Details
| Original language | English |
|---|---|
| Pages (from-to) | 3491-3507 |
| Number of pages | 17 |
| Journal | Engineering with computers |
| Volume | 39 |
| Issue number | 5 |
| Early online date | 7 Dec 2022 |
| Publication status | Published - Oct 2023 |
Abstract
In this paper, the weak form of bond-associated peridynamic differential operator is proposed to solve differential equations. The presented method inherits the advantages of the original peridynamic differential operator and enables directly and efficiently to determine the nonlocal weak form for local differential equations and obtain the corresponding symmetrical tangent stiffness matrix in the smaller size using variational principles. The concept of bond-associated family is introduced to suppress the numerical oscillation and zero-energy modes in this study. Several typical elasticity problems, taken as examples, are presented to show the application and capabilities of this method. The accuracy, convergence, and stability of the proposed method are demonstrated by seven numerical examples including linear and nonlinear, steady and transient state problems, and eigenvalue problems in 1D, 2D, and 3D cases.
Keywords
- Bond-associated, Peridynamic differential operator, Variational principles, Zero-energy mode
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. 5, 10.2023, p. 3491-3507.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Weak form of bond-associated peridynamic differential operator for solving differential equations
AU - Li, Zhiyuan
AU - Huang, Dan
AU - Ren, Huilong
AU - Rabczuk, Timon
N1 - Funding Information: The authors acknowledge the supports from the National Natural Science Foundation of China [No. 12072104, 51679077] and the Fundamental Research Funds for the Central Universities in China [No. B210203025], and the China Scholarship Council [No. 202006710119].
PY - 2023/10
Y1 - 2023/10
N2 - In this paper, the weak form of bond-associated peridynamic differential operator is proposed to solve differential equations. The presented method inherits the advantages of the original peridynamic differential operator and enables directly and efficiently to determine the nonlocal weak form for local differential equations and obtain the corresponding symmetrical tangent stiffness matrix in the smaller size using variational principles. The concept of bond-associated family is introduced to suppress the numerical oscillation and zero-energy modes in this study. Several typical elasticity problems, taken as examples, are presented to show the application and capabilities of this method. The accuracy, convergence, and stability of the proposed method are demonstrated by seven numerical examples including linear and nonlinear, steady and transient state problems, and eigenvalue problems in 1D, 2D, and 3D cases.
AB - In this paper, the weak form of bond-associated peridynamic differential operator is proposed to solve differential equations. The presented method inherits the advantages of the original peridynamic differential operator and enables directly and efficiently to determine the nonlocal weak form for local differential equations and obtain the corresponding symmetrical tangent stiffness matrix in the smaller size using variational principles. The concept of bond-associated family is introduced to suppress the numerical oscillation and zero-energy modes in this study. Several typical elasticity problems, taken as examples, are presented to show the application and capabilities of this method. The accuracy, convergence, and stability of the proposed method are demonstrated by seven numerical examples including linear and nonlinear, steady and transient state problems, and eigenvalue problems in 1D, 2D, and 3D cases.
KW - Bond-associated
KW - Peridynamic differential operator
KW - Variational principles
KW - Zero-energy mode
UR - http://www.scopus.com/inward/record.url?scp=85143403348&partnerID=8YFLogxK
U2 - 10.1007/s00366-022-01763-x
DO - 10.1007/s00366-022-01763-x
M3 - Article
AN - SCOPUS:85143403348
VL - 39
SP - 3491
EP - 3507
JO - Engineering with computers
JF - Engineering with computers
SN - 0177-0667
IS - 5
ER -