Detection of loading/geometrical singularities in isotropic elastic media with the use of Gröbner bases

• Κύριος συγγραφέας: Ioakimidis, Nikolaos
• Άλλοι συγγραφείς: Ιωακειμίδης, Νικόλαος
• Μορφή: Technical Report
• Γλώσσα: English
• Έκδοση: 2018
• Θέματα: Elasticity; Stresses and strains; Compatibility equations; Concentrated forces; Cracks; Detection/location of singularities; Loading/geometrical singularities; Elimination algorithms; Gröbner bases; Buchberger's algorithm; Computer algebra; Ελαστικότητα; Τάσεις και παραμορφώσεις; Εξισώσεις συμβιβαστού; Συγκεντρωμένες δυνάμεις; Ρωγμές; Ανίχνευση/εύρεση της θέσεως ιδιομορφιών; Ιδιομορφίες στη φόρτιση/γεωμετρία; Αλγόριθμοι απαλοιφής; Βάσεις Gröbner; Αλγόριθμος του Buchberger; Υπολογιστική άλγεβρα

The method of Gröbner bases in computer algebra is applied to the detection and location of loading or geometrical singularities inside two- or three-dimensional isotropic elastic media. The approach consists in using available experimental data concerning the stress/strain components away from the singularity in order to decide whether these components verify the relations corresponding to the particular singularity or not. These conditions can frequently be obtained by the method of Gröbner bases and the related Buchberger algorithm. In the case of an affirmative conclusion, we can further proceed to the location of the singularity. Alternatively, the present approach yields compatibility equations for the stress/strain components in elastic media with loading/geometrical singularities. These equations are displayed in detail for some common stress fields corresponding to concentrated forces as well as to a crack tip.