The boundary contour method for two-dimensional linear elasticity with quadratic boundary elements

1997 ◽  
Vol 20 (4) ◽  
pp. 310-319 ◽  
Author(s):  
A.-V. Phan ◽  
Subrata Mukherjee ◽  
J. R. René Mayer
Keyword(s):  
Linear Elasticity ◽  
Boundary Elements ◽  
Contour Method ◽  
Two Dimensional ◽  
Boundary Contour ◽  
Boundary Contour Method

The Hypersingular Boundary Contour Method for Three-Dimensional Linear Elasticity

1998 ◽  
Vol 65 (2) ◽  
pp. 300-309 ◽  
Author(s):  
S. Mukherjee ◽  
Y. X. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Boundary Elements ◽  
Contour Method ◽  
Boundary Contour ◽  
Shape Functions ◽  
Boundary Contour Method ◽  
Element Method

A variant of the usual boundary element method, called the boundary contour method, has been presented in the literature in recent years. In the boundary contour method in three-dimensions, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. The boundary contour method employs global shape functions with the weights, in the linear combinations of these shape functions, being defined piecewise on boundary elements. A very useful consequence of this approach is that stresses at points on the boundary of a body, where they are continuous, can be easily obtained from the boundary contour method. The hypersingular boundary element method has many important applications in diverse areas such as wave scattering, fracture mechanics, symmetric Galerkin formulations, and adaptive analysis. This paper first presents the derivation of a regularized hypersingular boundary contour method for three-dimensional linear elasticity. This is followed by a discussion of special cases of the general formulation, as well as some numerical results.

The hypersingular boundary contour method for two-dimensional linear elasticity

1998 ◽  
Vol 130 (3-4) ◽  
pp. 209-225 ◽  
Author(s):  
A. -V. Phan ◽  
S. Mukherjee ◽  
J. R. R. Mayer
Keyword(s):  
Linear Elasticity ◽  
Contour Method ◽  
Two Dimensional ◽  
Boundary Contour ◽  
Boundary Contour Method

The Boundary Contour Method for Three-Dimensional Linear Elasticity

1996 ◽  
Vol 63 (2) ◽  
pp. 278-286 ◽  
Author(s):  
A. Nagarajan ◽  
S. Mukherjee ◽  
E. Lutz
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Boundary Contour ◽  
Boundary Contour Method ◽  
Novel Variant ◽  
Elasticity Problems ◽  
Element Method

This paper presents a novel variant of the boundary element method, here called the boundary contour method, applied to three-dimensional problems of linear elasticity. In this work, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. Thus, in this formulation, only line integrals have to be numerically evaluated for three-dimensional elasticity problems—even for curved surface elements of arbitrary shape. Numerical results are presented for some three-dimensional problems, and these are compared against analytical solutions.

A Novel Boundary Element Method for Linear Elasticity With No Numerical Integration for Two-Dimensional and Line Integrals for Three-Dimensional Problems

1994 ◽  
Vol 61 (2) ◽  
pp. 264-269 ◽  
Author(s):  
A. Nagarajan ◽  
E. Lutz ◽  
S. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Integration ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Boundary Contour Method ◽  
Element Method

This paper presents a novel application of the boundary element method to solve problems in linear elasticity. The new method is called the Boundary Contour Method. This approach requires no numerical integration at all for two-dimensional problems and numerical evaluation of line integrals only for three-dimensional problems; even for curved line or surface boundary elements of arbitrary shape! Numerical results are presented for some two-dimensional problems.

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