Application of Mathematica to the Rayleigh–Ritz method for plane elasticity problems

• Κύριος συγγραφέας: Ioakimidis, Nikolaos
• Άλλοι συγγραφείς: Ιωακειμίδης, Νικόλαος
• Μορφή: Technical Report
• Γλώσσα: English
• Έκδοση: 2018
• Θέματα: Rayleigh–Ritz method; Plane elasticity; Isotropic elasticity; Biharmonic equation; Airy stress function; Symbolic computations; Numerical computations; Approximate solutions; Computer algebra; Mathematica; Μέθοδος των Rayleigh–Ritz; Επίπεδη ελαστικότητα; Ισότροπη ελαστικότητα; Διαρμονική εξίσωση; Τασική συνάρτηση του Airy; Συμβολικοί υπολογισμοί; Αριθμητικοί υπολογισμοί; Προσεγγιστικές λύσεις; Υπολογιστική άλγεβρα

The classical Rayleigh–Ritz method for plane isotropic elasticity problems governed by the well-known biharmonic equation (satisfied by the Airy stress function) is revisited. The modern and powerful computer algebra system Mathematica was employed for the symbolic/numerical approximate solution of the biharmonic equation. A related simple procedure was prepared and the classical problem of a rectangular elastic region loaded by a parabolic tensile loading was chosen as an example of the application of the approach. The available symbolic/numerical results in the literature and additional more complicated analogous results were directly derived by using the aforementioned procedure. Further related possibilities and generalizations are also discussed in brief.