scholarly journals Generalities on finite element discretization for fractional pressure diffusion equation in the fractal continuum

2019 ◽  
Vol 65 (3) ◽  
pp. 251
Author(s):  
H. D. Sánchez Chávez ◽  
C. A. López-Ortiz ◽  
And L. Flores-Cano
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Differential Operators ◽  
Analytic Solution ◽  
Three Dimensional ◽  
The Novel ◽  
The Finite Element Method ◽  
Element Discretization ◽  
Pressure Diffusion ◽  
Interpolation Functions

In this study we explore the application of the novel fractional calculus in fractal continuum (FCFC), together with the finite element method (FEM), in order to analize explicitly how these differential operators act in the process of discretizing the generalized fractional pressure diffusion equation for a three-dimensional anisotropic continuous fractal flow. The master finite element equation (MFEE) for arbitrary interpolation functions is obtained. As an example, MFEE for the case of a generic linear tetrahedron in $\mathbb{R}^3$ is shown. Analytic solution for the spatial variables is determined over a canonical tetrahedral finite element in global coordinates.

Comparison of Conventional and Pontic Fixed Partial Dentures Over Implants Using the Finite Element Method: Three-Dimensional Analysis of Cortical and Medullary Bone Stress

2020 ◽  
Vol 46 (3) ◽  
pp. 175-181
Author(s):  
Marcelo Bighetti Toniollo ◽  
Mikaelly dos Santos Sá ◽  
Fernanda Pereira Silva ◽  
Giselle Rodrigues Reis ◽  
Ana Paula Macedo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Medullary Bone ◽  
Principal Stresses ◽  
Bone Stress ◽  
Bone Damage ◽  
Rehabilitation System ◽  
Minimum Requirements

Rehabilitation with implant prostheses in posterior areas requires the maximum number of possible implants due to the greater masticatory load of the region. However, the necessary minimum requirements are not always present in full. This project analyzed the minimum principal stresses (TMiP, representative of the compressive stress) to the friable structures, specifically the vestibular face of the cortical bone and the vestibular and internal/lingual face of the medullary bone. The experimental groups were as follows: the regular splinted group (GR), with a conventional infrastructure on 3 regular-length Morse taper implants (4 × 11 mm); and the regular pontic group (GP), with a pontic infrastructure on 2 regular-length Morse taper implants (4 × 11 mm). The results showed that the TMiP of the cortical and medullary bones were greater for the GP in regions surrounding the implants (especially in the cervical and apical areas of the same region) but they did not reach bone damage levels, at least under the loads applied in this study. It was concluded that greater stress observed in the GP demonstrates greater fragility with this modality of rehabilitation; this should draw the professional's attention to possible biomechanical implications. Whenever possible, professionals should give preference to use of a greater number of implants in the rehabilitation system, with a focus on preserving the supporting tissue with the generation of less intense stresses.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

scholarly journals Approximation of noisy data using multivariate splines and finite element methods

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Bishnu P Lamichhane ◽  
Elizabeth Harris ◽  
Quoc Thong Le Gia
Keyword(s):  
Finite Element ◽  
Differential Operators ◽  
Impulsive Noise ◽  
Noisy Data ◽  
Multivariate Splines ◽  
The Finite Element Method ◽  
Data Smoothing ◽  
Multivariate Spline ◽  
Partial Differential Operators ◽  
Mixture Of Gaussian

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.

Engineering Analysis of Shoulder Dystocia in the Human Birth Process by the Finite Element Method

1992 ◽  
Vol 206 (4) ◽  
pp. 243-250 ◽  
Author(s):  
A Meghdari ◽  
R Davoodi ◽  
F Mesbah
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Shoulder Dystocia ◽  
Point Of View ◽  
Engineering Analysis ◽  
The Finite Element Method ◽  
Birth Process ◽  
Beam Elements ◽  
Finite Element Package ◽  
Human Birth

This paper presents an engineering analysis of shoulder dystocia (SD) in the human birth process which usually results in damaging the brachial plexus nerves and the humerus and/or clavicle bones of the baby. The goal is to study these injuries from the mechanical engineering point of view. Two separate finite element models of the neonatal neck and the clavicle bone have been simulated using eight-node three-dimensional elements and beam elements respectively. Simulated models have been analysed under suitable boundary conditions using the ‘SAP80’ finite element package. Finally, results obtained have been verified by comparing them with published clinical and experimental observations.

The Convergence of the H-P Version of the Finite Element Method with Quasi-Uniform Meshes for Three Dimensional Poisson Problems with Edge Singularity

2014 ◽  
Vol 644-650 ◽  
pp. 1551-1555
Author(s):  
Jian Ming Zhang ◽  
Yong He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weighted Sobolev Spaces ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Smooth Functions ◽  
Edge Singularity ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Element Method

This paper is concerned with the convergence of the h-p version of the finite element method for three dimensional Poisson problems with edge singularity on quasi-uniform meshes. First, we present the theoretical results for the convergence of the h-p version of the finite element method with quasi-uniform meshes for elliptic problems on polyhedral domains on smooth functions in the framework of Jacobi-weighted Sobolev spaces. Second, we investigate and analyze numerical results for three dimensional Poission problems with edge singularity. Finally, we verified the theoretical predictions by the numerical computation.

scholarly journals The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fubiao Lin ◽  
Junying Cao ◽  
Zhixin Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Local Defect ◽  
Local Refinement ◽  
Element Discretization ◽  
One Dimensional ◽  
Correction Technique ◽  
Polar Coordinate ◽  
Multiscale Finite Element

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.

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