Approximate Solutions of a Hypersingular Boundary Integral Equation

2009 ◽  
Author(s):  
Lihua Mu ◽  
Hong Du ◽  
Jihong Shen
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Approximate Solutions ◽  
Boundary Integral ◽  
Hypersingular Boundary Integral Equation

A quadratic formulation for two-dimensional elastoplastic analysis using the boundary integral equation method

1986 ◽  
Vol 21 (3) ◽  
pp. 159-175 ◽  
Author(s):  
K H Lee ◽  
R T Fenner
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Numerical Differentiation ◽  
Approximate Solutions ◽  
Boundary Integral ◽  
Test Problems ◽  
Two Dimensional ◽  
Element Analysis ◽  
Perfectly Plastic

An isoparametric quadratic formulation of the boundary integral equation (BIE) method for two-dimensional elasto-plastic analysis is presented. The initial strain approach is adopted but, unlike in finite element analysis, it is capable of accurately treating perfectly-plastic and weakly strain-hardening materials. Two methods of evaluating internal stress and strain rates, namely, via the elementwise numerical differentiation of the displacement rates, and the pointwise use of integral identities, are included in the solution algorithm, and their relative efficiency is discussed. The use of correction factors is suggested in some cases to ensure that the von Mises flow rules are implemented in a consistent manner. Results to test problems are given and compared with exact or existing approximate solutions.

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