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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.

Beam and shell elements for thin-walled aluminium structures

Wriggers P., Chavan K.

Foundations of Civil and Environmental Engineering

2006

No. 7

397-412

In this paper, the finite element formulation of a beam and shell clement for numerical modeling of thin-walled aluminum made beam-like structures has been described. Modern thin-walled beam-like members made up of aluminum arc used extensively in the construction industry because of their characteristic features like lightness, rccy c lability, corrosion resistance and, ease of workability. The constitutive behavior of aluminum alloys is different from the structural steel, especially in plastic deformation range. In the case of aluminum alloys, progressive yielding is seen which can not be modeled with normal elasto-plastic material model with isotropic hardening. Having a better constitutive model leads to a more accurate structural behavior in case of extreme loading and failure of the structure and also determination of the load carrying capacity. The Ramberg-Osgood constitutive law is most popularly used to model the elasto-plastic behavior of aluminum material. Here the material model based on Ramberg-Osgood law is implemented in a beam and a shell element, results are compared with the available experimental results illustrating the validity and the application of the formulation in the analysis of aluminum structures.