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Numerical and Computational Methods in Structural Engineering and Mechanics
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Numerical and Computational Methods in Structural Engineering and Mechanics

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

Deadline for manuscript submissions: 20 December 2024 | Viewed by 9150

Special Issue Editors

Prof. Dr. Joaquim Infante Barbosa

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Guest Editor
1. CIMOSM, ISEL—Centro de Investigação em Modelação e Optimização de Sistemas Multifuncionais, Instituto Superior de Engenharia de Lisboa, 1959-007 Lisboa, Portugal
2. IDMEC, IST—Instituto de Engenharia Mecânica, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Interests: structural mechanics; finite element analysis; structural optimization; composite materials; numerical computation; symbolic computation
Special Issues, Collections and Topics in MDPI journals
Dr. José Alberto Rodrigues

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Guest Editor
1. CIMA, Department of Mathematics, ISEL-Higher Institute of Engineering of Lisbon, Lisbon, Portugal
2. CIMOSM—Centro de Investigação em Modelação e Otimização de Sistemas Multifuncionais, ISEL/IPL, Lisbon, Portugal
Interests: mathematical analysis; mathematical modeling; finite element method; isogeometric analysis; physics-informed neural networks; image processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many complex problems arising from different areas of science and engineering can be successfully studied by applying mathematical models, demonstrating the multidisciplinary nature of mathematical modeling. In this process, a wide variety of issues are usually addressed in order to obtain robust and accurate numerical schemes.

Thus, this Special Issue aims to bring together modeling approaches that consider mathematical models, serving as a reference to existing structural engineering and mechanics problems.

The key problems addressed in this issue are also the automation and systematization of complex mechanical problems enabling significant time savings, the advantages of merging numerical and computational facets of the problems’ solving process and the development of hybrid analytical-numerical techniques. Topics of interest include (but are not limited to) the following:

  • Design of robust computational methods and simulations;
  • Development of parameter fitting methods and inverse problem strategies in ordinary and partial differential equations;
  • Numerical simulation in structural engineering;
  • Design optimization of complex structural systems;
  • Computational methods in mathematics and structural engineering;
  • Integrated numerical/computational methods.

Prof. Dr. Joaquim Infante Barbosa
Dr. José Alberto Rodrigues
Guest Editors

Manuscript Submission Information

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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

  • structural engineering
  • mechanical problems
  • fluid-structure interactions
  • soil-structure interactions
  • structural reliability
  • mathematical modeling
  • numerical schemes
  • optimization
  • control methods
  • ordinary differential equations
  • partial differential equations

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Published Papers (7 papers)

