期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 286, 期 -, 页码 87-106出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.12.005
关键词
Meshless methods; Smooth-Particle Hydrodynamics; Collocation methods; Hour-glassing
This paper presents a stabilization scheme which addresses the rank-deficiency problem in meshless collocation methods for solid mechanics. Specifically, Smooth-Particle Hydrodynamics (SPH) in the Total Lagrangian formalism is considered. This method is rank-deficient in the sense that the SPH approximation of the deformation gradient is not unique with respect to the positions of the integration points. The non-uniqueness can result in the formation of zero-energy modes. If undetected, these modes can grow and completely dominate the solution. Here, an algorithm is introduced, which effectively suppresses these modes in a fashion similar to hour-glass control mechanisms in Finite-Element methods. Simulations utilizing this control algorithm exhibit much improved stability, accuracy, and error convergence properties. In contrast to an alternative method which eliminates zero-energy modes, namely the use of additional integration points, the here presented algorithm is easy to implement and computationally very efficient. (C) 2014 Elsevier B.V. All rights reserved.
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