Numerical evaluation of two-dimensional singular boundary integrals: theory and Fortran code

In this paper, an approach is presented for the numerical evaluation of weakly, strongly, hyper- and supersingular boundary integrals which exist in the Cauchy principal value sense in two-dimensional problems. In this approach, the singularities involved in integration kernels are analytically removed by expressing the nonsingular parts of the integration kernels as polynomials of the distance r. A self-contained Fortran code is listed and described for implementation of the proposed approach. The attached code is also able to evaluate general regular integrals using Gaussian quadrature, which enables the code to evaluate any two-dimensional boundary integral. Some examples are provided to verify the correctness of the presented formulations and the included code.

[1]  J. Sládek,et al.  Regularization of hypersingular integrals in BEM formulations using various kinds of continuous elements , 1996 .

[2]  J. Sládek,et al.  Regularization Techniques Applied to Boundary Element Methods , 1994 .

[3]  M. H. Aliabadi,et al.  Boundary element hyper‐singular formulation for elastoplastic contact problems , 2000 .

[4]  O. Huber,et al.  Evaluation of the stress tensor in 3D elastostatics by direct solving of hypersingular integrals , 1993 .

[5]  Xiao-Wei Gao,et al.  Evaluation of regular and singular domain integrals with boundary-only discretization-theory and Fortran code , 2005 .

[6]  F. Rizzo,et al.  A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations , 1992 .

[7]  M. Guiggiani,et al.  Direct computation of Cauchy principal value integrals in advanced boundary elements , 1987 .

[8]  G. Karami,et al.  An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis , 1999 .

[9]  Jan Sladek,et al.  Singular integrals in boundary element methods , 1998 .

[10]  Norio Kamiya,et al.  A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity , 2002 .

[11]  Xiao-Wei Gao,et al.  Boundary element analysis in thermoelasticity with and without internal cells , 2003 .

[12]  P. K. Banerjee.  The Boundary Element Methods in Engineering , 1994 .

[13]  Xiaowei Gao,et al.  An effective boundary element algorithm for 2D and 3D elastoplastic problems , 2000 .

[14]  L. Schmerr,et al.  Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering , 1990 .

[15]  Xiao-Wei Gao,et al.  The radial integration method for evaluation of domain integrals with boundary-only discretization , 2002 .

[16]  T. A. Cruse,et al.  Weakly singular stress-BEM for 2D elastostatics , 1999 .

[17]  L. F. Martha,et al.  Hypersingular integrals in boundary element fracture analysis , 1990 .

[18]  Tg Davies,et al.  Boundary Element Programming in Mechanics , 2002 .

[19]  S. Mukherjee.  CPV and HFP integrals and their applications in the boundary element method , 2000 .

[20]  N. Kamiya,et al.  Nearly singular approximations of CPV integrals with end- and corner-singularities for the numerical solution of hypersingular boundary integral equations , 2003 .

[21]  C. Brebbia,et al.  Boundary Element Techniques , 1984 .