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Mathematics
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Finite Element Analysis
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Finite Element Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 9798

Special Issue Editor

Prof. Dr. Carlos Agelet de Saracibar

E-Mail Website
Guest Editor
Department of Civil and Environmental Engineering, School of Civil Engineering, Technical University of Catalonia, UPC BarcelonaTech, Barcelona, Spain
Interests: Computational Mechanics; Contact Mechanics; Nonlinear Coupled Thermomechanical Models; Finite Element Analysis (FEA); VMS Stabilization Methods; Casting Processes; Friction Stir Welding (FSW) Processes; Electron Beam Welding (EBW) Processes; Additive Manufacturing (AM) Processes

Special Issue Information

Dear Colleagues,

Since the early developments in the 1960s and 1970s, carried out by pioneers like R.W. Clough at the UC Berkeley, J.H. Argyris at the University of Stuttgart, and O.C. Zienkiewicz at the University of Swansea, the use of the Finite Element Method (FEM) has been continuously growing, becoming the leading method in the numerical simulation of mathematical, science and engineering problems.

Nowadays, the FEM is applied to a large variety of mathematical and multi-physics and multi-scale science and engineering problems, including computational solid mechanics, computational fluid dynamics, coupled thermomechanical problems, coupled electromechanical problems, or coupled electromagnetics problems.

This special issue on “Finite Element Analysis” intends to collect selected review works written by well-known researchers in the field, as well as current developments in the application of the FEM to mathematical and multi-physics multi-scale physical problems in engineering and science.

Topics addressed in this special issue include, but are not limited to:

  • Finite Element Analysis in Mathematics
  • Finite Element Analysis of Multi-physics and Multi-scale physical problems in engineering and science
  • Stabilization methods in the Finite Element Analysis of Computational Solid Mechanics and Computational Fluid Dynamics
  • Finite Element Analysis in the numerical simulation of material forming processes

Prof. Dr. Carlos Agelet de Saracibar
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Finite Element Analysis (FEA)
  • Finite Element Method (FEM)
  • Computational Modeling
  • Numerical Simulation
  • Mathematical Problems
  • Multi-physics Multi-scale Problems
  • Engineering Problems

Published Papers (3 papers)

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Research

20 pages, 831 KiB  
Article
Numerical Analysis of an Osseointegration Model
by Jacobo Baldonedo, José R. Fernández and Abraham Segade
Mathematics 2020, 8(1), 87; https://doi.org/10.3390/math8010087 - 5 Jan 2020
Cited by 6 | Viewed by 1986
Abstract
In this work, we study a bone remodeling model used to reproduce the phenomenon of osseointegration around endosseous implants. The biological problem is written in terms of the densities of platelets, osteogenic cells, and osteoblasts and the concentrations of two growth factors. Its [...] Read more.
In this work, we study a bone remodeling model used to reproduce the phenomenon of osseointegration around endosseous implants. The biological problem is written in terms of the densities of platelets, osteogenic cells, and osteoblasts and the concentrations of two growth factors. Its variational formulation leads to a strongly coupled nonlinear system of parabolic variational equations. An existence and uniqueness result of this variational form is stated. Then, a fully discrete approximation of the problem is introduced by using the finite element method and a semi-implicit Euler scheme. A priori error estimates are obtained, and the linear convergence of the algorithm is derived under some suitable regularity conditions and tested with a numerical example. Finally, one- and two-dimensional numerical results are presented to demonstrate the accuracy of the algorithm and the behavior of the solution. Full article
(This article belongs to the Special Issue Finite Element Analysis)
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17 pages, 6602 KiB  
Article
Development of Preform for Simulation of Cold Forging Process of A V8 Engine Camshaft Free from Flash & Under-Filling
by A.N. Saquib, H.M.T. Khaleed, Irfan Anjum Badruddin, Ali Algahtani, M.F. Addas, A.B. Abdullah, Abdulgaphur Athani, Sarfaraz Kamangar and T.M. Yunus Khan
Mathematics 2019, 7(11), 1026; https://doi.org/10.3390/math7111026 - 31 Oct 2019
Cited by 1 | Viewed by 4810
Abstract
Finite Element Method based techniques apply to a wide spectrum of engineering applications including manufacturing. The flexibility to achieve optimized results by simulations adds another dimension to process-development. The efficiency due to simulation is enhanced many folds for developing desired components by reducing [...] Read more.
Finite Element Method based techniques apply to a wide spectrum of engineering applications including manufacturing. The flexibility to achieve optimized results by simulations adds another dimension to process-development. The efficiency due to simulation is enhanced many folds for developing desired components by reducing the cost as well as time. This paper investigates cold forging process to be adopted to produce camshafts with a target to minimize flash as well as under filling. These two factors being major problems encountered when cold forging is to be adopted for complex shaped products. The current work is primarily concerned with the development of an optimized preform design for a V8 engine camshaft. The work involved the Solid modeling of the camshaft on AutoCAD and further analyzing the developed model through finite element analysis using Deform 3D. The analysis involved understanding of metal flow, volumetric analysis and die stresses in the forging process. The materials considered for the work-piece and the dies are AISI 8620 and AISI-H-26 respectively. The sample camshaft was taken from a standard Dodge Challenger V8 engine. 10 different cases are analyzed to find out the best possible scenario. It is fund that the stress level for the developed model was very much within the design limit of the material. Full article
(This article belongs to the Special Issue Finite Element Analysis)
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18 pages, 3197 KiB  
Article
Multiblock Mortar Mixed Approach for Second Order Parabolic Problems
by Muhammad Arshad, Madiha Sana and Muhammad Mustahsan
Mathematics 2019, 7(4), 325; https://doi.org/10.3390/math7040325 - 2 Apr 2019
Cited by 2 | Viewed by 2155
Abstract
In this paper, the multiblock mortar mixed approximation of second order parabolic partial differential equations is considered. In this method, the simulation domain is decomposed into the non-overlapping subdomains (blocks), and a physically-meaningful boundary condition is set on the mortar interface between the [...] Read more.
In this paper, the multiblock mortar mixed approximation of second order parabolic partial differential equations is considered. In this method, the simulation domain is decomposed into the non-overlapping subdomains (blocks), and a physically-meaningful boundary condition is set on the mortar interface between the blocks. The governing equations hold locally on each subdomain region. The local problems on blocks are coupled by introducing a special approximation space on the interfaces of neighboring subdomains. Each block is locally covered by an independent grid and the standard mixed finite element method is applied to solve the local problem. The unique solvability of the discrete problem is shown, and optimal order convergence rates are established for the approximate velocity and pressure on the subdomain. Furthermore, an error estimate for the interface pressure in mortar space is presented. The numerical experiments are presented to validate the efficiency of the method. Full article
(This article belongs to the Special Issue Finite Element Analysis)
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