TY - JOUR
T1 - On simple formulations of weakly-singular traction & displacement BIE, and their solutions through Petrov-Galerkin approaches
AU - Han, Z. D.
AU - Atluri, S. N.
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2003
Y1 - 2003
N2 - Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are presented. A large number of "intrinsic properties" of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weakly-singular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type "boundary element methods", or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As special cases, the Galerkin type methods, which lead to symmetric systems of equations, are also discussed.
AB - Using the directly derived non-hyper singular integral equations for displacement gradients [as in Okada, Rajiyah, and Atluri (1989a)], simple and straight-forward derivations of weakly singular traction BIE's for solids undergoing small deformations are presented. A large number of "intrinsic properties" of the fundamental solutions in elasticity are developed, and are used in rendering the tBIE and dBIE to be only weakly-singular, in a very simple manner. The solutions of the weakly singular tBIE and dBIE through either global Petrov-Galerkin type "boundary element methods", or, alternatively, through the meshless local Petrov-Galerkin (MLPG) methods, are discussed. As special cases, the Galerkin type methods, which lead to symmetric systems of equations, are also discussed.
UR - http://www.scopus.com/inward/record.url?scp=0242285518&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0242285518
VL - 4
SP - 5
EP - 20
JO - CMES - Computer Modeling in Engineering and Sciences
JF - CMES - Computer Modeling in Engineering and Sciences
SN - 1526-1492
IS - 1
ER -