Abstract
A large range of continuum mechanics problems can nowadays be solved using boundary rather than domain solutions. In particular, the Boundary Element Method has been applied to analyse many fluid mechanics and stress analysis problems [1], [2]. The advantages of the technique versus classical domain solutions such as finite differences or finite elements have been discussed in many published references but can be summarised as follows:-
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(i)
The method requires only the discretisation of the surface of the body into a series of elements similar to the well known finite element method but with one degree less of dimensionality. This characteristic not only reduces the number of unknowns but more important, considerably simplifies the amount of data required to run a problem.
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(ii)
By using influence solutions which are valid at infinity, the solution of unbound problems does not require any special treatment. This implies that a large number of cases where the domain under consideration extends to infinity can be solved without resource to large meshes and artificial body conditions.
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(iii)
The standard approach used in boundary elements is a mixed type of formulation which ensures that different variables in a problem (such as fluxes and temperatures, stresses and displacements, etc) are found with the same degree of accuracy. This extra accuracy makes the method well suited to problems such as stress concentration and those with high temperature gradient regions, etc.
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(iv)
Contrary to domain techniques, boundary element analysis codes are easy to interface with standard CAD systems as they do not require complex pre and post processing facilities. The surface meshes needed to run a programme are easy to generate and the post processing can be done ‘a posteriori’, ie once the boundary solution is found the designer can request the internal points on a particular plane or line.
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Brebbia, C.A. (1984). The Solution of Continuum Mechanics Problems Using Boundary Elements. In: Brebbia, C.A., Keramidas, G.A. (eds) Computational Methods and Experimental Measurements. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06375-0_22
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DOI: https://doi.org/10.1007/978-3-662-06375-0_22
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