Advances in Applied Mathematics, Mechanics and Engineering

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3219

Special Issue Editors

Faculty of Mechanics, University of Craiova, 200512 Dolj, Romania
Interests: industrial and biological robots; mechanisms; car bodies and mechanical transmissions; computer-aided design; modeling and simulation with finite elements
Faculty of Mechanics, University of Craiova, 200512 Dolj, Romania
Interests: geometric modeling; finite element analysis; modeling technological processes; programming languages development of API applications on commercial graphics cores; virtual prototyping

Special Issue Information

Dear Colleagues,

Applied Mathematics, Mechanics, and Engineering cover many research domains, and this issue represents a fountain flowing with innovative development. This Special Issue aims to create a research core of high-quality refereed articles discussing various aspects of applied mathematics in mechanics, and mechanical engineering modeling phenomena and their peculiarities. Thus, the proposed topics will highlight research articles dedicated to the mathematical modeling of technical problems arising in domains such as  engineering, applied mechanics, medicine, robotics, science, technology, etc.

This Special Issue will be represented by high-quality articles related to the following interest topics:

  • Mechanical systems modeling; simulations methodology and algorithms.
  • Dynamic analysis of mechanical systems.
  • Kinematics of mobile mechanical systems and their application.
  • Vibrations and impact phenomena modeling.
  • Mathematical models applied in mechanical engineering.

Prof. Dr. Nicolae Dumitru
Dr. Adrian Sorin Rosca
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

  • computational mechanics
  • kinematics
  • dynamics and control of mechanical systems
  • modeling and simulations in biomechanics
  • robotics and mechatronics
  • experimental mechanics
  • composite materials
  • algorithms
  • advanced methods for optimizing in mechanical engineering

Published Papers (4 papers)

