Test Examples

Abstract

We have now developed all the software required to perform a boundary element analysis of problems in potential flow and elasticity. The examples which we can analyse will, however, be restricted to homogeneous domains and linear material behaviour. Before we proceed further in an attempt to eliminate these restrictions, it is opportune to pause and learn, on test examples, a few things about the method especially with respect to the accuracy that can be attained. The purpose of this chapter is twofold. Firstly, the reader will learn how problems are modelled using boundary elements, with examples of simple meshes in two and three dimensions. Secondly, we will show, by comparison with theory and results from finite element meshes, the accuracy which can be obtained. We will also point out possible pitfalls, which must be avoided. As with all numerical methods, examples can be presented that favour the method and others that don’t. Here we find that the BEM has difficulty dealing with cantilevers with small thickness where two opposing boundaries are close to each other. On the other hand it can deal very well with problems which involve an infinite domain. Also we will find that values at the surface are computed more accurately. This gives an indication of the range of applications where the method is superior as compared with others: those involving a large volume to surface ratio (including infinite domains) and those where the results at the boundary are important, for example stress concentration problems. In the following, several test examples will be presented ranging from the simple 2-D analysis of a cantilever beam to the 3-D analysis of a spherical excavation in an infinite continuum. In all cases we show the input file required to solve the problem with program 7.1 and 9.1 and the output obtained. The results are then analysed with respect to accuracy with different discretisations. Comparison is made with theoretical results and in some cases with finite element models.