Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 43, Issue 3-5, Pages 329-350Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0898-1221(01)00290-5
Keywords
particle methods; stability; kernel
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The stability of discretizations by particle methods with corrected derivatives is analyzed. It is shown that the standard particle method (which is equivalent to the element-free Galerkin method with an Eulerian kernel and nodal quadrature) has two sources of instability: (1) rank deficiency of the discrete equations, and (2) distortion of the material instability. The latter leads to the so-called tensile instability. It is shown that a Lagrangian kernel with the addition of stress points eliminates both instabilities. Examples that verify the stability of the new formulation are given. (C) 2002 Elsevier Science Ltd. All rights reserved.
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