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A weighted least squares particle‐in‐cell method for solid mechanics
Author(s) -
Wallstedt P. C.,
Guilkey J. E.
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3041
Subject(s) - moving least squares , kernel (algebra) , interpolation (computer graphics) , grid , computer science , material point method , meshfree methods , point (geometry) , least squares function approximation , grid method multiplication , algorithm , field (mathematics) , mathematics , mathematical optimization , computational science , geometry , artificial intelligence , engineering , structural engineering , finite element method , motion (physics) , statistics , combinatorics , estimator , pure mathematics
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.