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Mathematics
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Mathematical Applications in Mechanical and Civil Engineering
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Mathematical Applications in Mechanical and Civil Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 August 2025 | Viewed by 3391

Special Issue Editors

Prof. Dr. Enrique Castro

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Guest Editor
Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
Interests: acoustic emissions; machine learning; signal processing; network simulation method
Dr. Manuel Conesa

E-Mail Website
Guest Editor
Department of Applied Physics and Naval Technology, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: dimensional analysis; free convection; ordinary differential equations; network method; electrical simulation; multidisciplinary tools; education in science and engineeringon, multidisciplinary tools, education in science and engineering
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gonzalo García Ros

E-Mail Website
Guest Editor
Department of Civil Engineering Department, Technical University of Cartagena, Paseo Alfonso XIII 52, 30203 Cartagena, Spain
Interests: partial differential equations; mathematical modeling; applied mathematics in civil engineering; statistical treatment of acoustic emissions; nondimensionalization of engineering problems; ground engineeringstatistical treatment of acoustic emissions; nondimensionalization of engineering problems; ground engineering
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Juan Francisco Sánchez-Pérez

E-Mail Website
Guest Editor
Department of Applied Physics and Naval Technology, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: mathematical modeling; numerical simulation; network simulation method; nondimensionalization; dimensionless groups; engineering; applied physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue invites you to present papers that solve problems of interest in the fields of mechanical and civil engineering, through the application of different mathematical methodologies.

The mathematical modeling, analysis, and optimization of mechanical and civil engineering systems are usually required to design, implement, or build safer, more efficient, and sustainable systems, machines, or structures; therefore, it is necessary to use, develop, and evaluate mathematical methods that provide us with new capacities.

The main objective is to propose and apply mathematical tools to the mathematical modeling, analysis, and optimization of mechanical and civil engineering systems that provide us with a better understanding of them. Any topic related to this objective is welcome, but a list of potential applications includes the following:

  • Structural analysis and optimization;
  • Structural dynamics simulation and analysis;
  • Transport modeling and analysis;
  • Acoustic and vibration modeling and analysis;
  • Mathematical applications in soil mechanics;
  • Computational fluid dynamics;
  • Mathematical methods for condition monitoring analysis;
  • Numerical simulation of heat transfer problems;
  • Computational fracture mechanics;
  • Artificial intelligence and machine learning in mechanical and civil engineering applications;
  • Signal processing in mechanical and civil engineering systems.

We would like to encourage researchers to contribute their state-of-the-art research to this Special Issue and provide novel mathematical approaches to the mechanical and civil engineering community.

Prof. Dr. Enrique Castro
Dr. Manuel Conesa
Prof. Dr. Gonzalo García Ros
Prof. Dr. Juan Francisco Sánchez-Pérez
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

  • optimization
  • computational and numerical methods
  • signal processing
  • machine learning
  • mathematical modeling
  • control
  • engineering problems
  • dimensional analysis

