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Mathematics
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Mathematical and Computational Methods for Mechanics and Engineering
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Mathematical and Computational Methods for Mechanics and Engineering

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 3351

Special Issue Editor

Dr. Carlos Llopis-Albert

E-Mail Website
Guest Editor
Institute of Mechanical and Biomechanical Engineering, Universitat Politècnica de València–Camino de Vera s/n, 46022 Valencia, Spain
Interests: mathematical modeling of engineering problems; mechanical engineering; robotics; computational mechanics; vehicle dynamics; energy efficiency and sustainability; transportation; multibody dynamics; finite element modeling; biomechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The field of mechanics and engineering science is rapidly evolving, with a growing emphasis on advanced mathematical and computational methods in order to address complex challenges. This Special Issue aims to bring together cutting-edge research in the application of mathematical and computational techniques to problems in mechanics and engineering science.

We invite researchers to submit original research articles, reviews, and case studies on areas including, but not limited to, the following topics:

numerical methods for mechanics; computational fluid dynamics; finite element analysis; multiscale modeling; nonlinear dynamics; optimization in engineering applications; machine learning and artificial intelligence in mechanics; computational solid mechanics; fluid–structure interaction; bioengineering applications; robotics; vehicle engineering; mathematical applications in transportation, energy, and environmental issues; and fuzzy sets and systems, decision analysis, and business technologies related to mechanics and engineering science.

The primary objectives of this Special Issue encompass (1) presenting practical mathematical and computational approaches applicable to mechanics and engineering science in real-world scenarios, (2) disseminating the most recent advancements in harnessing these pioneering technologies, and (3) exchanging the insights acquired through these endeavors.

Dr. Carlos Llopis-Albert
Guest Editor

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

  • mathematical modeling
  • computational methods
  • finite element analysis
  • numerical simulations
  • multiscale modeling
  • computational fluid dynamics
  • structural mechanics
  • machine learning
  • optimization algorithms
  • robotics and artificial intelligence

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Published Papers (3 papers)

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20 pages, 6109 KiB  
Article
Dynamic Analysis and Approximate Solution of Transient Stability Targeting Fault Process in Power Systems
by Hao Wu and Jing Li
Mathematics 2024, 12(19), 3065; https://doi.org/10.3390/math12193065 - 30 Sep 2024
Viewed by 595
Abstract
Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the [...] Read more.
Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the fault process in power systems. Firstly, based on the inherent sinusoidal coupling characteristics of the power system swing equations, a generalized polynomial matrix description in perturbation form is presented using the Taylor expansion formula. Secondly, considering the staged characteristics of the stability process in power systems, the approximate solutions of the polynomial model during and after the fault are provided using coordinate transformation and regular perturbation techniques. Then, the structural characteristics of the approximate solutions are analyzed, revealing the mathematical basis of the stable motion patterns of the power grid, and a monotonicity rule of the system’s power angle oscillation amplitude is discovered. Finally, the effectiveness of the proposed methods and analyses is further validated by numerical examples of the IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
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23 pages, 6566 KiB  
Article
Structural Shape Optimization Based on Multi-Patch Weakly Singular IGABEM and Particle Swarm Optimization Algorithm in Two-Dimensional Elastostatics
by Zhenyu Chen and Longtao Xie
Mathematics 2024, 12(10), 1518; https://doi.org/10.3390/math12101518 - 13 May 2024
Cited by 1 | Viewed by 836
Abstract
In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the [...] Read more.
In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
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15 pages, 1543 KiB  
Article
Digital Twin-Based Approach for a Multi-Objective Optimal Design of Wind Turbine Gearboxes
by Carlos Llopis-Albert, Francisco Rubio, Carlos Devece and Dayanis García-Hurtado
Mathematics 2024, 12(9), 1383; https://doi.org/10.3390/math12091383 - 1 May 2024
Viewed by 1481
Abstract
Wind turbines (WT) are a clean renewable energy source that have gained popularity in recent years. Gearboxes are complex, expensive, and critical components of WT, which are subject to high maintenance costs and several stresses, including high loads and harsh environments, that can [...] Read more.
Wind turbines (WT) are a clean renewable energy source that have gained popularity in recent years. Gearboxes are complex, expensive, and critical components of WT, which are subject to high maintenance costs and several stresses, including high loads and harsh environments, that can lead to failure with significant downtime and financial losses. This paper focuses on the development of a digital twin-based approach for the modelling and simulation of WT gearboxes with the aim to improve their design, diagnosis, operation, and maintenance by providing insights into their behavior under different operating conditions. Powerful commercial computer-aided design tools (CAD) and computer-aided engineering (CAE) software are embedded into a computationally efficient multi-objective optimization framework (modeFrontier) with the purpose of maximizing the power density, compactness, performance, and reliability of the WT gearbox. High-fidelity models are used to minimize the WT weight, volume, and maximum stresses and strains achieved without compromising its efficiency. The 3D CAD model of the WT gearbox is carried out using SolidWorks (version 2023 SP5.0), the Finite Element Analysis (FEA) is used to obtain the stresses and strains, fields are modelled using Ansys Workbench (version 2024R1), while the multibody kinematic and dynamic system is analyzed using Adams Machinery (version 2023.3, Hexagon). The method has been successfully applied to different case studies to find the optimal design and analyze the performance of the WT gearboxes. The simulation results can be used to determine safety factors, predict fatigue life, identify potential failure modes, and extend service life and reliability, thereby ensuring proper operation over its lifetime and reducing maintenance costs. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods for Mechanics and Engineering)
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