Analytical formulae for potential integrals on triangles

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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 to the evaluation of the potential gradient outside the unit cube. In both cases, the method is shown to be accurate and convergent.
Original languageEnglish
Article number041008
Number of pages7
JournalJournal of Applied Mechanics: Transactions of the ASME
Issue number4
Early online date23 Oct 2012
Publication statusPublished - 16 May 2013


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