Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 15-29 |
| Seitenumfang | 15 |
| Fachzeitschrift | Engineering Analysis with Boundary Elements |
| Jahrgang | 108 |
| Frühes Online-Datum | 30 Aug. 2019 |
| Publikationsstatus | Veröffentlicht - Nov. 2019 |
| Extern publiziert | Ja |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Ingenieurwesen (insg.)
- Allgemeiner Maschinenbau
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Engineering Analysis with Boundary Elements, Jahrgang 108, 11.2019, S. 15-29.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -