Details
| Original language | English |
|---|---|
| Pages (from-to) | 723–743 |
| Number of pages | 21 |
| Journal | Computational mechanics |
| Volume | 70 |
| Issue number | 4 |
| Early online date | 12 Jul 2022 |
| Publication status | Published - Oct 2022 |
Abstract
This work presents a meshfree particle scheme designed for arbitrary deformations that possess the accuracy and properties of the Finite-Element-Method. The accuracy is maintained even with arbitrary particle distributions. Mesh-based methods mostly fail if requirements on the location of evaluation points are not satisfied. Hence, with this new scheme not only the range of loadings can be increased but also the pre-processing step can be facilitated compared to the FEM. The key to this new meshfree method lies in the fulfillment of essential requirements for spatial discretization schemes. The new approach is based on the correspondence theory of Peridynamics. Some modifications of this framework allows for a consistent and stable formulation. By applying the peridynamic differentiation concept, it is also shown that the equations of the correspondence theory can be derived from the weak form. Likewise, it is demonstrated that special moving least square shape functions possess the Kronecker-δ property. Thus, Dirichlet boundary conditions can be directly applied. The positive performance of this new meshfree method, especially in comparison to the Finite-Element-Method, is shown in the calculation of several test cases. In order to guarantee a fair comparison enhanced finite element formulations are also used. The test cases include the patch test, an eigenmode analysis as well as the investigation of loadings in the context of large deformations.
Keywords
- Correspondence theory, Method of least squares, Peridynamics, Requirements on spacial discretization schemes, Weak form
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 70, No. 4, 10.2022, p. 723–743.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Peridynamic Galerkin method
T2 - an attractive alternative to finite elements
AU - Bode, T.
AU - Weißenfels, C.
AU - Wriggers, P.
N1 - Funding Information: This project was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453)
PY - 2022/10
Y1 - 2022/10
N2 - This work presents a meshfree particle scheme designed for arbitrary deformations that possess the accuracy and properties of the Finite-Element-Method. The accuracy is maintained even with arbitrary particle distributions. Mesh-based methods mostly fail if requirements on the location of evaluation points are not satisfied. Hence, with this new scheme not only the range of loadings can be increased but also the pre-processing step can be facilitated compared to the FEM. The key to this new meshfree method lies in the fulfillment of essential requirements for spatial discretization schemes. The new approach is based on the correspondence theory of Peridynamics. Some modifications of this framework allows for a consistent and stable formulation. By applying the peridynamic differentiation concept, it is also shown that the equations of the correspondence theory can be derived from the weak form. Likewise, it is demonstrated that special moving least square shape functions possess the Kronecker-δ property. Thus, Dirichlet boundary conditions can be directly applied. The positive performance of this new meshfree method, especially in comparison to the Finite-Element-Method, is shown in the calculation of several test cases. In order to guarantee a fair comparison enhanced finite element formulations are also used. The test cases include the patch test, an eigenmode analysis as well as the investigation of loadings in the context of large deformations.
AB - This work presents a meshfree particle scheme designed for arbitrary deformations that possess the accuracy and properties of the Finite-Element-Method. The accuracy is maintained even with arbitrary particle distributions. Mesh-based methods mostly fail if requirements on the location of evaluation points are not satisfied. Hence, with this new scheme not only the range of loadings can be increased but also the pre-processing step can be facilitated compared to the FEM. The key to this new meshfree method lies in the fulfillment of essential requirements for spatial discretization schemes. The new approach is based on the correspondence theory of Peridynamics. Some modifications of this framework allows for a consistent and stable formulation. By applying the peridynamic differentiation concept, it is also shown that the equations of the correspondence theory can be derived from the weak form. Likewise, it is demonstrated that special moving least square shape functions possess the Kronecker-δ property. Thus, Dirichlet boundary conditions can be directly applied. The positive performance of this new meshfree method, especially in comparison to the Finite-Element-Method, is shown in the calculation of several test cases. In order to guarantee a fair comparison enhanced finite element formulations are also used. The test cases include the patch test, an eigenmode analysis as well as the investigation of loadings in the context of large deformations.
KW - Correspondence theory
KW - Method of least squares
KW - Peridynamics
KW - Requirements on spacial discretization schemes
KW - Weak form
UR - http://www.scopus.com/inward/record.url?scp=85134326123&partnerID=8YFLogxK
U2 - 10.1007/s00466-022-02202-w
DO - 10.1007/s00466-022-02202-w
M3 - Article
AN - SCOPUS:85134326123
VL - 70
SP - 723
EP - 743
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 4
ER -