Non‐singular boundary integral equation implementation

Publisher Website
Google Scholar
Abstract
The basis of the boundary integral equation (BIE) development is the singular field solution for the Kelvin point load problem. The presence of the mathematical singularity in an otherwise non‐singular problem has created over the years a variety of numerical coping strategies. The current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms. The resulting formulation is fully non‐singular and is shown to be amenable to simple, low‐order Gaussian integration. The critical class of problems involving thin sections and/or highly graded BIE meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear BIE equations. Extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi‐analytical BIE implementation reported herein.