NURBS-enhanced line integration boundary element method for 2D elasticity problems with body forces

2019 ◽  
Vol 77 (7) ◽  
pp. 2006-2028 ◽  
Author(s):  
Qiao Wang ◽  
Wei Zhou ◽  
Yonggang Cheng ◽  
Gang Ma ◽  
Xiaolin Chang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Body Forces ◽  
Elasticity Problems ◽  
2D Elasticity ◽  
Integration Boundary ◽  
Element 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.

Boundary Element Method by Dislocation Distribution

1987 ◽  
Vol 54 (1) ◽  
pp. 105-109 ◽  
Author(s):  
C. F. Sheng
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integral Equations ◽  
Local Stress ◽  
Extensive Investigation ◽  
Stress Evaluation ◽  
New Approach ◽  
Dislocation Distribution ◽  
Elasticity Problems ◽  
Element Method

The method of dislocation distribution has been applied extensively to crack related problems by many people in the last fifteen years. It has been proved to be very successful in terms of accuracy and versatility. However, the potential of applicability of this method has not been fully explored. This paper shows a way to apply this method to plane stress problems with any geometry and loading conditions. The method of dislocation distribution is similar to the Boundary Element Method in spirit, but has the advantage of enjoying the fully developed numerical schemes in solving the formulated system of singular integral equations. Without extensive investigation, it is hard to tell whether this new approach will produce better results than the traditional BIE method. However, as demonstrated by the excellent results from the numerical examples, this method should be competitive and have the potential to become one of the best candidates for the type of elasticity problems where local stress evaluation is needed.

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