Details
Original language | English |
---|---|
Pages (from-to) | 15-29 |
Number of pages | 15 |
Journal | Engineering Analysis with Boundary Elements |
Volume | 108 |
Early online date | 30 Aug 2019 |
Publication status | Published - Nov 2019 |
Externally published | Yes |
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
- Mathematics(all)
- Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Engineering Analysis with Boundary Elements, Vol. 108, 11.2019, p. 15-29.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Dual-support smoothed particle hydrodynamics in solid
T2 - variational principle and implicit formulation
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Rabczuk, Timon
AU - Zhu, He Hua
N1 - Funding information: The authors acknowledge the supports from the RISE-BESTOFRAC, COMBAT Program (Computational Modeling and Design of Lithium-ion Batteries, Grant No. 615132 ).
PY - 2019/11
Y1 - 2019/11
N2 - 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.
AB - 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.
KW - Geometric nonlinearity
KW - Hourglass energy
KW - Implicit formulation
KW - Smoothed particle hydrodynamics (SPH)
KW - Stiffness matrix
KW - Variational principle
KW - Zero-energy mode
UR - http://www.scopus.com/inward/record.url?scp=85071571188&partnerID=8YFLogxK
U2 - 10.1016/j.enganabound.2019.05.024
DO - 10.1016/j.enganabound.2019.05.024
M3 - Article
AN - SCOPUS:85071571188
VL - 108
SP - 15
EP - 29
JO - Engineering Analysis with Boundary Elements
JF - Engineering Analysis with Boundary Elements
SN - 0955-7997
ER -