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Dual-support smoothed particle hydrodynamics in solid: variational principle and implicit formulation

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Huilong Ren
  • Xiaoying Zhuang
  • Timon Rabczuk
  • He Hua Zhu

External Research Organisations

  • Bauhaus-Universität Weimar
  • Tongji University
  • Ton Duc Thang University

Details

Original languageEnglish
Pages (from-to)15-29
Number of pages15
JournalEngineering Analysis with Boundary Elements
Volume108
Early online date30 Aug 2019
Publication statusPublished - Nov 2019
Externally publishedYes

Abstract

We derive the dual-support smoothed particle hydrodynamics (DS-SPH) in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We propose an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is involved in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method.

Keywords

    Geometric nonlinearity, Hourglass energy, Implicit formulation, Smoothed particle hydrodynamics (SPH), Stiffness matrix, Variational principle, Zero-energy mode

ASJC Scopus subject areas

Cite this

Dual-support smoothed particle hydrodynamics in solid: variational principle and implicit formulation. / Ren, Huilong; Zhuang, Xiaoying; Rabczuk, Timon et al.
In: Engineering Analysis with Boundary Elements, Vol. 108, 11.2019, p. 15-29.

Research output: Contribution to journalArticleResearchpeer review

Ren H, Zhuang X, Rabczuk T, Zhu HH. Dual-support smoothed particle hydrodynamics in solid: variational principle and implicit formulation. Engineering Analysis with Boundary Elements. 2019 Nov;108:15-29. Epub 2019 Aug 30. doi: 10.1016/j.enganabound.2019.05.024
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AU - Ren, Huilong

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AU - Zhu, He Hua

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