Vol. 11, No. 1, 2016

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ISSN: 1559-3959
A study of elastic-plastic deformation in the plate with the incremental theory and the meshless methods

Malgorzata A. Jankowska and Jan Adam Kołodziej

Vol. 11 (2016), No. 1, 41–60
Abstract

The paper concerns an application of the successive-approximation iteration process together with the meshless methods, i.e., the method of fundamental solutions (MFS) and the method of particular solutions (MPS), for the analysis of strains and stresses in the plate with some kind of narrowing subjected to uniaxial tension. The elastoplastic boundary-value problem is based on the incremental theory of plasticity with the stress-strain relation given in the form proposed by Chakrabarty. In the iteration procedure a sequence of the successive distributions of the plastic strain increments corresponding to the appropriate increments of load is produced. A final set of the plastic strain increments is further used to obtain the total plastic strains. Furthermore, the solution of the elastoplastic boundary-value problem can be simultaneously taken into account when the stress state of the plate is required. Such approach is designated here to identify the regions of elastic and plastic behavior of the material.

Keywords
meshless methods, method of fundamental solutions, successive-approximation iteration process, elastic-plastic deformation, incremental theory
Milestones
Received: 2 January 2015
Revised: 29 July 2015
Accepted: 17 August 2015
Published: 13 January 2016
Authors
Malgorzata A. Jankowska
Institute of Applied Mechanics
Poznan University of Technology
Jana Pawla II 24
60-965 Poznan
Poland
Jan Adam Kołodziej
Institute of Applied Mechanics
Poznan University of Technology
Jana Pawła II 24
60-965 Poznan
Poland