Application of MATHEMATICA to the iterative SAN solution of singular integral equations appearing in crack problems
Application of MATHEMATICA to the iterative SAN solution of singular integral equations appearing in crack problems
Date
1992
Authors
Ioakimidis, Nikolaos
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science Publishers
Abstract
The modern computer algebra system MATHEMATICA is applied to the iterative solution of Cauchy-type singular integral equations of the first kind appearing in crack and related problems of plane and antiplane elasticity. This application is made directly without transforming the singular integral equation to a Fredholm integral equation of the second kind. The semi-analytical/numerical (SAN) results by this approach are expressed in appropriate Taylor–Maclaurin series of the parameter used. A related MATHEMATICA package is presented in detail as well as SAN applications to two problems of periodic arrays of cracks in plane isotropic elasticity. The obtained SAN results show the efficiency and convergence of the proposed approach.