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

19 pages, 3884 KiB  
Article
Theoretical Study on the Failure of Rocks with Preexisting Cracks Considering the Extension of the Crack Tip Plastic Zone
by Xuegui Zheng, Wei Gao, Xin Chen and Xu Wang
Mathematics 2025, 13(5), 718; https://doi.org/10.3390/math13050718 - 23 Feb 2025
Viewed by 380
Abstract
Rock failure, which causes instability in rock engineering, is an engineering accident that generally occurs through the coalescence of the preexisting cracks in rocks. Therefore, it is very important to research the coalescence of rock cracks to prevent rock engineering accidents. Based on [...] Read more.
Rock failure, which causes instability in rock engineering, is an engineering accident that generally occurs through the coalescence of the preexisting cracks in rocks. Therefore, it is very important to research the coalescence of rock cracks to prevent rock engineering accidents. Based on the mechanical theories of elastoplastic mechanics and fracture mechanics (the generalized Drucker–Prager (D-P) yield criterion and the core concept of the Kachanov method), the propagation of the plastic zones at rock crack tips affected by far-field uniform pressures is theoretically researched considering the interaction of two collinear cracks of unequal length. Moreover, for two cases of two cracks of equal length and unequal length in rocks, the basic laws of crack coalescence by the propagation of the plastic zones at rock crack tips are first studied, and the suggested threshold values of crack spacing for crack coalescence in rocks are provided. The results show that, for equal-length cracks, as the crack spacing decreases, the cracks propagate by a quadratic polynomial function, and the threshold is 0.2 of the ratio of crack spacing to crack length. Moreover, for unequal-length cracks, as the crack spacing decreases, the cracks propagate by a linear function, and the threshold is 0.3 of the ratio of crack spacing to secondary crack length. Finally, using the numerical simulation of a rock slope including equal-length and unequal-length cracks, and a laboratory test with a rock-like material specimen including unequal-length cracks, the main conclusions of the abovementioned theoretical studies have been verified. In this study, although the basic law of crack coalescence is first studied and the threshold value of crack coalescence is suggested first, the researched crack morphology and rock properties are relatively simple. Full article
(This article belongs to the Special Issue Mathematical Applications in Mechanical and Civil Engineering)
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15 pages, 2007 KiB  
Article
Assessing Air-Pocket Pressure Peaks During Water Filling Operations Using Dimensionless Equations
by Vicente S. Fuertes-Miquel, Oscar E. Coronado-Hernández, Francisco J. Sánchez-Romero, Manuel Saba and Modesto Pérez-Sánchez
Mathematics 2025, 13(2), 267; https://doi.org/10.3390/math13020267 - 15 Jan 2025
Viewed by 609
Abstract
Air pockets can become trapped at high points in pipelines with irregular profiles, particularly during service interruptions. The resulting issues, primarily caused by peak pressures generated during pipeline filling, are a well-documented topic in the literature. However, it is surprising that this subject [...] Read more.
Air pockets can become trapped at high points in pipelines with irregular profiles, particularly during service interruptions. The resulting issues, primarily caused by peak pressures generated during pipeline filling, are a well-documented topic in the literature. However, it is surprising that this subject has not received comprehensive attention. Using a model developed by the authors, this paper identifies the key parameters that define the phenomenon, presenting equations in a dimensionless format. The main advantage of this study lies in the ability to easily compute pressure surges without the need to solve a complex system of differential and algebraic equations. Numerous cases of filling operations were analysed to obtain dimensionless charts that can be used by water utilities to compute pressure surges during filling operations. Additionally, it provides charts that facilitate the rapid and reasonably accurate estimation of peak pressures. Depending on their transient characteristics, pressure peaks are either slow or fast, with separate charts provided for each type. A practical application involving a water pipeline with an irregular profile demonstrates the model’s effectiveness, showing strong agreement between calculated and chart-predicted (proposed methodology) values. This research provides water utilities with the ability to select the appropriate pipe’s resistance class required for water distribution systems by calculating the pressure peak value that may occur during filling procedures. Full article
(This article belongs to the Special Issue Mathematical Applications in Mechanical and Civil Engineering)
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68 pages, 5954 KiB  
Article
Mechanical and Civil Engineering Optimization with a Very Simple Hybrid Grey Wolf—JAYA Metaheuristic Optimizer
by Chiara Furio, Luciano Lamberti and Catalin I. Pruncu
Mathematics 2024, 12(22), 3464; https://doi.org/10.3390/math12223464 - 6 Nov 2024
Viewed by 1615
Abstract
Metaheuristic algorithms (MAs) now are the standard in engineering optimization. Progress in computing power has favored the development of new MAs and improved versions of existing methods and hybrid MAs. However, most MAs (especially hybrid algorithms) have very complicated formulations. The present study [...] Read more.
Metaheuristic algorithms (MAs) now are the standard in engineering optimization. Progress in computing power has favored the development of new MAs and improved versions of existing methods and hybrid MAs. However, most MAs (especially hybrid algorithms) have very complicated formulations. The present study demonstrated that it is possible to build a very simple hybrid metaheuristic algorithm combining basic versions of classical MAs, and including very simple modifications in the optimization formulation to maximize computational efficiency. The very simple hybrid metaheuristic algorithm (SHGWJA) developed here combines two classical optimization methods, namely the grey wolf optimizer (GWO) and JAYA, that are widely used in engineering problems and continue to attract the attention of the scientific community. SHGWJA overcame the limitations of GWO and JAYA in the exploitation phase using simple elitist strategies. The proposed SHGWJA was tested very successfully in seven “real-world” engineering optimization problems taken from various fields, such as civil engineering, aeronautical engineering, mechanical engineering (included in the CEC 2020 test suite on real-world constrained optimization problems) and robotics; these problems include up to 14 optimization variables and 721 nonlinear constraints. Two representative mathematical optimization problems (i.e., Rosenbrock and Rastrigin functions) including up to 1000 variables were also solved. Remarkably, SHGWJA always outperformed or was very competitive with other state-of-the-art MAs, including CEC competition winners and high-performance methods in all test cases. In fact, SHGWJA always found the global optimum or a best cost at most 0.0121% larger than the target optimum. Furthermore, SHGWJA was very robust: (i) in most cases, SHGWJA obtained a 0 or near-0 standard deviation and all optimization runs practically converged to the target optimum solution; (ii) standard deviation on optimized cost was at most 0.0876% of the best design; (iii) the standard deviation on function evaluations was at most 35% of the average computational cost. Last, SHGWJA always ranked 1st or 2nd for average computational speed and its fastest optimization runs outperformed or were highly competitive with their counterpart recorded for the best MAs. Full article
(This article belongs to the Special Issue Mathematical Applications in Mechanical and Civil Engineering)
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