Symbolic computations for the approximate solution of singular integral equations: application to a crack problem

• Main Author: Ioakimidis, Nikolaos
• Other Authors: Ιωακειμίδης, Νικόλαος
• Format: Technical Report
• Language: English
• Published: 2018
• Subjects: Boundary integral equations; Computer algebra; Symbolic computations; Semi-analytical–numerical computations; Singular integral equations; Gauss–Chebyshev method; Natural interpolation/extrapolation; Plane elasticity; Isotropic elasticity; Fracture mechanics; Cracks; Periodic array of collinear cracks; Συνοριακές ολοκληρωτικές εξισώσεις; Υπολογιστική άλγεβρα; Συμβολικοί υπολογισμοί; Ημιαναλυτικοί–αριθμητικοί υπολογισμοί; Ιδιόμορφες ολοκληρωτικές εξισώσεις; Μέθοδος των Gauss–Chebyshev; Φυσική παρεμβολή/προεκβολή; Επίπεδη ελαστικότητα; Ισότροπη ελαστικότητα; Θραυστομηχανική; Ρωγμές; Περιοδική διάταξη συγγραμμικών ρωγμών

We propose the application of symbolic SAN (semi-analytical–numerical) computations to the numerical solution of SIEs (singular integral equations), which are the BIEs (boundary integral equations) for crack problems in plane and antiplane, isotropic and anisotropic elasticity. The case of a periodic array of collinear cracks (with a variable distance of the cracks) together with the modified Gauss–Chebyshev method (also based on the natural interpolation/extrapolation formula) for the numerical solution of SIEs are used for the illustration of the proposed approach. The obtained SAN results are seen to be very good approximations of the analytical exact results even for a very small number of nodes in the modified Gauss–Chebyshev method. The computer algebra system Derive has been used for the derivation of the present SAN results.