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Chin. Phys. B, 2015, Vol. 24(3): 030204    DOI: 10.1088/1674-1056/24/3/030204
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Hybrid natural element method for large deformation elastoplasticity problems

Ma Yong-Qia b, Zhou Yan-Kaia
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mechanics, Shanghai University, Shanghai 200444, China
Abstract  

We present the hybrid natural element method (HNEM) for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger-Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system. Compared with the natural element method (NEM), the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.

Keywords:  hybrid natural element method      large deformation elastoplasticity      Hellinger-Reissner variational principle      meshless method  
Received:  05 October 2014      Revised:  21 October 2014      Published:  05 March 2015
PACS:  02.60.Cb (Numerical simulation; solution of equations)  
  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  46.15.-x (Computational methods in continuum mechanics)  
Fund: 

Project supported by the Natural Science Foundation of Shanghai, China (Grant No. 13ZR1415900).

Corresponding Authors:  Ma Yong-Qi     E-mail:  mayq@staff.shu.edu.cn

Cite this article: 

Ma Yong-Qi, Zhou Yan-Kai Hybrid natural element method for large deformation elastoplasticity problems 2015 Chin. Phys. B 24 030204

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