A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh
Xu, Xu, Liu, Gui-Rong , Gu, YuanTong, Zhang, GuiYong , Luo, J .W. , & Peng, J. X. (2010) A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh. Finite Elements in Analysis and Design, 46(10), pp. 862-874.
A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.
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|Item Type:||Journal Article|
|Keywords:||Finite Element Method, Meshfree methods, Point interpolationmethod, Solution bounds, Extended Galerkin|
|Subjects:||Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering|
Past > Schools > School of Engineering Systems
|Copyright Owner:||Copyright 2010 Elsevier|
|Deposited On:||18 Aug 2010 09:36|
|Last Modified:||01 Mar 2012 00:17|
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