Numerical Integration Technique in Computation of Extended Finite Element Method

2012 ◽  
Vol 446-449 ◽  
pp. 3557-3560 ◽  
Author(s):  
Feng Wang ◽  
Di Zhang ◽  
Jing Yu ◽  
Hui Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Displacement Mode ◽  
Integration Techniques ◽  
Discontinuous Medium ◽  
Control Equation ◽  
Element Method

The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and reserves all merits of CFEM. In other side, it needs not mesh repartition to geometric and physical interface. Numerical integration techniques of the XFEM computation are studied, including displacement mode of the XFEM, control equation and infirm solution form of discontinuous medium mechanics problem, region scatteration, element integral strategy.

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

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.

Study of Crack Growth Based on Extended Finite Element Method

2012 ◽  
Vol 446-449 ◽  
pp. 3639-3642
Author(s):  
Hui Xu ◽  
Feng Wang ◽  
Di Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Growth ◽  
Extended Finite Element Method ◽  
Homogeneous Medium ◽  
Dynamic Crack ◽  
Extended Finite Element ◽  
Crack Penetration ◽  
Displacement Mode ◽  
Element Method

A special method based on the extended finite element method is developed for the simulation of dynamic crack growth. It shows great advantages in the simulations of moving crack and mixed mode crack. The extended finite element method for two-dimensional crack is described in this paper. The crack form of the extended finite element in the homogeneous medium is studied in detail, and the internal detail in crack tip element and crack penetration element is analyzed. At last, the displacement mode is generated.

Research of the Penetration Process for Concrete Target Based on the Extended Finite Element Method

2014 ◽  
Vol 644-650 ◽  
pp. 429-432
Author(s):  
Ke Bin Yan ◽  
Zheng Xiang Huang ◽  
Rong Zhong Liu ◽  
Feng Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Criterion ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Concrete Material ◽  
Penetration Process ◽  
Displacement Mode ◽  
Concrete Target ◽  
Element Method

The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and needs not mesh repartition to geometric and physical interface, so it reserves all merits of the conventional finite element method (CFEM). The XFEM was applied to the penetration process for concrete target in the paper, and the displacement mode of elements with cracks and fracture criterion were presented. Then the weak solutions of control equations were discretized in different areas. The numerical examples for steel rod penetrating in the concrete target concluded that the method and program were reasonable and effective. The effect discipline of crack growth to the concrete material penetration process was summarized, and it would establish theoretic base for the further application of the XFEM.

scholarly journals A mesh-independent framework for crack tracking in elastodamaging materials through the regularized extended finite element method

2021 ◽  
Author(s):  
Elena Benvenuti ◽  
Nicola Orlando
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Damage Evolution ◽  
Extended Finite Element Method ◽  
Mesh Adaptivity ◽  
Extended Finite Element ◽  
Evolution Law ◽  
Crack Paths ◽  
Original Crack ◽  
Element Method

AbstractWe propose a formulation for tracking general crack paths in elastodamaging materials without mesh adaptivity and broadening of the damage band. The idea is to treat in a unified way both the damaging process and the development of displacement discontinuities by means of the regularized finite element method. With respect to previous authors’ contributions, a novel damage evolution law and an original crack tracking framework are proposed. We face the issue of mesh objectivity through several two-dimensional tests, obtaining smooth crack paths and reliable structural results.

scholarly journals An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 507
Author(s):  
K. Yakoubi ◽  
S. Montassir ◽  
Hassane Moustabchir ◽  
A. Elkhalfi ◽  
Catalin Iulian Pruncu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Extended Finite Element Method ◽  
Research Study ◽  
Extended Finite Element ◽  
T Stress ◽  
Cracked Structures ◽  
Element Method

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

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