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Special Issue "Finite Element Modeling in Computational Friction Contact Mechanics"

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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 14865

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Prof. Dr. Nicolae Pop

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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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Prof. Dr. Marin Marin

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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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Prof. Dr. Sorin Vlase

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Guest Editor

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

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
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 (11 papers)

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Editorial

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Open AccessEditorial

Mathematics in Finite Element Modeling of Computational Friction Contact Mechanics 2021–2022

Nicolae Pop

Marin Marin

and

Sorin Vlase

Mathematics 2023, 11(1), 255; https://doi.org/10.3390/math11010255 - 03 Jan 2023

Viewed by 1445

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 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

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Open AccessArticle

Generalized Thermoelastic Interactions in an Infinite Viscothermoelastic Medium under the Nonlocal Thermoelastic Model

Tareq Saeed

Mathematics 2022, 10(23), 4425; https://doi.org/10.3390/math10234425 - 24 Nov 2022

Cited by 1 | Viewed by 619

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 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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Open AccessArticle

Experimental Validation of Model Heat Transfer in Rectangular Hole Beams Using Modern Dimensional Analysis

and

Mathematics 2022, 10(3), 409; https://doi.org/10.3390/math10030409 - 27 Jan 2022

Cited by 10 | Viewed by 1475

Abstract

Based on the Szirtes’ modern dimensional analysis (MDA), the authors apply the theory to a real structure in order to validate by experimental measurements its applicability. After a presentation of the basic elements of the model law (ML), deduced for two relevant cases, the authors conceived the set of prototypes and models, based on the case of an actual construction pillar, physically performed at scales of 1:1, 1:2, and 1:4. The combination of these structural elements, made at different scales, resulted in three sets of prototypes and models. In this paper, taking into consideration the ML for two relevant cases, the following are presented: the original test stand of these structural elements; block diagram of the original electronic heating and control system; the basic considerations regarding the particularity of this heating system from the point of view of heat transfer; measurement data, obtained for both nonthermally protected elements and for those protected with layers of intumescent paints. In the last part of the paper, the values obtained by rigorous direct measurements with those offered by the ML on the elements considered as prototypes and models are compared. Almost identical values were obtained from the direct measurements with those provided by the ML, thus resulting in the validation of these laws. The same thermal regimes were applied to all these structural elements, with registration of every parameter related to these thermal regimes. Depending on the role of a structural element within a certain set (prototype-model), some of the measurement data were considered as data acquired directly through measurements, and others served as reference elements for those for which we had to obtain through the model law. In the last part of the paper, the sizes obtained by rigorous direct measurements are compared with those offered by the model law on the elements considered as prototypes and models. Identical practical values of the quantities were obtained from the direct measurements with those provided by the model law, thus resulting in the validation of these laws. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

Thermo-Optical Mechanical Waves in a Rotating Solid Semiconductor Sphere Using the Improved Green–Naghdi III Model

Ahmed E. Abouelregal

Marin Marin

and

Sameh Askar

Mathematics 2021, 9(22), 2902; https://doi.org/10.3390/math9222902 - 15 Nov 2021

Cited by 12 | Viewed by 1349

Abstract

The current study investigates thermophotovoltaic interactions using a new mathematical model of thermoelasticity established on a modification of the Green–Naghdi model of type III (GN-III). The basic equations, in which the heat transfer is in the form of the Moore–Gibson–Thompson (MGT) equation, are derived by adding a single delay factor to the GN-III model. The impact of temperature and electrical elastic displacement of semiconductors throughout the excited thermoelectric mechanism can be studied theoretically using this model. The proposed model was used to investigate the interactions between the processes of thermoelastic plasma in a rotating semiconductor solid sphere that was subjected to a thermal shock and crossed to an externally applied magnetic field. The influence of rotation parameters on various photothermal characteristics of silicon solid was presented and explored using the Laplace technique. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

