Symmetric BE method in two-dimensional elasticity: evaluation of double integrals for curved elements

A procedure for the evaluation of the double integrals involved in the symmetric BE method is proposed, which consists in a regularization via integration by parts and in a successive numerical evaluation of weakly singular integrals. The procedure is applicable to curved elements and higher order shape functions and lends itself to a fairly straightforward implementation. Continuity is required for displacement modelling, while tractions may be modelled as piece-wise continuous. Some example problems characterized by the presence of curved boundaries or of cracks are analyzed using the proposed technique to demonstrate its effectiveness.

[1]  C. Polizzotto,et al.  An energy approach to the boundary element method. Part I: elastic solids , 1988 .

[2]  C. Katz,et al.  Boundary elements and symmetry , 1985 .

[3]  G. Maier,et al.  Boundary integral equation analysis in linear viscoelasticity: variational and saddle point formulations , 1991 .

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

[5]  C. Polizzotto.  An energy approach to the boundary element method. Part 1 1: elastic-plastic solids , 1988 .

[6]  Giulio Maier,et al.  A Galerkin approach to boundary element elastoplastic analysis , 1987 .

[7]  A. Portela.  Dual Boundary Element Analysis of Crack Growth , 1993 .

[8]  Stefan M. Holzer.  On the Engineering Analysis of 2D Problems by the Symmetric Galerkin Boundary Element Method and Coupled BEM/FEM , 1993 .

[9]  J. H. Kane,et al.  Symmetric Galerkin boundary formulations employing curved elements , 1993 .

[10]  G. Maier,et al.  Extremum, convergence and stability properties of the finite-increment problem in elastic-plastic boundary element analysis , 1992 .

[11]  V. Mantič.  On computing boundary limiting values of boundary integrals with strongly singular and hypersingular kernels in 3D BEM for elastostatics , 1994 .

[12]  G. Maier,et al.  Symmetric Galerkin boundary element method in plasticity and gradient plasticity , 1995 .

[13]  On the implementation of the galerkin approach in the boundary element method , 1989 .

[14]  M. Bonnet.  A regularized galerkin symmetric {BIE}formulation for mixed elastic boundary-value problems. , 1993 .

[15]  Marc Bonnet,et al.  Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity , 1995 .

[16]  M. Bonnet,et al.  Regularization of the Displacement and Traction BIE for 3D Elastodynamics Using Indirect Methods , 1993 .

[17]  S. Mukherjee,et al.  A New Boundary Element Method Formulation for Linear Elasticity , 1986 .

[18]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[19]  Stefan M. Holzer,et al.  How to deal with hypersingular integrals in the symmetric BEM , 1993 .

[20]  G. Maier,et al.  A variational approach to boundary element elastodynamic analysis and extension to multidomain problems , 1991 .

[21]  Leonard J. Gray,et al.  Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements: Thermal conduction formulation , 1994 .

[22]  G. Maier,et al.  Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact problems , 1993, Computational Mechanics.

[23]  G. Maier,et al.  Variational formulation of the boundary element method in transient heat conduction , 1991 .

[24]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  S. Miccoli,et al.  Symmetric Coupling of Finite Elements and Boundary Elements , 1993 .

[26]  Stefano Miccoli,et al.  A galerkin symmetric boundary‐element method in elasticity: Formulation and implementation , 1992 .

[27]  G. Maier,et al.  A Variational Formulation of The Boundary Element Method in Transient Poroelasticity , 1995 .