Open Access

ABSTRACT

On the Use of the Tangential Differential Operator in the Traction Boundary Integral Equation of the Dual Boundary Element Method for Three Dimensional Problems

L. Palermo Jr., L.P.C.P.F. Almeida¹

1 State University of Campinas, Faculty of Civil Engineering, Architectural and Urban Design, Brazil, Caixa Postal 6021, 13083-970, leandro@fec.unicamp.br.

The International Conference on Computational & Experimental Engineering and Sciences 2008, 7(2), 83-88. https://doi.org/10.3970/icces.2008.007.083

Abstract

The differentiation of the kernels of integrals in the displacement BIE to obtain one for stresses increases the order of the kernel singularity and additional care are necessary to treat the improper integrals. The application of the tangential differential operator (TDO) can reduce the order of the kernel singularity when the stress BIE employs Kelvin type fundamental solutions. This paper presents the numerical formulation for the TDO to three-dimensional problems. The TDO uses the derivatives of the shape function for displacements instead of introducing another interpolation function. Furthermore, the paper shows the additional integrals for the TDO to be applied to non-conformal interpolations or when the boundary surface is piecewise smooth.

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