On the numerical integration in generalized/extended finite element method analysis for crack propagation problems
Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the co...
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| Vydáno v: | Engineering computations Ročník 38; číslo 1; s. 180 - 220 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Bradford
Emerald Publishing Limited
27.01.2021
Emerald Group Publishing Limited |
| Témata: | |
| ISSN: | 0264-4401, 1758-7077 |
| On-line přístup: | Získat plný text |
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| Abstract | Purpose
The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.
Design/methodology/approach
Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.
Findings
Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.
Originality/value
This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies. |
|---|---|
| AbstractList | Purpose
The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.
Design/methodology/approach
Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.
Findings
Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.
Originality/value
This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies. PurposeThe purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.Design/methodology/approachNumerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.FindingsKnown numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.Originality/valueThis study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies. |
| Author | Barros, Felício Bruzzi Penna, Samuel Silva Campos, Bruna Caroline |
| Author_xml | – sequence: 1 givenname: Bruna Caroline surname: Campos fullname: Campos, Bruna Caroline email: bu_caroline@hotmail.com – sequence: 2 givenname: Felício Bruzzi surname: Barros fullname: Barros, Felício Bruzzi email: feliciobbarros@gmail.com – sequence: 3 givenname: Samuel Silva surname: Penna fullname: Penna, Samuel Silva email: spenna@dees.ufmg.br |
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| Keywords | Computational mechanics Fracture mechanics Numerical integration Generalized/extended finite element method Partition of unity methods |
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The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve... PurposeThe purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve... |
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| SubjectTerms | Approximation Crack propagation Finite element analysis Finite element method Fracture mechanics Integrals Linear elastic fracture mechanics Methods Numerical integration Parameters Propagation Quadratures Stress intensity factors |
| Title | On the numerical integration in generalized/extended finite element method analysis for crack propagation problems |
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