TY - JOUR
T1 - Numerical analysis of singularities in two dimensions. Part 2: Computation of generalized flux/stress intensity factors
T2 - Computation of generalized flux/stress intensity factors
AU - Szabo, BA
AU - Yosibash, Z
PY - 1996/2/15
Y1 - 1996/2/15
N2 - A numerical method for the computation of the generalized flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties. Such singularities are of great interest from the point of view of failure initiation The eigenpairs, computed in a companion paper,1 characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy reading in particular straining modes. For this reason, failure theories directly or indirectly involve tbe GFIFs/GSIFs. This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.
AB - A numerical method for the computation of the generalized flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties. Such singularities are of great interest from the point of view of failure initiation The eigenpairs, computed in a companion paper,1 characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy reading in particular straining modes. For this reason, failure theories directly or indirectly involve tbe GFIFs/GSIFs. This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.
KW - finite element methods
KW - p-version
KW - singular points
KW - stress intensity factors
KW - flux intensity factors
KW - complementary energy
KW - fracture mechanics
KW - bi-material interfaces
UR - http://www.scopus.com/inward/record.url?scp=0030072041&partnerID=8YFLogxK
U2 - https://doi.org/10.1002/(SICI)1097-0207(19960215)39:3<409::AID-NME861>3.0.CO;2-P
DO - https://doi.org/10.1002/(SICI)1097-0207(19960215)39:3<409::AID-NME861>3.0.CO;2-P
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SN - 0029-5981
VL - 39
SP - 409
EP - 434
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
IS - 3
ER -