Analytical treatment of boundary integrals in direct boundary element analysis of plan potential and elasticity problems

2001 ◽  
Vol 22 (6) ◽  
pp. 664-673 ◽  
Author(s):  
Zhang Yao-ming ◽  
Sun Huan-chun
Keyword(s):  
Boundary Element ◽  
Analytical Treatment ◽  
Boundary Integrals ◽  
Element Analysis ◽  
Elasticity Problems ◽  
Boundary Element Analysis

Regularization of the Boundary Integrals in the Bem Analysis of 3D Potential Problems

2012 ◽  
Vol 29 (3) ◽  
pp. 385-401 ◽  
Author(s):  
Y. C. Shiah ◽  
M. R. Hematiyan ◽  
Y. H. Chen
Keyword(s):  
Boundary Element ◽  
Local Coordinate System ◽  
Computer Code ◽  
Boundary Integral ◽  
Boundary Integrals ◽  
Element Analysis ◽  
Numerical Tests ◽  
Potential Problems ◽  
Boundary Element Analysis ◽  
Proper Values

AbstractIn the conventional boundary element analysis, near-singularities are present in the associated boundary integral equation for problems involving ultra-thin media. For this case, any conventional numerical schemes will fail to yield proper values for the integrals. In this paper, the boundary integrals of the boundary element method for 3D potential problems are fully regularized by the technique of integration by parts under the local coordinate system. The fully regularized integrands are expressed as very explicit formulations that can be easily programmed into a computer code. Numerical tests carried out for a typical case have verified the accuracy of the approach for any orders of small distance between the source and the element under integration.

Boundary element analysis for elasticity problems using expanding element interpolation method

2019 ◽  
Vol 37 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Jianming Zhang ◽  
Lei Han ◽  
Yudong Zhong ◽  
Yunqiao Dong ◽  
Weicheng Lin
Keyword(s):  
Boundary Element ◽  
Shape Function ◽  
Interpolation Method ◽  
Boundary Integral ◽  
Shape Functions ◽  
Element Analysis ◽  
Content Type ◽  
Elasticity Problems ◽  
Discontinuous Elements ◽  
Boundary Element Analysis

Purpose This paper aims to propose a boundary element analysis of two-dimensional linear elasticity problems by a new expanding element interpolation method. Design/methodology/approach The expanding element is made up based on a traditional discontinuous element by adding virtual nodes along the perimeter of the element. The internal nodes of the original discontinuous element are referred to as source nodes and its shape function as raw shape function. The shape functions of the expanding element constructed on both source nodes and virtual nodes are referred as fine shape functions. Boundary variables are interpolated by the fine shape functions, while the boundary integral equations are collocated on source nodes. Findings The expanding element inherits the advantages of both the continuous and discontinuous elements while overcomes their disadvantages. The polynomial order of fine shape functions of the expanding elements increases by two compared with their corresponding raw shape functions, while the expanding elements still keep independence to each other as the original discontinuous elements. This feature makes the expanding elements able to naturally and accurately interpolate both continuous and discontinuous fields. Originality/value Numerical examples are presented to verify the proposed method. Results have demonstrated that the accuracy, efficiency and convergence rate of the expanding element method.

Sign in / Sign up

Export Citation Format

Share Document