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A weighted least squares particle‐in‐cell method for solid mechanics

2010; Wiley; Volume: 85; Issue: 13 Linguagem: Inglês

10.1002/nme.3041

1097-0207

P. C. Wallstedt, James E. Guilkey,

Electromagnetic Simulation and Numerical Methods

Abstract A novel meshfree method is proposed that incorporates features of the material point (MPM) and generalized interpolation material point (GIMP) methods and can be used within an existing MPM/GIMP implementation. Weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients. Integration is performed over cells of the background grid and material boundaries are approximated with an implicit surface. The proposed method avoids nearest‐neighbor searches while significantly improving accuracy over MPM and GIMP. Implementation is discussed in detail and several example problems are solved, including one manufactured solution which allows measurement of dynamic, non‐linear, large deformation performance. Advantages and disadvantages of the method are discussed. Copyright © 2010 John Wiley & Sons, Ltd.