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Elastic-plastic torsion problem with non-linear hardenings using the method of fundamental solution

Moayyedian Farzad, Grabski Jakub Krzysztof

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 4

334--354

In the current research, a torsion of isotropic prismatic rods with elastic–plastic behavior under non-linear hardening behavior, such as Swift, Voce, and Ramberg-Osgood relations, is investigated with the method of fundamental solutions. Based on the Saint-Venant displacement assumption and deformation theory of plasticity for the stress-strain relation, the non-linear boundary value problem for the stress function is formulated. The purpose of the current research is study the elastic–plastic torsion problem with non-linear hardenings in a new simple form and solving the presented equations with the method of fundamental solutions and radial basis functions. The non-linear torsion problem is solved by means of the Picard iteration method. The proposed algorithm is based on solution of the linear Poisson equation at each iteration step.