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Computational Mechanics and Applied Mathematics
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Computational Mechanics and Applied Mathematics

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

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 8482

Special Issue Editor

Dr. Matjaz Skrinar

E-Mail Website
Guest Editor
Associate Professor, Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, FGPA, Smetanova 17, 2000 Maribor, Slovenia
Interests: computational mechanics; finite element methods

Special Issue Information

Dear Colleagues,

Structural engineering and mathematics have always existed mutually. Structural engineering deals with mechanics, providing complex adequate computational models, while mathematics provides computational solution algorithms. Structural analysis is therefore one of the most important and demanding engineering processes, as it combines several parts (proper structural computational model selection, the implementation of mathematical methods, the critical evaluation of the results with the possible modification or upgrade of the computational model and recalculation, and the execution of details following the obtained results), which, although carried out separately, lead to reliable and safe solutions as a whole. The almost natural synergy between mathematics and mechanics thus presents a potent tool in computational structural mechanics, allowing engineers to design structures reliably without the help of experiments.

The evident and rapid progress in computational mechanics in recent decades (both in mathematical models and computational algorithms) has already raised the level of knowledge through various numerical methods (such as finite volume, finite element, boundary element, and meshless methods) and simulations for various problems in the fields of computational mechanics and engineering. This progress, supported by the simultaneous development of computer technology, has allowed new models and approaches to become more comprehensive and complex (including more information and detail), fast (i.e., computationally more efficient), robust, and accurate.

Nevertheless, there is still room for improvement, and moreover, recent unfortunate natural disasters have reinforced the need for advanced and thorough constitutive modeling and structural analyses.

We therefore invite articles for submission to this Special Issue, focused on “Computational Mechanics and Applied Mathematics”. The scope of this Special Issue covers areas related to the application of new mathematical models, methods, or techniques in computational engineering mechanics, including the analytical, semi-numerical, and numerical-based computational modeling and analysis of structural engineering problems. 

Dr. Matjaz Skrinar
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

  • computational mechanics
  • structural analysis
  • numerical procedures and mathematical methods

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Published Papers (10 papers)

