Five-degrees-of-freedom model for static analysis of linear roller bearing subjected to external loading

2018 ◽  
Vol 233 (8) ◽  
pp. 2920-2938 ◽  
Author(s):  
Sun-Woong Kwon ◽  
Van-Canh Tong ◽  
Seong-Wook Hong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Static Analysis ◽  
Degrees Of Freedom ◽  
Roller Bearing ◽  
Hertzian Contact ◽  
External Loading ◽  
Contact Loads ◽  
Commercial Program ◽  
Element Method

This paper presents a novel five degrees-of-freedom model for the static analysis of linear roller bearings subjected to external loading. In this study, first, a rigid analytical model was developed to obtain the roller contact loads and displacements of carriage caused by the elastic deformation at the roller–carriage and roller–rail contacts. The non-Hertzian contact loads between the rollers and raceways were utilized to consider the profiled roller and/or profiled guide rail. Next, the structural deformations of the carriage owing to the contact loads were computed using the finite element method. The associated displacements of the carriage top were derived systematically. Then, the total displacements of the carriage top were obtained by summing the displacements estimated from the rigid model and the induced structural displacements obtained by finite element method. The proposed model was validated by comparing the calculated displacements of the carriage with those from a commercial program under various loading conditions. Further investigation regarding the effect of preload on displacements of the linear roller bearing was conducted. The simulation results showed the dependence of carriage rigidity and internal load distribution on the linear roller bearing characteristics.

scholarly journals Fractal Two-Level Finite Element Method For Free Vibration of Cracked Beams

1998 ◽  
Vol 5 (1) ◽  
pp. 61-68 ◽  
Author(s):  
A.Y.T. Leung ◽  
R.K.L. Su
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Degrees Of Freedom ◽  
Mode Shapes ◽  
Generalized Displacements ◽  
Commercial Program ◽  
Small Set ◽  
Element Method ◽  
Cracked Beams

The fractal two-level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial program.

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 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.

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
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