Finite Element Modeling in Computational Friction Contact Mechanics

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

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 16558

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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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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Department of Mechanics, “Transilvania” University of Brasov, Brasov, Romania
Interests: mechanics; vibrations; elasticity; composite materials; analytical mechanics
Special Issues, Collections and Topics in MDPI journals

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 regularisation
 

Published Papers (3 papers)

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Editorial

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5 pages, 198 KiB  
Editorial
Mathematics in Finite Element Modeling of Computational Friction Contact Mechanics 2021–2022
by Nicolae Pop, Marin Marin and Sorin Vlase
Mathematics 2023, 11(1), 255; https://doi.org/10.3390/math11010255 - 3 Jan 2023
Cited by 3 | Viewed by 2337
Abstract
In engineering practice, structures with identical components or parts are useful from several points of view: less information is needed to describe the system; designs can be conceptualized quicker and easier; components are made faster than during traditional complex assembly; and finally, the [...] Read more.
In engineering practice, structures with identical components or parts are useful from several points of view: less information is needed to describe the system; designs can be conceptualized quicker and easier; components are made faster than during traditional complex assembly; and finally, the time needed to achieve the structure and the cost involved in manufacturing decrease. Additionally, the subsequent maintenance of this system then becomes easier and cheaper. The aim of this Special Issue is to provide an opportunity for international researchers to share and review recent advances in the finite element modeling of computational friction contact mechanics. Numerical modeling in mathematics, mechanical engineering, computer science, computers, etc. presents many challenges. The finite element method applied in solid mechanics was designed by engineers to simulate numerical models in order to reduce the design costs of prototypes, tests and measurements. This method was initially validated only by measurements but gave encouraging results. After the discovery of Sobolev spaces, the abovementioned results were obtained, and today, numerous researchers are working on improving this method. Some of applications of this method in solid mechanics include mechanical engineering, machine and device design, civil engineering, aerospace and automotive engineering, robotics, etc. Frictional contact is a complex phenomenon that 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 the dynamic system so that an approximation of the complex phenomena can be made. To solve these linear or nonlinear dynamic systems, which often have non-differentiable terms, or discontinuities, software that considers these high-performance numerical methods and computers with high computing power are needed. This Special Issue is dedicated to this kind of mechanical structure and to describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are also considered. Additionally, theoretical models, mathematical methods and numerical analysis of these systems, such as the finite element method and experimental methods, are used in these studies. Machine building, automotive, aerospace and civil engineering are the main areas in which such applications appear, but they can also be found in most other engineering fields. With this Special Issue, we want to disseminate knowledge among researchers, designers, manufacturers and users in this exciting field. Full article
(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

Research

Jump to: Editorial

11 pages, 3771 KiB  
Article
Generalized Thermoelastic Interactions in an Infinite Viscothermoelastic Medium under the Nonlocal Thermoelastic Model
by Tareq Saeed
Mathematics 2022, 10(23), 4425; https://doi.org/10.3390/math10234425 - 24 Nov 2022
Cited by 1 | Viewed by 1104
Abstract
The wave propagation in viscothermoelastic materials is discussed in the present work using the nonlocal thermoelasticity model. This model was created using the Lord and Shulman generalized thermoelastic model due to the consequences of delay times in the formulations of heat conduction and [...] Read more.
The wave propagation in viscothermoelastic materials is discussed in the present work using the nonlocal thermoelasticity model. This model was created using the Lord and Shulman generalized thermoelastic model due to the consequences of delay times in the formulations of heat conduction and the motion equations. This model was created using Eringen’s theory of the nonlocal continuum. The linear Kelvin–Voigt viscoelasticity model explains the viscoelastic properties of isotropic material. The analytical solutions for the displacement, temperature, and thermal stress distributions are obtained by the eigenvalues approach with the integral transforms in the Laplace transform techniques. The field functions, namely displacement, temperature, and stress, have been graphically depicted for local and nonlocal viscothermoelastic materials to assess the quality of wave propagation in various outcomes of interest. The results are displayed graphically to illustrate the effects of nonlocal thermoelasticity and viscoelasticity. Comparisons are made with and without thermal relaxation time. The outcomes show that Eringen’s nonlocal viscothemoelasticity theory is a promising criterion for analyzing nanostructures, considering the small size effects. Full article
(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)
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17 pages, 8208 KiB  
Article
Meshing Drive Mechanism of Double Traveling Waves for Rotary Piezoelectric Motors
by Dawei An, Weiqing Huang, Weiquan Liu, Jinrui Xiao, Xiaochu Liu and Zhongwei Liang
Mathematics 2021, 9(4), 445; https://doi.org/10.3390/math9040445 - 23 Feb 2021
Cited by 3 | Viewed by 1867
Abstract
Rotary piezoelectric motors based on converse piezoelectric effect are very competitive in the fields of precision driving and positioning. Miniaturization and larger output capability are the crucial design objectives, and the efforts on structural modification, new materials application and optimization of control systems [...] Read more.
Rotary piezoelectric motors based on converse piezoelectric effect are very competitive in the fields of precision driving and positioning. Miniaturization and larger output capability are the crucial design objectives, and the efforts on structural modification, new materials application and optimization of control systems are persistent but the effectiveness is limited. In this paper, the resonance rotor excited by stator is investigated and the meshing drive mechanism of double traveling waves is proposed. Based on the theoretical analysis of bending vibration, the finite element method (FEM) is used to compare the modal shape and modal response in the peripheric, axial, and radial directions for the stator and three rotors. By analyzing the phase offset and vibrational orientation of contact particles at the interface, the principle of meshing traveling waves is discussed graphically and the concise formula obtaining the output performance is summarized, which is analogous with the principles of gear connection. Verified by the prototype experimental results, the speed of the proposed motor is the sum of the velocity of the stator’s contact particle and the resonance rotor’s contact particle, while the torque is less than twice the motor using the reference rotor. Full article
(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)
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