TY - JOUR

T1 - Generalized Westergaard stress functions as fundamental solutions

AU - Dumont, N. A.

AU - Mamani, E. Y.

PY - 2011

Y1 - 2011

N2 - A particular implementation of the hybrid boundary element method is presented for the two-dimensional analysis of potential and elasticity problems, which, although general in concept, is suited for fracture mechanics applications. Generalized Westergaard stress functions, as proposed by Tada, Ernst and Paris in 1993, are used as the problem's fundamental solution. The proposed formulation leads to displacement-based concepts that resemble those presented by Crouch and Starfield, although in a variational framework that leads to matrix equations with clear mechanical meanings. Problems of general topology, such as in the case of unbounded and multiply-connected domains, may be modeled. The formulation, which is directly applicable to notches and generally curved, internal or external cracks, is specially suited for the description of the stress field in the vicinity of crack tips and is an easy means of evaluating stress intensity factors and of checking some basic concepts laid down by Rice in 1968. The paper focuses on the mathematical fundamentals of the formulation. One validating numerical example is presented.

AB - A particular implementation of the hybrid boundary element method is presented for the two-dimensional analysis of potential and elasticity problems, which, although general in concept, is suited for fracture mechanics applications. Generalized Westergaard stress functions, as proposed by Tada, Ernst and Paris in 1993, are used as the problem's fundamental solution. The proposed formulation leads to displacement-based concepts that resemble those presented by Crouch and Starfield, although in a variational framework that leads to matrix equations with clear mechanical meanings. Problems of general topology, such as in the case of unbounded and multiply-connected domains, may be modeled. The formulation, which is directly applicable to notches and generally curved, internal or external cracks, is specially suited for the description of the stress field in the vicinity of crack tips and is an easy means of evaluating stress intensity factors and of checking some basic concepts laid down by Rice in 1968. The paper focuses on the mathematical fundamentals of the formulation. One validating numerical example is presented.

KW - Hellinger-Reissner potential

KW - Hybrid boundary element

KW - Variational methods

KW - Westergaard stress functions

UR - http://www.scopus.com/inward/record.url?scp=82055199198&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:82055199198

SN - 1526-1492

VL - 78

SP - 109

EP - 149

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

IS - 2

ER -