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# Application of Meshless Local Petrov-Galerkin (MLPG) Method to Three Dimensional Elasto-Plastic Problems Based on Deformation Theory of Plasticity

A. Rezaei Mojdehi1,2, A. Darvizeh3, A. Basti2

Wind Turbines Technology Development Center, Niroo Research Institute, Tehran, Iran
Department of Mechanical engineering, Faculty of Engineering, The University of Guilan, Iran
Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Anzali Branch, Bandar-e Anzali, Iran

Computer Modeling in Engineering & Sciences 2011, 77(1), 1-32. https://doi.org/10.3970/cmes.2011.077.001

## Abstract

In this paper, a meshless method based on the local petrov-galerkin approach is proposed for the three dimensional (3D) elasto-plastic problems. Galerkin weak-form formulation is applied to derive the discrete governing equations. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a unit test function. Nodal points are distributed in the 3D analyzed domain and each node is surrounded by a cubic sub-domain to which a local integral equation is applied. Three dimensional Moving Least-Square (MLS) approximation is used as shape function to approximate the field variable of scattered nodes in the problem domain. Hencky's total deformation theory is used to define effective elastic material parameters, which are treated as spatial field variables and considered as functions of the equilibrium stress state and material properties. These effective material parameters are obtained in an iterative process. Several example problems are presented to illustrate the effectiveness of the numerical approach.

## Keywords

Mojdehi, A. R., Darvizeh, A., Basti, A. (2011). Application of Meshless Local Petrov-Galerkin (MLPG) Method to Three Dimensional Elasto-Plastic Problems Based on Deformation Theory of Plasticity. CMES-Computer Modeling in Engineering & Sciences, 77(1), 1–32.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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