An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems

Le, P. and Mai-Duy, N. and Tran-Cong, T. and Baker, G. (2008) An IRBFN cartesian grid method based on displacement-stress formulation for 2D elasticity problems. In: 8th World Congress on Computational Mechanics (WCCM8), 30 Jun-4 Jul 2008, Venice, Italy.

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Abstract

Traditional finite element methods (FEM) and boundary element methods (BEM) have been based on weak-form formulations. Recently, weak-form meshless (meshfree) methods are being developed as an alternative approach. Weak-form methods have the following advantages. a) They have good stability and reasonable accuracy for many problems. b) The traction (derivative or Neumann) boundary conditions can be naturally and conveniently incorporated into the same weak-form equation. However, elements have to be used for the integration of a weak form over the global problem domain and the numerical integration is still computationally expensive for these weak-form methods. On the other hand, collocation methods are based on strong-form governing equations and have been found to possess the following attractive advantages. a) There is no need for numerical integration of the governing equations. b) The implementation is simple. However, the strong-form approach is less stable due to the pointwise nature of error minimisation. Furthermore, strong-form methods such as finite difference and pseudo spectral methods are restricted to regular domains.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Poster)
Refereed: No
Item Status: Live Archive
Additional Information: © International Center for Numerical Methods in Engineering (CIMNE). Includes the 5th European Congress on Computational Methods in Applied Sciences and Engineering.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 22 May 2009 03:06
Last Modified: 18 Nov 2014 04:30
Uncontrolled Keywords: RBF; collocation method; elasticity; cartesian grid; mixed formulation
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/4586

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