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Modelling of Microstructured Media
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Modelling of Microstructured Media

A special issue of Materials (ISSN 1996-1944).

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 6642

Special Issue Editors

Prof. Jarosław Jędrysiak

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Guest Editor
Department of Structural Mechanics, Lodz University of Technology, al. Politechniki 6, 90-924 Lodz, Poland
Interests: microstructure; mechanical behavior of materials; mechanics of materials; mathematical modeling; engineering, applied and computational mathematics; solid mechanics; nonlinear analysis; structural analysis; structural dynamics; materials
Special Issues, Collections and Topics in MDPI journals
Dr. Łukasz Domagalski

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Guest Editor
Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, 90-924 Lodz, Poland
Interests: stability and dynamics of structures; variable stiffness beams and plates; large deflections of plates; nonlinear vibrations of beams and plates
Dr. Ewelina Kubacka

E-Mail Website
Guest Editor
Department of Structural Mechanics, Lodz University of Technology, 93-590 Lodz, Poland
Interests: laminates; composites; microstructured media; heat transfer; thermoelasticity; tolerance modelling; Finite Difference Method; optimization
Dr. Jakub Marczak

E-Mail Website
Guest Editor
Department of Structural Mechanics, Lodz University of Technology, al. Politechniki 6, 90-924 Lodz, Poland
Interests: structural mechanics; sandwich plates; dynamics; buckling analysis; microheterogeneous structures

Special Issue Information

Dear Colleagues,

It is our great pleasure to announce a collection of papers related to the three-day seminar Modelling of Microstructured Media, which will be held on October 17–19, 2022, in Łódź, Poland.

The aim of the seminar is to unite scientists dealing with inhomogeneous media and structures, especially composites, and provide a platform for them exchange information and scientific experience in the field.

Seminar topics are related with various approaches in tackling thermomechanical problems of microstructured media, such as the mathematical modelling of laminates, fiber-reinforced composites, as well as beams, plates, and shells with internal microstructures (including dynamics problems; stability problems; heat conduction modelling problems; and coupled problems in the mechanics of composites, computer modelling, experimental research).

Prof. Jarosław Jędrysiak
Dr. Łukasz Domagalski
Dr. Ewelina Kubacka
Dr. Jakub Marczak
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. Materials 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

  • advanced materials
  • composites
  • inhomogeneous media
  • laminates
  • heat conduction problems
  • mathematical modelling

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Published Papers (6 papers)

