The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition, giving explicit formulae for the regular and for the principal value and finite part integrals used in hypersingular formulations. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a field point lying in the plane of the element. Results are presented for the evaluation of the potential and its gradients, where the integrals must be treated as principal values or finite parts, for elements with constant and linearly varying source terms. These results are tested by application to a single triangular element, and to the evaluation of a potential gradient outside the unit cube. In both cases, the method is shown to be accurate and convergent.
Analytical Formulae for Potential Integrals on Triangles
Manuscript received January 27, 2012; final manuscript received October 15, 2012; accepted manuscript posted October 22, 2012; published online May 16, 2013. Assoc. Editor: Glaucio H. Paulino.
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Carley, M. J. (May 16, 2013). "Analytical Formulae for Potential Integrals on Triangles." ASME. J. Appl. Mech. July 2013; 80(4): 041008. https://doi.org/10.1115/1.4007853
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