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Research

22 pages, 7564 KiB  
Article
Computational Modeling of Natural Convection in Nanofluid-Saturated Porous Media: An Investigation into Heat Transfer Phenomena
by Janja Kramer Stajnko, Jure Ravnik, Renata Jecl and Matjaž Nekrep Perc
Mathematics 2024, 12(23), 3653; https://doi.org/10.3390/math12233653 - 21 Nov 2024
Viewed by 237
Abstract
A numerical study was carried out to analyze the phenomenon of natural convection in a porous medium saturated with nanofluid. In the study, the boundary element method was used for computational modeling. The fluid flow through a porous matrix is described using the [...] Read more.
A numerical study was carried out to analyze the phenomenon of natural convection in a porous medium saturated with nanofluid. In the study, the boundary element method was used for computational modeling. The fluid flow through a porous matrix is described using the Darcy–Brinkman–Forchheimer momentum equation. In addition, a mathematical model for nanofluids was used, which follows a single-phase approach and assumes that the nanoparticles within a fluid can be treated as an independent fluid with effective properties. A combination of single- and sub-domain boundary element methods was used to solve the relevant set of partial differential equations. The method was originally developed for pure flow scenarios, but also proves to be effective in the context of fluid flow through porous media. The results are calculated for the case of two- and three-dimensional square cavities. In addition to various values of dimensionless control parameters, including the porous Rayleigh number (Rap), Darcy number (Da), porosity (ϕ) and nanoparticle volume fractions (φ), the effects of the inclination angle of the cavity on the overall heat transfer (expressed by the Nusselt number (Nu)) and fluid flow characteristics were investigated. The results indicate a pronounced dependence of the overall heat transfer on the introduction of nanoparticles and inclination angle. The heat transfer in a two-dimensional cavity is increased for higher values of Darcy number in the conduction flow regime, while it is suppressed for lower values of Darcy number in the Darcy flow regime. In the case of a three-dimensional cavity, increasing the volume fraction of nanoparticles leads to a decrease in heat transfer, and furthermore, increasing the inclination angle of the cavity considerably weakens the buoyancy flow. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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19 pages, 1861 KiB  
Article
Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling
by Denis Imamović and Matjaž Skrinar
Mathematics 2024, 12(21), 3327; https://doi.org/10.3390/math12213327 - 23 Oct 2024
Viewed by 639
Abstract
This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported [...] Read more.
This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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17 pages, 6405 KiB  
Article
Mathematical Modeling of the Floating Sleeper Phenomenon Supported by Field Measurements
by Mojmir Uranjek, Denis Imamović and Iztok Peruš
Mathematics 2024, 12(19), 3142; https://doi.org/10.3390/math12193142 - 8 Oct 2024
Viewed by 610
Abstract
This article aims to provide an accurate mathematical model with the minimum number of degrees of freedom for describing the floating sleeper phenomenon. This was accomplished using mathematical modeling supported by extensive field measurements of the railway track. Although the observed phenomenon is [...] Read more.
This article aims to provide an accurate mathematical model with the minimum number of degrees of freedom for describing the floating sleeper phenomenon. This was accomplished using mathematical modeling supported by extensive field measurements of the railway track. Although the observed phenomenon is very complex, the simplified single degree of freedom (SDOF) mathematical model proved accurate enough for its characterization. The progression of the deterioration of the railway track was successfully correlated to changes in the maximal dynamic factor for different types of pulse loading. The results of the presented study might enable the enhanced construction and maintenance of railroads, particularly in karst areas. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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18 pages, 1333 KiB  
Article
Strain-Rate and Stress-Rate Models of Nonlinear Viscoelastic Materials
by Claudio Giorgi and Angelo Morro
Mathematics 2024, 12(19), 3011; https://doi.org/10.3390/math12193011 - 26 Sep 2024
Viewed by 546
Abstract
The paper is devoted to the modeling of nonlinear viscoelastic materials. The constitutive equations are considered in differential form via relations between strain, stress, and their derivatives in the Lagrangian description. The thermodynamic consistency is established by using the Clausius–Duhem inequality through a [...] Read more.
The paper is devoted to the modeling of nonlinear viscoelastic materials. The constitutive equations are considered in differential form via relations between strain, stress, and their derivatives in the Lagrangian description. The thermodynamic consistency is established by using the Clausius–Duhem inequality through a procedure that involves two uncommon features. Firstly, the entropy production is regarded as a positive-valued constitutive function per se. This view implies that the inequality is in fact an equation. Secondly, this statement of the second law is investigated by using an algebraic representation formula, thus arriving at quite general results for rate terms that are usually overlooked in thermodynamic analyses. Starting from strain-rate or stress-rate equations, the corresponding finite equations are derived. It then emerges that a greater generality of the constitutive equations of the classical models, such as those of Boltzmann and Maxwell, are obtained as special cases. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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13 pages, 4945 KiB  
Article
Topology Optimization for Quasi-Periodic Cellular Structures Using Hybrid Moving Morphable Components and the Density Approach
by Pengfei Xiao, Chunping Zhou, Yongxin Qu, Yunfeng Luo and Quhao Li
Mathematics 2024, 12(15), 2401; https://doi.org/10.3390/math12152401 - 1 Aug 2024
Viewed by 679
Abstract
Porous hierarchical structures are extensively utilized in engineering for their high specific strength, enhanced corrosion resistance, and multifunctionality. Over the past two decades, multiscale topology optimization for these structures has garnered significant attention. This paper introduces a novel hybrid MMCs (Moving Morphable Components)–density [...] Read more.
Porous hierarchical structures are extensively utilized in engineering for their high specific strength, enhanced corrosion resistance, and multifunctionality. Over the past two decades, multiscale topology optimization for these structures has garnered significant attention. This paper introduces a novel hybrid MMCs (Moving Morphable Components)–density topology optimization method for quasi-periodic cellular structures. The term ‘quasi-periodic’ refers to microstructures whose different macroscopic points exhibit similar topologies with varying parameters. The primary concept involves using the MMC method to describe microstructural topology, while employing variable density to depict macro layouts. This approach leverages the advantage of MMCs in explicitly describing structural topology alongside the variable density of arbitrary microstructures. Sensitivity analyses of the optimization functions concerning design variables are shown, and a gradient optimization solver is employed to solve the optimization model. The examples effectively show the efficacy of the proposed method, illustrating that quasi-periodic cellular structures outperform single-scale solid structures. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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15 pages, 4384 KiB  
Article
Concurrent Topology Optimization of Curved-Plate Structures with Double-Sided Stiffeners
by Kai Xu, Fengtong Zhang, Yunfeng Luo and Quhao Li
