Details
| Original language | English |
|---|---|
| Pages (from-to) | 23-44 |
| Number of pages | 22 |
| Journal | Engineering with computers |
| Volume | 39 |
| Issue number | 1 |
| Early online date | 15 Sept 2021 |
| Publication status | Published - Feb 2023 |
Abstract
The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.
Keywords
- Dual-support, Energy form, Explicit time integration, Fracture, Peridynamics, Variational principle, Weak form
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Computer Science(all)
- Computer Science Applications
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In: Engineering with computers, Vol. 39, No. 1, 02.2023, p. 23-44.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Oterkus, Erkan
AU - Zhu, Hehua
AU - Rabczuk, Timon
PY - 2023/2
Y1 - 2023/2
N2 - The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.
AB - The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.
KW - Dual-support
KW - Energy form
KW - Explicit time integration
KW - Fracture
KW - Peridynamics
KW - Variational principle
KW - Weak form
UR - http://www.scopus.com/inward/record.url?scp=85114950986&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2103.08696
DO - 10.48550/arXiv.2103.08696
M3 - Article
AN - SCOPUS:85114950986
VL - 39
SP - 23
EP - 44
JO - Engineering with computers
JF - Engineering with computers
SN - 0177-0667
IS - 1
ER -