A linearly conforming point interpolation method (LC-PIM) for perfect Visco-Elastoplastic analysis of 2D solids

Bui Xuan Thang, Nguyen Thoi Trung, Nguyen Xuan Hung and Phung Van Phuc ()
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Bui Xuan Thang: Department of Mechanics, Faculty of Mathematics & Computer Science, University of Science, Vietnam National University – HCMC, Vietnam
Nguyen Thoi Trung: Division of Computational Mechanics, Ton Duc Thang University, Vietnam
Nguyen Xuan Hung: Division of Computational Mechanics, Ton Duc Thang University, Vietnam
Phung Van Phuc: Division of Computational Mechanics, Ton Duc Thang University, Vietnam

HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE - ENGINEERING AND TECHNOLOGY, 2013, vol. 3, issue 1, 11-23

Abstract: A linearly conforming point interpolation method (LC-PIM) was recently proposed for the solid mechanics problems. In this paper, the LC-PIM is further extended to perfect visco-elastoplastic analyses of 2D solids. A dual formulation for the LC-PIM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl-Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacementdependent. The numerical results show that the LC-PIM is much more accurate than the FEM and possesses the upper bound property which is very meaningful for the viscoelastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, LC-PIM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

Keywords: Numerical methods; mesh-free methods; linearly conforming point interpolation method (LC-PIM); upper bound; visco-elastoplastic analyses. (search for similar items in EconPapers)
Date: 2013
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