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Research

26 pages, 1793 KiB  
Article
Numerical Simulation of Shock Wave in Gas–Water Interaction Based on Nonlinear Shock Wave Velocity Curve
by Zongduo Wu, Dapeng Zhang, Jin Yan, Jianhua Pang and Yifang Sun
Mathematics 2024, 12(20), 3268; https://doi.org/10.3390/math12203268 - 18 Oct 2024
Viewed by 441
Abstract
In a gas–water interaction problem, the nonlinear relationship between shock wave velocity is introduced into a Hugoniot curve, and a Mie–Grüneisen Equation of state (EOS) is established by setting the Hugoiot curve as the reference state. Unlike other simple EOS based on the [...] Read more.
In a gas–water interaction problem, the nonlinear relationship between shock wave velocity is introduced into a Hugoniot curve, and a Mie–Grüneisen Equation of state (EOS) is established by setting the Hugoiot curve as the reference state. Unlike other simple EOS based on the thermodynamics laws of gas (such as the Tait EOS), the Mie–Grüneisen EOS uses reference states to cover an adiabatic impact relationship and considers the thermodynamics law separately. However, the expression of the EOS becomes complex, and it is not adaptive to many methods. A multicomponent Mie–Grüneisen mixture model is employed in this study to conquer the difficulty of the complex form of an EOS. In this model, some coefficients in the Mie–Grüneisen EOS are regarded as variables and solved using newly constructed equations. The performance of the Mie–Grüneisen mixture model in the gas–water problem is tested by low-compression cases and high-compression cases. According to these two tests, it is found that the numerical solutions of the shock wave under the Mie–Grüneisen EOS agrees with empirical data. When compared to other simple-form EOSs, it is seen that the Mie–Grüneisen EOS has slight advantages in the low-compression case, but it plays an important role in the high-compression case. The comparison results show that the solution of the simple-form EOS clearly disagrees with the empirical data. A further study shows that the gap between the Mie–Grüneisen EOS and other simple-form EOSs becomes larger as the initial pressure and particle velocity increase. The impact effects on the pressure, density and particle velocity are studied. Moreover, the gas–water interaction in a spherical coordinate plane and a two-dimensional coordinate is a significant part of our work. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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18 pages, 7899 KiB  
Article
Research on Auxetic Lattice Structure for Impact Absorption in Machines and Mechanisms
by Levente Széles, Richárd Horváth and Livija Cveticanin
Mathematics 2024, 12(13), 1983; https://doi.org/10.3390/math12131983 - 27 Jun 2024
Cited by 1 | Viewed by 739
Abstract
In this paper, a new type of filled doubly re-entrant auxetic lattice structure for application in damping and energy absorption devices is considered. The structure is modeled to give protection for machines and mechanisms of intensive impact. The suggested structure is the modified [...] Read more.
In this paper, a new type of filled doubly re-entrant auxetic lattice structure for application in damping and energy absorption devices is considered. The structure is modeled to give protection for machines and mechanisms of intensive impact. The suggested structure is the modified version of the auxetic one with silicone fillings. The unit of the structure is assumed as a re-entrant hexagon with four quadrangular absorbers. For the assumed model of unit, the deformation properties and the Poisson’s ratio were computed. The obtained results were experimentally tested. Specimens of filled and unfilled structures were investigated under quasi-static compression. The measured results show that the energy dissipation is more than two times higher for filled structure than for unfilled ones. In the filled structure, the absorber’s rigidity has the crucial role. If the rigidity is small, the absorber, inside the unit, continues to deform from rectangle into rhomboid. Otherwise, if the rigidity is high, units with absorbers form a beam-like structure that buckles and shows high energy absorption effect. The experimentally obtained results are in good agreement with the theoretical ones. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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16 pages, 13482 KiB  
Article
A p-Refinement Method Based on a Library of Transition Elements for 3D Finite Element Applications
by Adnan Shahriar and Ahmed Jenan Mostafa
Mathematics 2023, 11(24), 4954; https://doi.org/10.3390/math11244954 - 14 Dec 2023
Cited by 1 | Viewed by 1197
Abstract
Wave propagation or acoustic emission waves caused by impact load can be simulated using the finite element (FE) method with a refined high-fidelity mesh near the impact location. This paper presents a method to refine a 3D finite element mesh by increasing the [...] Read more.
Wave propagation or acoustic emission waves caused by impact load can be simulated using the finite element (FE) method with a refined high-fidelity mesh near the impact location. This paper presents a method to refine a 3D finite element mesh by increasing the polynomial order near the impact location. Transition elements are required for such a refinement operation. Three protocols are defined to implement the transition elements within the low-order FE mesh. Due to the difficulty of formulating shape functions and verification, there are no transition elements beyond order two in the current literature for 3D elements. This paper develops a complete set of transition elements that facilitate the transition from first- to fourth-order Lagrangian elements, which facilitates mesh refinement following the protocols. The shape functions are computed and verified, and the interelement compatibility conditions are checked for each element case. The integration quadratures and shape function derivative matrices are also computed and made readily available for FE users. Finally, two examples are presented to illustrate the applicability of this method. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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24 pages, 2887 KiB  
Article
Seismo-VLAB: An Open-Source Software for Soil–Structure Interaction Analyses
by Danilo S. Kusanovic, Elnaz E. Seylabi, Peyman Ayoubi, Kien T. Nguyen, Joaquin Garcia-Suarez, Albert R. Kottke and Domniki Asimaki
Mathematics 2023, 11(21), 4530; https://doi.org/10.3390/math11214530 - 3 Nov 2023
Cited by 2 | Viewed by 1982
Abstract
In the fields of structural and geotechnical engineering, improving the understanding of soil–structure interaction (SSI) effects is critical for earthquake-resistant design. Engineers and practitioners often resort to finite element (FE) software to advance this objective. Unfortunately, the availability of software equipped with boundary [...] Read more.
