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Derivation of the Singular Integral Equations for Curvilinear Cracks with Computer Algebra Software

N. Ioakimidis
Journal / Anthology

Engineering Fracture Mechanics
Year: 1992
Volume: 43
Issue: 4
Page range: 671-676

The classical Cauchy-type complex singular integral equation for the general curvilinear crack problem in plane isotropic elasticity is rederived by using an appropriate computer procedure, based on the Mathematica computer algebra system. Both cases of one crack (or a system of cracks) and of a periodic array of cracks are considered in detail and the Mathematica procedure is displayed. The approach can also be generalized to additional arrays of cracks (like a doubly-periodic or a star-shaped array of curvilinear cracks). The present approach permits the direct error-free construction of sufficiently complicated complex singular integral equations of direct use in fracture mechanics in a simple and powerful way, which rid us of complicated manual, probably error-prone, computations. The approach is based on the knowledge stored in the Mathematica kernel and on additional knowledge (like the Plemelj formulae) provided to the procedure itself. The subsequent use of a numerical algorithm for the solution of the derived complex singular integral equation is also possible.

*Engineering > Mechanical and Structural Engineering