Stress Analysis using Boundary Elements

Abstract

Although finite element techniques remain the most commonly used methods of numerical stress analysis, boundary element methods offer significant advantages for at least some types of problems, particularly linear ones. Perhaps the most important of these advantages is the ease of mesh data preparation. In two-dimensional problems, only simple line elements are required, for which data are easily generated. In three-dimensional problems, only the two-dimensional boundary surfaces have to be discretised into elements, a task very similar to that encountered in two-dimensional finite element analysis. Also, using boundary element methods, much less unwanted information is generated. In the vast majority of stress analysis problems, the maximum stresses occur on the boundary, and it is unnecessary to compute internal values. Boundary element methods are usually substantially more economical of both computing time and storage than other numerical methods. In order to achieve this economy, however, it is important that boundary element methods are carefully programmed, that efficient types of element are used, and that the mesh design is appropriate. For example, a boundary element mesh should not be simply a finite element mesh with the internal nodes and elements removed: a much coarser boundary element mesh is capable of giving results of the same accuracy. Another major advantage of boundary element methods is that they offer continuous and accurate modelling within the region of interest, giving high resolution of stresses and displacements. This makes them particularly good for solving stress concentration and crack problems.