In the fields of structural and geotechnical engineering, improving the understanding of soil–structure interaction (SSI) effects is critical for earthquake-resistant design. Engineers and practitioners often resort to finite element (FE) software to advance this objective. Unfortunately, the availability of software equipped with boundary representation for absorbing scattered waves and ensuring consistent input ground motion prescriptions, which is necessary for accurately representing SSI effects, is currently limited. To address such limitations, the authors developed Seismo-VLAB (SVL v1.0-stable) an open-source software designed to perform SSI simulations. The methodology considers the integration of advanced techniques, including the domain decomposition method (DDM), perfectly matched layers (PMLs), and domain reduction method (DRM), in addition to parallel computing capabilities to accelerate the solution of large-scale problems. In this work, the authors provide a detailed description of the implementation for addressing SSI modeling, validate some of the SVL’s features needed for such purpose, and demonstrate that the coupled DRM–PML technique is a necessary condition for accurately solving SSI problems. It is expected that SVL provides a significant contribution to the SSI research community, offering a self-contained and versatile alternative. The software’s practical application in analyzing SSI and directionality effects on 3D structures under seismic loading demonstrates its capability to model real-world earthquake responses in structural engineering. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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18 pages, 575 KiB  
Article
Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel
by Yuhua Zhou, Yanhu Zhang, Brighton Nyasha Chirukam, Jianwei Li, Congshan Lu, Masoud Babaei and Kamran Asemi
Mathematics 2023, 11(17), 3662; https://doi.org/10.3390/math11173662 - 24 Aug 2023
Cited by 3 | Viewed by 1471
Abstract
In this paper, the free vibration response of a stiffened functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer cylindrical shell panel is studied for the first time. The shell is stiffened by both stringers and rings. Additionally, the effect of reinforcing the shell panel, [...] Read more.
In this paper, the free vibration response of a stiffened functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer cylindrical shell panel is studied for the first time. The shell is stiffened by both stringers and rings. Additionally, the effect of reinforcing the shell panel, ring and stinger with GPLs is independently studied. Halpin–Tsai relations are employed to evaluate the mechanical properties of the shell panel, rings and stringers. The first-order shear deformation shell theory, accompanied by the Lekhnitsky smeared stiffener model, using the numerical finite element method and Hamilton principle, is employed to develop the governing motion equations of the shell panel. Four different types of GPL patterns, including FG-A, FG-X, FG-O and UD, are assumed across the thickness of the shell panel, rings and stringers. The effects of different factors, including various weight fractions and patterns of GPLs nanofillers, the geometry of the shell panel and stiffeners and two displacement boundary conditions, on the natural frequencies of the shell panel, have been studied. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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16 pages, 10872 KiB  
Article
Understanding In-Line Connections Behavior from Experimental and Numerical Analyses on Rectangular and Circular Hollow Section Elements
by Calin-Ioan Birdean, Ioan Both, Ioan Mărginean and Anghel Cernescu
Mathematics 2023, 11(15), 3416; https://doi.org/10.3390/math11153416 - 5 Aug 2023
Viewed by 999
Abstract
Depending on the connection type, especially semi-rigid connections, the analyses of building structures offer accurate results function of the rigidity and ductility. The present paper analyzes the in-line connection of rectangular and circular hollow sections, categorized as semi-rigid connections, suitable for an architectural [...] Read more.
Depending on the connection type, especially semi-rigid connections, the analyses of building structures offer accurate results function of the rigidity and ductility. The present paper analyzes the in-line connection of rectangular and circular hollow sections, categorized as semi-rigid connections, suitable for an architectural design of invisible joints. For such connection the standards do not cover an explicit design method. Experimental bending tests were performed on rectangular and circular hollow sections having the end plate fixed inside the profile and bolted by four and one high-strength bolts, respectively. The joint separation represents a serviceability criterion which was monitored using digital image correlation technique. Based on experimental results, a numerical model was validated using the finite element method. After the validation of the numerical model based on the experimental results, a parametric investigation was conducted to study the influence of the access hole, the preload level, the end plate thickness, and the axial force. The results show the small influence of the bolt preload, but the end plate thickness was of major importance. A reduction of the assembly rigidity was also caused by the manhole. The study shows the feasibility of the connection configuration with the end plate positioned inside the hollow profile. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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15 pages, 4685 KiB  
Article
A Self-Evolving Neural Network-Based Finite-Time Control Technique for Tracking and Vibration Suppression of a Carbon Nanotube
by Fawaz W. Alsaade, Mohammed S. Al-zahrani, Qijia Yao and Hadi Jahanshahi
Mathematics 2023, 11(7), 1581; https://doi.org/10.3390/math11071581 - 24 Mar 2023
Cited by 2 | Viewed by 1235
Abstract
The control of micro- and nanoscale systems is a vital yet challenging endeavor because of their small size and high sensitivity, which make them susceptible to environmental factors such as temperature and humidity. Despite promising methods proposed for these systems in literature, the [...] Read more.
The control of micro- and nanoscale systems is a vital yet challenging endeavor because of their small size and high sensitivity, which make them susceptible to environmental factors such as temperature and humidity. Despite promising methods proposed for these systems in literature, the chattering in the controller, convergence time, and robustness against a wide range of disturbances still require further attention. To tackle this issue, we present an intelligent observer, which accounts for uncertainties and disturbances, along with a chatter-free controller. First, the dynamics of a carbon nanotube (CNT) are examined, and its governing equations are outlined. Then, the design of the proposed controller is described. The proposed approach incorporates a self-evolving neural network-based methodology and the super-twisting sliding mode technique to eliminate the uncertainties’ destructive effects. Also, the proposed technique ensures finite-time convergence of the system. The controller is then implemented on the CNT and its effectiveness in different conditions is investigated. The numerical simulations demonstrate the proposed method’s outstanding performance in both stabilization and tracking control, even in the presence of uncertain parameters of the system and complicated disturbances. Full article
(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)
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