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Research

32 pages, 4663 KiB  
Article
Influence of Homo- and Hetero-Junctions on the Propagation Characteristics of Radially Propagated Cylindrical Surface Acoustic Waves in a Piezoelectric Semiconductor Semi-Infinite Medium
by Xiao Guo, Yilin Wang, Chunyu Xu, Zibo Wei and Chenxi Ding
Mathematics 2024, 12(1), 145; https://doi.org/10.3390/math12010145 - 02 Jan 2024
Viewed by 566
Abstract
This paper theoretically investigates the influence of homo- and hetero-junctions on the propagation characteristics of radially propagated cylindrical surface acoustic waves in a piezoelectric semiconductor semi-infinite medium. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are mathematically derived. Then, based on [...] Read more.
This paper theoretically investigates the influence of homo- and hetero-junctions on the propagation characteristics of radially propagated cylindrical surface acoustic waves in a piezoelectric semiconductor semi-infinite medium. First, the basic equations of the piezoelectric semiconductor semi-infinite medium are mathematically derived. Then, based on these basic equations and the transfer matrix method, two equivalent mathematical models are established concerning the propagation of radially propagated cylindrical surface acoustic waves in this piezoelectric semiconductor semi-infinite medium. Based on the surface and interface effect theory, the homo- or hetero-junction is theoretically treated as a two-dimensional electrically imperfect interface in the first mathematical model. To legitimately confirm the interface characteristic lengths that appear in the electrically imperfect interface conditions, the homo- or hetero-junction is equivalently treated as a functional gradient thin layer in the second mathematical model. Finally, based on these two mathematical models, the dispersion and attenuation curves of radially propagated cylindrical surface acoustic waves are numerically calculated to discuss the influence of the homo- and hetero-junctions on the dispersion and attenuation characteristics of radially propagated cylindrical surface acoustic waves. The interface characteristic lengths are legitimately confirmed through the comparison of dispersion and attenuation curves calculated using the two equivalent mathematical models. As piezoelectric semiconductor energy harvesters usually work under elastic deformation, the establishment of mathematical models and the revelation of physical mechanisms are both fundamental to the analysis and optimization of micro-scale surface acoustic wave resonators, energy harvesters, and acoustic wave amplification based on the propagation of surface acoustic waves. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics, Mechanics and Engineering)
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14 pages, 1478 KiB  
Article
Formulation and Numerical Solution of Plane Problems of the Theory of Elasticity in Strains
by Dilmurod Turimov, Abduvali Khaldjigitov, Umidjon Djumayozov and Wooseong Kim
Mathematics 2024, 12(1), 71; https://doi.org/10.3390/math12010071 - 25 Dec 2023
Cited by 2 | Viewed by 507
Abstract
This article is devoted to the formulation and numerical solution of boundary-value problems in the theory of elasticity with respect to deformations. Similar to the well-known Beltrami–Michell stress equations, the Saint-Venant compatibility conditions are written in the form of differential equations for strains. [...] Read more.
This article is devoted to the formulation and numerical solution of boundary-value problems in the theory of elasticity with respect to deformations. Similar to the well-known Beltrami–Michell stress equations, the Saint-Venant compatibility conditions are written in the form of differential equations for strains. A new version of plane boundary-value problems in strains is formulated. It is shown that for the correctness of plane boundary value problems, in addition to the usual conditions, one more special boundary condition is required using the equilibrium equation. To discretize additional boundary conditions and differential equations, it is convenient to use the finite difference method. By resolving grid equations and additional boundary conditions with respect to the desired quantities at the diagonal nodal points, we obtained convergent iterative relations for the internal and boundary nodes. To solve grid equations, the elimination method was also used. By comparing with the Timoshenko–Goodyear solution on the tension of a rectangular plate with a parabolic load, the validity of the formulated boundary value problems in strains and the reliability of the numerical results are shown. The accuracy of the results has been increased by an average of 15%. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics, Mechanics and Engineering)
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18 pages, 7989 KiB  
Article
Experimental and Numerical Investigation of Folding Process—Prediction of Folding Force and Springback
by Lotfi Ben Said, Hamdi Hentati, Taoufik Kamoun and Mounir Trabelsi
Mathematics 2023, 11(19), 4103; https://doi.org/10.3390/math11194103 - 28 Sep 2023
Viewed by 627
Abstract
The folding process is characterized by the springback phenomenon. Several experimental folding tests are elaborated and illustrated in this paper. The precision and the quality of the folded sheet workpiece are related to the reduction in the springback phenomena. For that, two tools [...] Read more.
The folding process is characterized by the springback phenomenon. Several experimental folding tests are elaborated and illustrated in this paper. The precision and the quality of the folded sheet workpiece are related to the reduction in the springback phenomena. For that, two tools are designed and used for the folding process. An accurate design of the folding tool plays a significant role in contributing to the folding process and reducing potential defects related to springback. An experimental solution is presented to avoid the forming of defaults and compensate the workpiece springback after its removal from the die. Moreover, an accurate numerical modeling enables an efficient prediction of the springback. This allows us to obtain precise parts through the folding process. For that, a modified Johnson–Cook model is implemented on ABAQUS software in order to predict the folding force and the springback in a U-die folding process. In addition to the isotropic hardening law, a nonlinear kinematic hardening rule is used. To ensure the model’s accuracy and reliability, we conducted validation experiments. The model’s predictions are compared with experimental tests to show its capability to simulate the folding process effectively. The developed mechanical model can adequately predict and analyze springback effects and folding force evolution, helping designers compensate for them and achieve the desired final shape. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics, Mechanics and Engineering)
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16 pages, 8234 KiB  
Article
Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations
by Peng Zhi, Yuching Wu, Cheng Qi, Tao Zhu, Xiao Wu and Hongyu Wu
Mathematics 2023, 11(12), 2723; https://doi.org/10.3390/math11122723 - 15 Jun 2023
Cited by 2 | Viewed by 1049
Abstract
The purpose of this study is to investigate the role that a deep learning approach could play in computational mechanics. In this paper, a convolutional neural network technique based on modified loss function is proposed as a surrogate of the finite element method [...] Read more.
The purpose of this study is to investigate the role that a deep learning approach could play in computational mechanics. In this paper, a convolutional neural network technique based on modified loss function is proposed as a surrogate of the finite element method (FEM). Several surrogate-based physics-informed neural networks (PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). According to the authors’ knowledge, the proposed method has been applied for the first time to solve boundary value problems with elliptic partial differential equations as the governing equations. The results of the proposed surrogate-based approach are in good agreement with those of the conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is demonstrated that to some extent, the deep learning approach could replace the conventional numerical method as a significant surrogate model. Full article
(This article belongs to the Special Issue Advances in Applied Mathematics, Mechanics and Engineering)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Simulation and optimization of a dual-axis solar tracking mechanism
Authors: Catalin Alexandru
Affiliation: Transilvania University of Brasov
Abstract: This paper deals with the simulation and optimization based on virtual prototyping tools of a tracking mechanism used to increase the efficiency of photovoltaic (PV) systems. The proposed solar tracker is one with two degrees of freedom (so called dual-axis, or bi-axial mechanism) of the equatorial type, which is able of reproducing with great accuracy the real movements of the sun-earth astronomical system. Another advantage of such a system is that the two movements (diurnal and elevation) are independent, which allows the control process to be simplified. The actuation of the tracking system is carried out with two linear actuators, one for each of the two movements. The optimization process is approached from three points of view, each influencing in a specific way the energy efficiency of the PV tracking system, as follows: optimizing the mechanical device of the solar tracker, which intend to determine the optimal arrangement of the two actuators; optimizing the open-loop control system, which aims at optimal tuning of the control elements; optimizing the bi-axial tracking program, with the aim of maximizing the amount of incident solar radiation captured by the PV module. The study is carried out using a virtual prototyping platform that integrates, into the mechatronic concept, the commercial software packages ADAMS (for designing the mechanical device) and EASY5 (for designing the control system).

Title: The Rebound of Impact with Granular and Plastic Surface
Authors: Ahmet Faruk Akhan; Dan B Marghitu
Affiliation: Motion Capture Laboratory, Department of Mechanical Engineering Auburn University
Abstract: The study aims to investigate the normal and oblique impact of a sphere (tennis ball) on a granular surface (clay) and two different plastic tape lines. In this research, we model the impact force with a mathematical elasto-plastic force model, and a differential approach is used. The model is applied for the impact with granular material (green clay) and plastic surfaces (line tapes). We investigated the normal and oblique impact dynamics of a sphere, a tennis ball. The impact duration is divided into two phases: compression with an elastoplastic force and restitution with an elastic force. The laboratory experiments in various configurations are recorded with a high frame-per-second camera and analyzed using image processing methods. The mathematical model for the impact with rebounds is verified with the experimental set-up for the considered surfaces. The viscoelastic and the elastic forces agree well with the experimental data. The impact parameters are compared between the granular surface and plastic tapes. The ANOVA test suggests a robust statistical significance in the coefficient of restitution between granular surfaces and plastic tapes. Our force model for impact performs well, and the impact response of the sphere on the granular surface and the plastic line tapes are significantly different.

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