Implementation of sinh method in integration space forboundary integrals with near singularity in potential problems

As a widely used numerical method, boundaryelement method （BEM） is efficient for computer aidedengineering （CAE）. However, boundary integrals withnear singularity need to be calculated accurately andefficiently to implement BEM for CAE analysis on thinbodies successfully. In this paper, the distance in thedenominator of the fundamental solution is first designedas an equivalent form using approximate expansion and theoriginal sinh method can be revised into a new formconsidering the minimum distance and the approximateexpansion. Second, the acquisition of the projection pointby Newton-Raphson method is introduced. We acquire thenearest point between the source point and element edgeby solving a cubic equation if the location of the projectionpoint is outside the element, where boundary integrals withnear singularity appear. Finally, the subtriangles of thelocal coordinate space are mapped into the integrationspace and the sinh method is applied in the integrationspace. The revised sinh method can be directly performedin the integration element. A verification test of our methodis proposed. Results demonstrate that our method iseffective for regularizing the boundary integrals withnear singularity.