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Research

18 pages, 1592 KiB  
Article
Dynamics of Functionally Graded Laminated (FGL) Media—Theoretical Tolerance Modelling
by Jarosław Jędrysiak
Materials 2023, 16(22), 7162; https://doi.org/10.3390/ma16227162 - 14 Nov 2023
Viewed by 763
Abstract
Dynamic problems of elastic non-periodically laminated solids are considered in this paper. It is assumed that these laminates have a functionally graded structure on the macrolevel along the x1-axis and non-periodic structure on the microlevel. However, along the other two directions, [...] Read more.
Dynamic problems of elastic non-periodically laminated solids are considered in this paper. It is assumed that these laminates have a functionally graded structure on the macrolevel along the x1-axis and non-periodic structure on the microlevel. However, along the other two directions, i.e., x2 and x3, their properties are constant. The effects of the size of a microstructure (the microstructure effect) on the behaviour of the composites can play a significant role. This effect can be described using the tolerance modelling method. This method allows us to derive model equations with slowly varying coefficients. Some of these terms can depend on the size of the microstructure. These governing equations of the tolerance model make it possible to determine formulas describing not only fundamental lower-order vibrations related to the macrostructure of these composite solids, but also higher-order vibrations related to the microstructure. Here, the application of the tolerance modelling procedure is shown to lead to equations of the tolerance model that can be used for non-periodically laminated solids. Then, these model equations are mainly used to analyse a simple example of vibrations for functionally graded composites with non-periodically laminated microstructure (FGL). Similar problems were investigated in the framework of the homogenised (macrostructural) model (Jędrysiak et al. 2006); the resulting equations neglect the microstructure effect. Full article
(This article belongs to the Special Issue Modelling of Microstructured Media)
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18 pages, 8818 KiB  
Article
Influence of Composite Structure on Temperature Distribution—An Analysis Using the Finite Difference Method
by Ewelina Kubacka and Piotr Ostrowski
Materials 2023, 16(14), 5193; https://doi.org/10.3390/ma16145193 - 24 Jul 2023
Viewed by 961
Abstract
Among composites, we can distinguish periodic structures, biperiodic structures, and structures with a functional gradation of material properties made of two or more materials. The selection of the composite’s constituent materials and the way they are distributed affects the weight of the composite, [...] Read more.
Among composites, we can distinguish periodic structures, biperiodic structures, and structures with a functional gradation of material properties made of two or more materials. The selection of the composite’s constituent materials and the way they are distributed affects the weight of the composite, its strength, and other properties, as well as the way it conducts heat. This work is about studying the temperature distribution in composites, depending on the type of component material and its location. For this purpose, the Tolerance Averaging Technique and the Finite Difference Method were used. Differential equations describing heat conduction phenomena were obtained using the Tolerance Averaging Technique, while the Finite Difference Method was used to solve them. In terms of results, temperature distribution plots were produced showing the effect of the structure of the composite on the heat transfer properties. Full article
(This article belongs to the Special Issue Modelling of Microstructured Media)
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27 pages, 15678 KiB  
Article
The Machine Learning Methods in Non-Destructive Testing of Dynamic Properties of Vacuum Insulated Glazing Type Composite Panels
by Damian Kozanecki, Izabela Kowalczyk, Sylwia Krasoń, Martyna Rabenda, Łukasz Domagalski and Artur Wirowski
Materials 2023, 16(14), 5055; https://doi.org/10.3390/ma16145055 - 17 Jul 2023
Cited by 1 | Viewed by 1102
Abstract
The VIG (Vacuum Insulated Glazing) unit, composite glazing in which the space between glass panes is filled with vacuum, is one of the most advanced technologies. The key elements of the construction of VIG plates are the support pillars. Therefore, an important issue [...] Read more.
The VIG (Vacuum Insulated Glazing) unit, composite glazing in which the space between glass panes is filled with vacuum, is one of the most advanced technologies. The key elements of the construction of VIG plates are the support pillars. Therefore, an important issue is the analysis of their mechanical properties, such as Young’s modulus and their variability over a long period of time. Machine learning (ML) methods are undergoing tremendous development these days. Among the many different techniques included in AI, neural networks (NN) and extreme gradient boosting (XGB) algorithms deserve special attention. In this study, to train selected methods of machine learning, numerical data developed in the VIG plate modelling process using Abaqus program were used. The test method proposed in this article is based on the VIG plate subjected to forced vibrations of specific frequencies and then the reading of the dynamic response of the composite plate. Such collected and pre-developed experimental data were used to obtain the mechanical parameters of the steel elements located inside the analysed vacuum glazing. In the future, the proposed research methods can be used to analyse the mechanical properties of other types of composite panels. Full article
(This article belongs to the Special Issue Modelling of Microstructured Media)
