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Adaptive Meshless LBIEM for the Analysis of 2D Elasticity Problems

In: Computational Mechanics

Author

Listed:
  • H. B. Chen

    (University of Science and Technology of China, CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics)

  • D. J. Fu

    (University of Science and Technology of China, CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics)

  • P. Q. Zhang

    (University of Science and Technology of China, CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics)

Abstract

Local boundary integral equation method (LBIEM) is a significant meshless method and it can be looked on as the special form of meshless local Petrov-Galerkin (MLPG) method when the test function is derived from the fundamental solution in BEM. LBIEM needs no background meshes for the integration, thus is a so-called truly meshless method, and it has been widely applied to potential problems, elastostatics, elastodynamics, thermoelasticity, plate bending problems, and so on [1]. In the implementation of LBIEM, nodes can be easily moved, added and deleted because the trial functions are based on regularly or arbitrarily distributed nodes without dependence on meshes in the domain while integrations are only along the local boundary of subdomain or over the subdomain for each node, which leads to more convenient and attractive to perform adaptivity analysis. In the current paper, schemes of error estimation and sequent adaptivity procedure based on the LBIEM are both investigated for the two-dimensional (2D) elasticity problems. For the adaptive analysis, because error estimation scheme is the key component when generally the analytical solution is unavailable, we pay more attention to seeking for difference between original numerical solutions and referenced solutions to define reliable a-posteriori error estimators which can induct adaptive procedure effectively. Some schemes, e.g., the post-processing technology with Taylor expansion and moving least square approximation (MLSA) to obtain the referenced solutions [2, 3], are investigated in detail for 2D elasticity problems. The h-type adaptivity procedures are applied to verify the proposed schemes of a-posteriori error estimations.

Suggested Citation

  • H. B. Chen & D. J. Fu & P. Q. Zhang, 2007. "Adaptive Meshless LBIEM for the Analysis of 2D Elasticity Problems," Springer Books, in: Computational Mechanics, pages 351-351, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75999-7_151
    DOI: 10.1007/978-3-540-75999-7_151
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