A sub‒domain smoothed Galerkin method for solid mechanics problems |
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Authors: | Dean Hu Yigang Wang G. R. Liu Tong Li Xu Han Y. T. Gu |
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Affiliation: | 1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, , Changsha 410082, China;2. School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, , GPO Box 2434, Brisbane, QLD 4001, Australia;3. School of Aerospace Systems, University of Cincinnati, , 2851 Woodside Dr, Cincinnati, OH 45221, USA |
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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. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | galerkin method mesh‒ free method FEM MK interpolation strain smoothing technique condensation of DOF |
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