A sub‒domain smoothed Galerkin method for solid mechanics problems

Hu, Dean, Wang, Yigang, Liu, Gui-Rong, Li, Tong, Han, Xu, & Gu, YuanTong (2014) A sub‒domain smoothed Galerkin method for solid mechanics problems. International Journal for Numerical Methods in Engineering, 98(11), pp. 781-798.

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Abstract

A sub‒domain smoothed Galerkin method is proposed to integrate the advantages of mesh‒free Galerkin method and FEM. Arbitrarily shaped sub‒domains are predefined in problems domain with mesh‒free nodes. In each sub‒domain, based on mesh‒free Galerkin weak formulation, the local discrete equation can be obtained by using the moving Kriging interpolation, which is similar to the discretization of the high‒order finite elements. Strain smoothing technique is subsequently applied to the nodal integration of sub‒domain by dividing the sub‒domain into several smoothing cells. Moreover, condensation of DOF can also be introduced into the local discrete equations to improve the computational efficiency. The global governing equations of present method are obtained on the basis of the scheme of FEM by assembling all local discrete equations of the sub‒domains. The mesh‒free properties of Galerkin method are retained in each sub‒domain. Several 2D elastic problems have been solved on the basis of this newly proposed method to validate its computational performance. These numerical examples proved that the newly proposed sub‒domain smoothed Galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency, good accuracy, and convergence.

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ID Code: 70132
Item Type: Journal Article
Refereed: Yes
Additional Information: Article first published online: 19 FEB 2014
Additional URLs:
Keywords: galerkin method, mesh‒free method, FEM, MK interpolation, strain smoothing technique, condensation of DOF
DOI: 10.1002/nme.4650
ISSN: 1097-0207
Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Solid Mechanics (091308)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014 John Wiley & Sons, Ltd.
Copyright Statement: This is the accepted version of the following article: Hu, D., Wang, Y., Liu, G. R., Li, T., Han, X. and Gu, Y. T. (2014), A sub‒domain smoothed Galerkin method for solid mechanics problems. Int. J. Numer. Meth. Engng.. doi: 10.1002/nme.4650, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.4650/abstract
Deposited On: 14 Apr 2014 02:21
Last Modified: 01 Jul 2015 14:01

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