Details
| Original language | English |
|---|---|
| Pages (from-to) | 5047-5068 |
| Number of pages | 22 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 124 |
| Issue number | 22 |
| Publication status | Published - 10 Oct 2023 |
Abstract
In this article, a novel weak-form zonal Petrov–Galerkin free element method is proposed for two- and three-dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong-form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two- and three-dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.
Keywords
- free element method, mesh-free method, weak-form Petrov–Galerkin method
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 124, No. 22, 10.10.2023, p. 5047-5068.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems
AU - Xu, Bing Bing
AU - Gao, Xiao Wei
N1 - Funding Information: The first author of the article thanks the Humboldt Foundation for its support.
PY - 2023/10/10
Y1 - 2023/10/10
N2 - In this article, a novel weak-form zonal Petrov–Galerkin free element method is proposed for two- and three-dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong-form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two- and three-dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.
AB - In this article, a novel weak-form zonal Petrov–Galerkin free element method is proposed for two- and three-dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong-form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two- and three-dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.
KW - free element method
KW - mesh-free method
KW - weak-form Petrov–Galerkin method
UR - http://www.scopus.com/inward/record.url?scp=85166618283&partnerID=8YFLogxK
U2 - 10.1002/nme.7337
DO - 10.1002/nme.7337
M3 - Article
AN - SCOPUS:85166618283
VL - 124
SP - 5047
EP - 5068
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 22
ER -