Finite Element Modeling in Mechanical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 June 2024) | Viewed by 3680

Special Issue Editors


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1. Institute of Solid Mechanics of Romanian Academy, Str. Constantin Mille No. 15, 030167 Bucharest, Romania
2. Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Interests: computational mechanics
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Guest Editor
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania
Interests: differential equations; partial differential equations; equations of evolution; integral equations; mixed initial-boundary value problems for PDE; termoelasticity; media with microstretch; environments goals; nonlinear problems
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Guest Editor
Department of Mechanics, “Transilvania” University of Brasov, Brasov, Romania
Interests: mechanics; vibrations; elasticity; composite materials; analytical mechanics
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Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to provide an opportunity for international researchers to share and review recent advances used in finite element modeling in computational friction contact mechanics. Numerical modeling presents many challenges in mathematics, mechanical engineering, computer science, computers, etc. The finite element method applied in solid mechanics was designed by engineers with the idea of being able to simulate numerical models in order to reduce the design costs for prototypes, tests and measurements.

The method was initially validated only by measurements, but which gave encouraging results. After the discovery of the Sobloev spaces, the results mentioned above were obtained, and today, numerous researchers are working on improving this method. Some of the method’s application fields in the domain of mechanics of the solid include mechanical engineering, machine and device design, civil engineering, aerospace and automotive engineering, robotics, etc.

Frictional contact is a complex phenomenon which has led to research in mechanical engineering, computational contact mechanics, composite material design, rigid body dynamics, robotics, etc. A good simulation requires that the dynamics of contact with friction be included in the formulation of dynamic systems that can approximate the complex phenomena that occur. To solve these linear or nonlinear dynamic systems that can often have non-differentiable terms, or discontinuities, software that includes high-performance numerical methods as well as high-computing-power computers are needed.

All interested researchers are kindly invited to contribute to this Special Issue with their original research articles, short communications and review articles.

Prof. Dr. Nicolae Pop
Prof. Dr. Marin Marin
Prof. Dr. Sorin Vlase
Guest Editors

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Keywords

  • finite element analysis
  • weak solutions
  • convergence results
  • shape and topology optimization
  • elastic material
  • composites
  • boundary control
  • active vibration control
  • contact problems
  • variational inequalities
  • friction laws
  • static
  • kinetic or sliding friction
  • collisions
  • isotropic and anisotropic friction
  • optimal control
  • non-differentiability
  • stick–slip contact
  • frictional quasistatic contact
  • penalization and regularization

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Published Papers (2 papers)

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Research

17 pages, 1994 KiB  
Article
An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod
by Ahmed E. Abouelregal, Marin Marin and Sahar M. Abusalim
Mathematics 2023, 11(7), 1739; https://doi.org/10.3390/math11071739 - 5 Apr 2023
Cited by 8 | Viewed by 1563
Abstract
By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be [...] Read more.
By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be addressed using classical thermoelasticity, extended thermoelasticity models have been derived. The thermo-mechanical response of a piezoelectric functionally graded (FG) rod due to a moveable axial heat source is considered in this paper, utilizing the dual-phase-lag (DPL) heat transfer model. It was supposed that the physical characteristics of the FG rod varied exponentially along the axis of the body. Both ends hold the rod, and there is no voltage across them. The Laplace transform and decoupling techniques were used to obtain the physical fields that have been analyzed. A range of heterogeneity, rotation, and heat source velocity measures were used to compare the results presented here and those in the previous literature. Full article
(This article belongs to the Special Issue Finite Element Modeling in Mechanical Systems)
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14 pages, 382 KiB  
Article
Numerical Analysis of a Swelling Poro-Thermoelastic Problem with Second Sound
by Noelia Bazarra, José R. Fernández and María Rodríguez-Damián
Mathematics 2023, 11(6), 1456; https://doi.org/10.3390/math11061456 - 17 Mar 2023
Cited by 1 | Viewed by 1464
Abstract
In this paper, we analyze, from the numerical point of view, a swelling porous thermo-elastic problem. The so-called second-sound effect is introduced and modeled by using the simplest Maxwell–Cattaneo law. This problem leads to a coupled system which is written by using the [...] Read more.
In this paper, we analyze, from the numerical point of view, a swelling porous thermo-elastic problem. The so-called second-sound effect is introduced and modeled by using the simplest Maxwell–Cattaneo law. This problem leads to a coupled system which is written by using the displacements of the fluid and the solid, the temperature and the heat flux. The numerical analysis of this problem is performed applying the classical finite element method with linear elements for the spatial approximation and the backward Euler scheme for the discretization of the time derivatives. Then, we prove the stability of the discrete solutions and we provide an a priori error analysis. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximations, the exponential decay of the discrete energy and the dependence on a coupling parameter. Full article
(This article belongs to the Special Issue Finite Element Modeling in Mechanical Systems)
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