scholarly journals Parameterized Extended Finite Element Method for high thermal gradients

2017 ◽  
Vol 5 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Christian Zeller ◽  
Binu Surendran ◽  
Micheal F. Zaeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element ◽  
Extended Finite Element Method ◽  
Thermal Gradients ◽  
Extended Finite Element ◽  
Time Step ◽  
High Gradients ◽  
Parameterized Problem ◽  
Element Method

Abstract The Finite Element Method results in inaccuracies for temperature changes at the boundary if the mesh is too coarse in comparison with the applied time step. Oscillations occur as the adjacent elements balance the excessive energy of the boundary element. An Extended Finite Element Method (XFEM) with extrinsic enrichment of the boundary element by a parameterized problem-specific ansatz function is presented. The method is able to represent high thermal gradients at the boundary with a coarse mesh as the enrichment function compensates for the excessive energy at the element affected by the temperature change. The parameterization covers the temporal change of the gradient and avoids the enrichment by further ansatz functions. The introduced parameterization variable is handed over to the system of equations as an additional degree of freedom. Analytical integration is used for the evaluation of the integrals in the weak formulation as the ansatz function depends non-linearly on the parameterization variable. Highlights Parameterized problem-specific ansatz functions. Avoidance of a fine mesh in the area of high gradients. Representation of high gradients with one additional DOF.

scholarly journals Propagation of a Crack in a Composite Plate

2018 ◽  
Vol 55 (2) ◽  
pp. 179-183
Author(s):  
Ionel Iacob ◽  
Ionel Chirica ◽  
Elena Felicia Beznea
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Composite Plate ◽  
Extended Finite Element Method ◽  
Fem Analysis ◽  
The Finite Element Method ◽  
Extended Finite Element ◽  
Time Step ◽  
Element Method

In this paper, a model of a composite plate with a central elliptical cut-out and with an initial fissure was subjected to a tension load in the finite element method (FEM) software Abaqus to observe the propagation of that crack during a certain amount of time that elapsed in the FEM analysis. Due to symmetry, only half of the plate was modeled, as a shell, and the extended finite element method (XFEM) was used for the crack. The material properties that were assigned to the plate were taken from the database of the Ansys Mechanical software. In the vicinity of the crack a finer mesh was applied to be able to better observe the evolution of the fissure and the changes of the Von Misses stress graphs for each time step of the analysis.

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.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

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