Aatef D. Hobiny

and

Ibrahim A. Abbas

Mathematics 2021, 9(21), 2782; https://doi.org/10.3390/math9212782 - 02 Nov 2021

Cited by 2 | Viewed by 974

Abstract

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

Effect of Voids and Internal State Variables in Elasticity of Porous Bodies with Dipolar Structure

and

Mathematics 2021, 9(21), 2741; https://doi.org/10.3390/math9212741 - 28 Oct 2021

Cited by 1 | Viewed by 815

Abstract

In this study, we will prove that the presence of the voids and of the internal state variables in an elastic body with dipolar structure have no effect on the result of uniqueness regarding the solution of the initial-boundary value problem from this context. First, we put down the basic equations and conditions which define the initial-boundary value problem in the context. Then, by means of three theorems, we prove some auxiliary estimates that underlie the result of uniqueness. Finally, by means of these estimates and by using the Gronwall’s inequality, we prove our main result. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

Open AccessFeature PaperArticle

The Effects of Fractional Time Derivatives in Porothermoelastic Materials Using Finite Element Method

Marin Marin

Aatef Hobiny

and

Ibrahim Abbas

Mathematics 2021, 9(14), 1606; https://doi.org/10.3390/math9141606 - 07 Jul 2021

Cited by 17 | Viewed by 1216

Abstract

In this work, a new model for porothermoelastic waves under a fractional time derivative and two time delays is utilized to study temperature increments, stress and the displacement components of the solid and fluid phases in porothermoelastic media. The governing equations are presented under Lord–Shulman theory with thermal relaxation time. The finite element method has been adopted to solve these equations due to the complex formulations of this problem. The effects of fractional parameter and porosity in porothermoelastic media have been studied. The numerical outcomes for the temperatures, the stresses and the displacement of the fluid and the solid are presented graphically. These results will allow future studies to gain a detailed insight into non-simple porothermoelasticity with various phases. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

Finite Element Analysis of Nonlinear Bioheat Model in Skin Tissue Due to External Thermal Sources

Marin Marin

Aatef Hobiny

and

Ibrahim Abbas

Mathematics 2021, 9(13), 1459; https://doi.org/10.3390/math9131459 - 22 Jun 2021

Cited by 12 | Viewed by 1404

Abstract

In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

An Approximation of Solutions for the Problem with Quasistatic Contact in the Case of Dry Friction

Nicolae Pop

Miorita Ungureanu

and

Adrian I. Pop

Mathematics 2021, 9(8), 904; https://doi.org/10.3390/math9080904 - 19 Apr 2021

Cited by 3 | Viewed by 1431

Abstract

In this paper, we discuss the question of finding an optimal control for the solutions of the problem with dry friction quasistatic contact, in the case that the friction law is modeled by a nonlocal version of Coulomb’s law. In order to get the necessary optimality conditions, we use some regularization techniques, and this leads us to a problem of control for an inequality of the variational type. The optimal control problem consists, in our case, of minimizing a sequence of optimal control problems, where the control variable is given by a Neumann-type boundary condition. The state system is represented by a limit of a sequence, whose terms are obtained from the discretization, in time with finite difference and space with the finite element method of a regularized quasistatic contact problem with Coulomb friction. The purpose of this optimal control problem is that the traction force (the control variable) acting on one side of the boundary (the Neumann boundary condition) of the elastic body produces a displacement field (the state system solution) close enough to the imposed displacement field, and the traction force from the boundary remains small enough. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

Vibration Response of a Concrete Structure with Repetitive Parts Used in Civil Engineering

Sorin Vlase

Marin Marin

Maria Luminita Scutaru

and

Catalin Pruncu

Mathematics 2021, 9(5), 490; https://doi.org/10.3390/math9050490 - 27 Feb 2021

Cited by 2 | Viewed by 1386

Abstract

The paper studies the vibration behavior of a concrete structure, currently used in civil engineering. The truss structure considered has symmetries that can be used to facilitate both the design and construction of the building. Moreover, the symmetries encountered can be used to simplify the calculation of vibrations of the system. Based on the mechanical model built, eigenvalues and eigenvectors of such mechanical system are determined, and properties, specific to these symmetries, are identified. In this way, the dynamic analysis of the structure can be simplified and also, the design as well as the costs related to this stage. Full article

(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)

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Open AccessArticle

Meshing Drive Mechanism of Double Traveling Waves for Rotary Piezoelectric Motors

and

Mathematics 2021, 9(4), 445; https://doi.org/10.3390/math9040445 - 23 Feb 2021

Cited by 3 | Viewed by 1380

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 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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