The method of fundamental solutions with dual reciprocity for some problems in elasticity

摘要

The Method of Fundamental Solutions is an indirect boundary technique, which avoids singularities by defining a fictitious surface which includes the problem domain. The method can be combined with the Dual Reciprocity Method (DRM), for handling body force terms, which would give rise to domain integrals in the Boundary Element Method. In addition to its simplicity and accuracy, the method permits results for stresses to be obtained at both boundary and internal points without the use of special techniques. Here the fictitious surface is considered to be a circle as first proposed by Bogomolny [SIAM J 22 (1985) 644], and application is made to some linear elastic problems. Examples without body forces are considered involving symmetric and non-symmetric load distributions. Examples are also considered including gravitational, centrifugal and thermal loading. In the case of a symmetric problem, results are found to be independent of the radius of the fictitious circle. In the case of non-symmetric loading, it is found that results are dependent on the radius of the circle, however, there exists a range of values of the radius for which the results are practically unchanged. Similar behaviour was found for the case of problems with body forces. For the examples involving DRM, Polyharmonic spline approximation functions were employed. In order to obtain the unknown coefficients, Singular Value Decomposition was found to be more accurate in some cases.