TY - JOUR
T1 - Weakly-singular traction and displacement boundary integral equations and their meshless local Petrov-Galerkin approaches
AU - Han, Zhidong
AU - Yao, Zhenhan
AU - Atluri, S. N.
PY - 2005/2
Y1 - 2005/2
N2 - The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and traction boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straightforward derivations of weakly singular traction BIEs for solids undergoing small deformations are also presented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the present methods are very promising, especially for solving the elastic problems in which the singularities in displacements, strains, and stresses are of primary concern.
AB - The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and traction boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straightforward derivations of weakly singular traction BIEs for solids undergoing small deformations are also presented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the present methods are very promising, especially for solving the elastic problems in which the singularities in displacements, strains, and stresses are of primary concern.
KW - Boundary integral equation (BIE)
KW - MLPG/BIE
KW - Meshless local Petrov-Galerkin (MLPG) approach
KW - Moving least squares (MLS)
KW - Non-hyper-singular dBIE/tBIE
UR - http://www.scopus.com/inward/record.url?scp=14744289525&partnerID=8YFLogxK
U2 - 10.1016/S1007-0214(05)70002-X
DO - 10.1016/S1007-0214(05)70002-X
M3 - Article
AN - SCOPUS:14744289525
SN - 1007-0214
VL - 10
SP - 1
EP - 7
JO - Tsinghua Science and Technology
JF - Tsinghua Science and Technology
IS - 1
ER -