Details
| Original language | English |
|---|---|
| Article number | 106235 |
| Journal | Computers and Structures |
| Volume | 233 |
| Early online date | 14 Mar 2020 |
| Publication status | Published - Jun 2020 |
Abstract
The nonlocal operator method (NOM) is initially proposed as a particle-based method, which has difficulties in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with approximation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed as a special case of NOM with approximation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method. As a consequence, the requirement of the operator energy functional in particle-based NOM is avoided. We demonstrate the capabilities of the proposed method by solving gradient elasticity problems and comparing the numerical results with exact solutions.
Keywords
- Gradient solid, Modified variational principle, Nonlocal operator method, Numerical integration, Peridynamics
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Mathematics(all)
- Modelling and Simulation
- Materials Science(all)
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Computers and Structures, Vol. 233, 106235, 06.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nonlocal operator method with numerical integration for gradient solid
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Rabczuk, Timon
N1 - Funding Information: The first author acknowledges the support from the COMBAT Program ( Computational Modeling and Design of Lithium-ion Batteries , Grant No. 615132 ).
PY - 2020/6
Y1 - 2020/6
N2 - The nonlocal operator method (NOM) is initially proposed as a particle-based method, which has difficulties in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with approximation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed as a special case of NOM with approximation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method. As a consequence, the requirement of the operator energy functional in particle-based NOM is avoided. We demonstrate the capabilities of the proposed method by solving gradient elasticity problems and comparing the numerical results with exact solutions.
AB - The nonlocal operator method (NOM) is initially proposed as a particle-based method, which has difficulties in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with approximation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed as a special case of NOM with approximation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method. As a consequence, the requirement of the operator energy functional in particle-based NOM is avoided. We demonstrate the capabilities of the proposed method by solving gradient elasticity problems and comparing the numerical results with exact solutions.
KW - Gradient solid
KW - Modified variational principle
KW - Nonlocal operator method
KW - Numerical integration
KW - Peridynamics
UR - http://www.scopus.com/inward/record.url?scp=85081666435&partnerID=8YFLogxK
U2 - 10.1016/j.compstruc.2020.106235
DO - 10.1016/j.compstruc.2020.106235
M3 - Article
AN - SCOPUS:85081666435
VL - 233
JO - Computers and Structures
JF - Computers and Structures
SN - 0045-7949
M1 - 106235
ER -