Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods

For both linear and nonlinear analysis, finite element method (FEM) software packages, whether commercial or in-house, have contributed significantly to ease the analysis of simple and complex structures with various working conditions. However, the literature offers other discretization techniques...

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Bibliographic Details
Published in:Applied sciences 2022-12, Vol.12 (24), p.12842
Main Authors: Belinha, Jorge, Aires, Miguel
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Benchmarks
Boundary conditions
Connectivity
Elastoplasticity
Elastostatics
Fractures
Interpolation
Linear analysis
Mechanics
Meshless methods
Methods
Newton-Raphson method
Nonlinear analysis
plates
radial point interpolation method
Variables
Working conditions
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Summary:For both linear and nonlinear analysis, finite element method (FEM) software packages, whether commercial or in-house, have contributed significantly to ease the analysis of simple and complex structures with various working conditions. However, the literature offers other discretization techniques equally accurate, which show a higher meshing flexibility, such as meshless methods. Thus, in this work, the radial point interpolation meshless method (RPIM) is used to obtain the required variable fields for a nonlinear elastostatic analysis. This work focuses its attention on the nonlinear analysis of two benchmark plate-bending problems. The plate is analysed as a 3D solid and, in order to obtain the nonlinear solution, modified versions of the Newton–Raphson method are revisited and applied. The material elastoplastic behaviour is predicted assuming the von Mises yield surface and isotropic hardening. The nonlinear algorithm is discussed in detail. The analysis of the two benchmark plate examples allows us to understand that the RPIM version explored is accurate and allows to achieve smooth variable fields, being a solid alternative to FEM.
ISSN:2076-3417
2076-3417
DOI:10.3390/app122412842