scholarly journals Quasi-3-D spectral wavelet method for a thermal quench simulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jonas Bundschuh ◽  
Laura A. M. D’Angelo ◽  
Herbert De Gersem
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spectral Method ◽  
Degrees Of Freedom ◽  
Hot Spot ◽  
Longitudinal Direction ◽  
Particle Accelerators ◽  
Wavelet Basis ◽  
Element Simulation ◽  
Element Method

AbstractThe finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.

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.

scholarly journals Adaptive modelling of variably saturated seepage problems

2021 ◽  
Author(s):  
B Ashby ◽  
C Bortolozo ◽  
A Lukyanov ◽  
T Pryer
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Water Flux ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Posteriori Error Estimate ◽  
Adaptive Finite Element ◽  
Element Method

Summary In this article, we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a nonlinear Darcy–Buckingham law with physical constraints on subsurface-atmosphere boundaries. This leads to the formulation of the problem as a variational inequality. The solutions to this problem are investigated using an adaptive finite element method based on a dual-weighted a posteriori error estimate, derived with the aim of reducing error in a specific target quantity. The quantity of interest is chosen as volumetric water flux across the seepage face, and therefore depends on an a priori unknown free boundary. We apply our method to challenging numerical examples as well as specific case studies, from which this research originates, illustrating the major difficulties that arise in practical situations. We summarise extensive numerical results that clearly demonstrate the designed method produces rapid error reduction measured against the number of degrees of freedom.

scholarly journals Analysis of Vertical Stiffness of Air Spring Based on Finite Element Method

2018 ◽  
Vol 153 ◽  
pp. 06006
Author(s):  
Jiatong Ye ◽  
Hua Huang ◽  
Chenchen He ◽  
Guangyuan Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Element Simulation ◽  
Element Model ◽  
Simulation Method ◽  
Bench Test ◽  
Air Spring ◽  
Vertical Stiffness ◽  
Element Simulation ◽  
Element Method

In this paper, a finite element model of membrane air spring in the vehicle is established, and its vertical stiffness characteristics under a certain inflation pressure are analysed. The result of finite element simulation method is compared with the result of the air spring bench test. The accuracy and reliability of the finite element simulation method in nonlinear analysis of air spring system are verified. In addition, according to the finite element method, the influence of the installation of the air spring limit sleeve on its stiffness is verified.

scholarly journals Nonconforming Finite Element Method Applied to the Driven Cavity Problem

2017 ◽  
Vol 21 (4) ◽  
pp. 1012-1038 ◽  
Author(s):  
Roktaek Lim ◽  
Dongwoo Sheen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Nonconforming Finite Element ◽  
Element Space ◽  
Nonconforming Finite Element Method ◽  
Driven Cavity ◽  
Dirichlet Data ◽  
Minimal Modification ◽  
Element Method

AbstractA cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangularmeshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

3-D Transient Magneto-Thermal Field Analysis Using Adaptive Degrees-of-Freedom Finite-Element Method

2020 ◽  
Vol 56 (3) ◽  
pp. 1-4
Author(s):  
Yunpeng Zhang ◽  
Xiaoyu Liu ◽  
Huihuan Wu ◽  
Siu-Lau Ho ◽  
Weinong Fu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Thermal Field ◽  
Field Analysis ◽  
Element Method

Wang Tiling Based Enrichment Functions for Extended Finite Element Method

2017 ◽  
Vol 1144 ◽  
pp. 102-108
Author(s):  
Martin Doškář ◽  
Jan Novák ◽  
Jan Zeman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Diffusion Problem ◽  
Two Dimensions ◽  
Extended Finite Element ◽  
Linear Diffusion ◽  
Wang Tiles ◽  
Element Method

The Extended Finite Element Method (XFEM) enhances the approximation space of the standard Finite Element Method (FEM) with functions reflecting local features in order to yield more accurate results with less degrees of freedom. XFEM performance is, thus, closely related to the quality of enrichment functions. Analogously to our previous works, in which we have employed the concept of Wang tiles to assembly microstructure geometries, in this contribution we use Wang tiles to assemble microstructure-informed enrichment functions. We compare two ways of generating the enrichments: (i) inspired by the first-order numerical homogenization and (ii) based on spectral analysis of the global stiffness matrix for the whole set. The methodology and performance of both approaches are illustrated through a linear diffusion problem in two dimensions

SINGULAR ENRICHMENT FINITE ELEMENT METHOD FOR ELASTODYNAMIC CRACK PROPAGATION

2004 ◽  
Vol 01 (01) ◽  
pp. 1-15 ◽  
Author(s):  
TED BELYTSCHKO ◽  
HAO CHEN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Propagation ◽  
Degrees Of Freedom ◽  
Time Integration ◽  
Integration Scheme ◽  
Dynamic Crack ◽  
Discrete Equations ◽  
Enrichment Technique ◽  
Element Method

An enrichment technique for accurately modeling two dimensional crack propagation within the framework of the finite element method is presented. The technique uses an enriched basis that spans the asymptotic dynamic crack-tip solution. The enrichment functions and their spatial derivatives are able to exactly reproduce the asymptotic displacement field and strain field for a moving crack. The stress intensity factors for Mode I and Mode II are taken as additional degrees of freedom. An explicit time integration scheme is used to solve the resulting discrete equations. Numerical simulations of linear elastodynamic problems are reported to demonstrate the accuracy and potential of the technique.

scholarly journals Feasibility of the Extended Finite Element Method for the Simulation of Composite Bonded Joints

2012 ◽  
Vol 730-732 ◽  
pp. 513-518 ◽  
Author(s):  
Raul D.S.G. Campilho ◽  
Arnaldo M.G. Pinto ◽  
Mariana D. Banea ◽  
Filipe J.P. Chaves ◽  
Lucas F.M. da Silva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Adhesive Bonding ◽  
Epoxy Adhesive ◽  
Pure Mode ◽  
Extended Finite Element ◽  
Damage Law ◽  
Element Method

Adhesive-bonding for the unions in multi-component structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of accurate damage models, to minimize design costs and time to market. Cohesive Zone Models (CZM’s) have been used for fracture prediction in structures. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on traction-separation laws similar to those of CZM’s but it allows the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom. This work proposes and validates a damage law to model crack propagation in a thin layer of a structural epoxy adhesive using the XFEM. The fracture toughness in pure mode I (GIc) and tensile cohesive strength (sn0) were defined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively, which permitted to build the damage law. The XFEM simulations of the DCB tests accurately matched the experimental load-displacement (P-d) curves, which validated the analysis procedure.

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