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|Title:||A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh|
Finite element method
Point interpolation method
|Source:||Xu, X.,Liu, G.R.,Gu, Y.T.,Zhang, G.Y.,Luo, J.W.,Peng, J.X. (2010-10). 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) : 862-874. ScholarBank@NUS Repository. https://doi.org/10.1016/j.finel.2010.05.005|
|Abstract:||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. © 2010 Elsevier B.V.|
|Source Title:||Finite Elements in Analysis and Design|
|Appears in Collections:||Staff Publications|
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