values assumed to vary in some manner within these elements. A set of equations may then be formulated in terms of nodal values, with the nodes this time only on the boundaries. The solution of these equations forces the best solution permitted by the assumption of boundary value variation along each boundary element. The attractions of such an approach are obvious. Only the boundary need be discretized thus reducing by one dimension the long list of nodal coordinates and connectivity tables which make the finite element method so tedious. The resulting equations are much fewer in number and so may be solved more readily on computers with limited storage. This idea is the basis of the method known as boundary elements [1,2]. Boundary elements are also weIl adapted to problems with infinite boundaries. The mathematical formulation of the boundary element method (BEM) is more complicated than in the FEM. Nevertheless the BEM has been applied successfully to problems in potential theory, elasticity, plasticity and time dependent problems such as those governed by the diffusion equation and the wave equation. C. A. Brebbia (ed.), Finite Element Systems © Springer-Verlag Berlin Heidelberg 1982
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SPECIFICATION
The general arehiteeture of BEASY is shown in Fig. 1. As ean be seen from Fig. 1 BEASY eonsists of six independent modules for the solution of problems in potential theory and linear isotropie stress analysis. The box labelied OPTIONS covers various more advaneed applieations of the BEM. Element Types BEASY uses eonstant, linear and quadratie non-eonforming boundary elements. These are illustrated in Fig. 2.
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