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20 pages, 12290 KiB  
Article
Genetic Algorithm Optimization of Beams in Terms of Maximizing Gaps between Adjacent Frequencies
by Łukasz Domagalski and Izabela Kowalczyk
Materials 2023, 16(14), 4963; https://doi.org/10.3390/ma16144963 - 12 Jul 2023
Viewed by 925
Abstract
The aim of this paper is to optimize the thickness variation function of simply supported and cantilever beams, in terms of maximizing gaps between chosen neighboring frequencies, and to analyze the obtained results. The optimization results are examined in terms of achieving the [...] Read more.
The aim of this paper is to optimize the thickness variation function of simply supported and cantilever beams, in terms of maximizing gaps between chosen neighboring frequencies, and to analyze the obtained results. The optimization results are examined in terms of achieving the objective function (related to eigenvalue problems), but also in terms of their dynamic stiffness (forced vibrations excited by a point harmonic load). In the optimization process, a genetic algorithm was used. Problems related to structural dynamics were solved by FEM implementation into the algorithm. Sample results were presented, and the developed algorithm was analyzed in terms of the results convergence by examining several variable parameters. The authors demonstrated the validity of applying the described optimization tool to the presented problems. Conclusions were drawn regarding the correlation between stiffness and mass distribution in the optimized beams and the natural frequency modes in terms of which they were optimized. Full article
(This article belongs to the Special Issue Modelling of Microstructured Media)
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15 pages, 5186 KiB  
Article
Numerical Analysis, Optimization, and Multi-Criteria Design of Vacuum Insulated Glass Composite Panels
by Izabela Kowalczyk, Damian Kozanecki, Sylwia Krasoń, Martyna Rabenda, Łukasz Domagalski and Artur Wirowski
Materials 2023, 16(13), 4722; https://doi.org/10.3390/ma16134722 - 29 Jun 2023
Viewed by 1000
Abstract
The subject of this study is Vacuum Insulated Glass (VIG) panels, which consist of two glass panes with an evacuated space and evenly distributed micro-support pillars between them. The deflection of panes towards the centre of the structure caused by atmospheric pressure is [...] Read more.
The subject of this study is Vacuum Insulated Glass (VIG) panels, which consist of two glass panes with an evacuated space and evenly distributed micro-support pillars between them. The deflection of panes towards the centre of the structure caused by atmospheric pressure is a mechanical problem that occurs in this type of structure. The aim of this study was to extend previous research on the optimal arrangement of support pillars in terms of eigenfrequencies and dynamics to include aesthetic aspects. Using Abaqus/CAE v2017 software, a large number of numerical models were created and subjected to a comprehensive multi-criteria analysis. Fractal analysis was employed to automatically assess the aesthetics of the proposed solutions. The study presents theoretical solutions that could be implemented in industrial production. The presented study shows that it is possible to effectively extend the criteria for optimizing the arrangement of pillars with new design criteria. Most studies focus on pillar placement, amount, or shape in terms of panes thermal or mechanical properties. Due to the increasing number of VIG panels applications in places exposed to external vibrations, other design criteria for VIG panels are also required and are provided by the following study. Full article
(This article belongs to the Special Issue Modelling of Microstructured Media)
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17 pages, 1533 KiB  
Article
Nonlinear Vibration of Double-Walled Carbon Nanotubes Subjected to Mechanical Impact and Embedded on Winkler–Pasternak Foundation
by Nicolae Herisanu, Bogdan Marinca and Vasile Marinca
Materials 2022, 15(23), 8599; https://doi.org/10.3390/ma15238599 - 2 Dec 2022
Cited by 5 | Viewed by 1279
Abstract
This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are [...] Read more.
This study was devoted to an investigation on the dynamics of double-walled carbon nanotubes (DWCNTs) under the influence of Winkler–Pasternak foundation near the primary resonance. Two Euler–Bernoulli beams embedded on nonlinear foundation, interacting through van der Waals forces, subjected to mechanical impact are considered. By means of Hamilton’s principle, Eringen’s nonlocal elastic theory, and taking into account the moving nanoparticles, the Galerkin–Bubnov method is applied and accordingly, governing partial differential equations are reduced to two differential equations with variable coefficients. The nonlinear damped and forced vibration is studied using the optimal auxiliary functions method (OAFM). An explicit and very accurate analytical solution is obtained by means of OAFM without considering simplifying hypotheses. An accurate analysis is for the first time reported considering the cumulated effects of nonlinearities simultaneously induced by the Winkler–Pasternak foundation, the curvature of beams and van der Waals force, and also the effect of discontinuities marked by the presence of the Dirac function. Finally, a stability analysis of the considered model is developed by means of the homotopy perturbation method (HPM) using the condition of existence of the two frequencies. It was shown that an increasing of some constitutive parameters substantially reduces the area of stability, all these being of much help in guiding the design of advanced nanoelectromechanical devices, in which nanotubes act as basic elements. Full article
(This article belongs to the Special Issue Modelling of Microstructured Media)
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