Mathematics 2024, 12(14), 2213; https://doi.org/10.3390/math12142213 - 15 Jul 2024
Viewed by 767
Abstract
Due to their high specific stiffness, particularly in bending, along with their strong design capabilities, stiffened plates have become a prevalent structural solution in aerospace and various other fields. In pursuit of optimizing such structures, a topology optimization method named Heaviside-function-based directional growth [...] Read more.
Due to their high specific stiffness, particularly in bending, along with their strong design capabilities, stiffened plates have become a prevalent structural solution in aerospace and various other fields. In pursuit of optimizing such structures, a topology optimization method named Heaviside-function-based directional growth topology parameterization (H-DGTP) was proposed in our previous work. However, this approach is limited to designing planar, single-sided stiffened structures. Thus, this paper extends the scope of this method to encompass double-sided, curved, stiffened panels, presenting a topology optimization technique tailored for such configurations. Specifically, considering the position, shape of the curved panels, and the arrangement and height of the stiffeners as design variables, while prioritizing structural stiffness as the objective, a topology optimization model for double-sided curved stiffened plate structures is established, and the corresponding sensitivities of the objective with respect to the design variables are analytically derived. Numerical examples illustrate that simultaneously optimizing the position and shape of the plate, as well as the layout and height of the stiffeners on both sides of the curved plate, results in greater stiffness compared to optimizing only part of these variables, validating the necessity and effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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41 pages, 6345 KiB  
Article
A Robust Flexible Optimization Model for 3D-Layout of Interior Equipment in a Multi-Floor Satellite
by Masoud Hekmatfar, M. R. M. Aliha, Mir Saman Pishvaee and Tomasz Sadowski
Mathematics 2023, 11(24), 4932; https://doi.org/10.3390/math11244932 - 12 Dec 2023
Viewed by 1151
Abstract
Defanging equipment layout in multi-floor satellites consists of two primary tasks: (i) allocating the equipment to the satellite’s layers and (ii) placing the equipment in each layer individually. In reviewing the previous literature in this field, firstly, the issue of assigning equipment to [...] Read more.
Defanging equipment layout in multi-floor satellites consists of two primary tasks: (i) allocating the equipment to the satellite’s layers and (ii) placing the equipment in each layer individually. In reviewing the previous literature in this field, firstly, the issue of assigning equipment to layers is observed in a few articles, and regarding the layout, the non-overlapping constraint has always been a challenge, particularly for components that do not have a circular cross-section. In addition to presenting a heuristic method for allocating equipment to different layers of the satellite, this article presents a robust flexible programming model (RFPM) for the placement of equipment at different layers, taking into account the inherent flexibility of the equipment in terms of placement and the subject of uncertainty. This model is based on the existing uncertainty between the distances between pieces of cuboid equipment, which has not been addressed in any of the previous research, and by comparing its outputs with cases from past studies, we demonstrate a significantly higher efficiency related to placing the equipment and meeting the limit of non-overlapping constraints between the equipment. Finally, it would be possible to reduce the design time in the conceptual and preparatory stages, as well as the satellite’s overall size, while still satisfying other constraints such as stability and thermal limitations, moments of inertia and center of gravity. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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21 pages, 5232 KiB  
Article
An Enhanced Hybrid-Level Interface-Reduction Method Combined with an Interface Discrimination Algorithm
by Seunghee Cheon and Jaehun Lee
Mathematics 2023, 11(23), 4867; https://doi.org/10.3390/math11234867 - 4 Dec 2023
Viewed by 1034
Abstract
This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been [...] Read more.
This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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13 pages, 5264 KiB  
Article
Study of Transversely Isotropic Visco-Beam with Memory-Dependent Derivative
by Kulvinder Singh, Iqbal Kaur and Eduard-Marius Craciun
Mathematics 2023, 11(21), 4416; https://doi.org/10.3390/math11214416 - 25 Oct 2023
Cited by 2 | Viewed by 884
Abstract
Based on the modified Moore–Gibson–Thompson (MGT) model, transversely isotropic visco-thermoelastic material is investigated for frequency shift and thermoelastic damping. The Green–Naghdi (GN) III theory of thermoelasticity with two temperatures is used to express the equations that govern heat conduction in deformable bodies based [...] Read more.
Based on the modified Moore–Gibson–Thompson (MGT) model, transversely isotropic visco-thermoelastic material is investigated for frequency shift and thermoelastic damping. The Green–Naghdi (GN) III theory of thermoelasticity with two temperatures is used to express the equations that govern heat conduction in deformable bodies based on the difference between conductive and dynamic temperature acceleration. A mathematical model for a simply supported scale beam is formed in a closed form using Euler Bernoulli (EB) beam theory. We have figured out the lateral deflection, conductive temperature, frequency shift, and thermoelastic damping. To calculate the numerical values of various physical quantities, a MATLAB program has been developed. Graphical representations of the memory-dependent derivative’s influence have been made. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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23 pages, 3541 KiB  
Article
Variational Solution and Numerical Simulation of Bimodular Functionally Graded Thin Circular Plates under Large Deformation
by Xiao-Ting He, Xiao-Guang Wang, Bo Pang, Jie-Chuan Ai and Jun-Yi Sun
Mathematics 2023, 11(14), 3083; https://doi.org/10.3390/math11143083 - 12 Jul 2023
Viewed by 1044
Abstract
In this study, the variational method and numerical simulation technique were used to solve the problem of bimodular functionally graded thin plates under large deformation. During the application of the variational method, the functional was established on the elastic strain energy of the [...] Read more.
In this study, the variational method and numerical simulation technique were used to solve the problem of bimodular functionally graded thin plates under large deformation. During the application of the variational method, the functional was established on the elastic strain energy of the plate while the variation in the functional was realized by changing undetermined coefficients in the functional. As a result, the classical Ritz method was adopted to obtain the important relationship between load and maximum deflection that is of great concern in engineering design. At the same time, the numerical simulation technique was also utilized by applying the software ABAQUS6.14.4, in which the bimodular effect and functionally graded properties of the materials were simulated by subareas in tension and compression, as well as the layering along the direction of plate thickness, respectively. This study indicates that the numerical simulation results agree with those from the variational solution, by comparing the maximum deflection of the plate, which verifies the validity of the variational solution obtained. The results presented in this study are helpful for the refined analysis and optimization design of flexible structures, which are composed of bimodular functionally graded materials, while the structure is under large deformation. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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