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Advances in Computational Solid Mechanics and Scientific Computing
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Advances in Computational Solid Mechanics and Scientific Computing

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

Deadline for manuscript submissions: 15 July 2024 | Viewed by 6995

Special Issue Editors

Dr. Subrat Kumar Jena

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Guest Editor
Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India
Interests: computational solid mechanics; nano and functionally graded structures; applied mathematics; computational methods; mathematical modeling; uncertainty quantification
Prof. Dr. Snehashish Chakraverty

E-Mail Website
Guest Editor
Department of Mathematics, National Institute of Technology Rourkela, Odisha 769008, India
Interests: differential equations (fractional, partial and ordinary); numerical analysis and computational methods; structural dynamics (FGM, nano); mathematical modeling and uncertainty modeling
Prof. Dr. Dineshkumar Harursampath

E-Mail Website
Guest Editor
Department of Aerospace Engineering, Indian Institute of Science, Bengaluru 560012, India
Interests: nonlinear mechanics; multifunctional composites; aerospace structures; variational asymptotic method; micro aerial vehicles.
Dr. Francesco Tornabene

grade E-Mail Website
Guest Editor
Department of Innovation Engineering, University of Salento, 73100 Lecce, Italy
Interests: theory of shells, plates, arches, and beams; generalized differential quadrature; FEM; SFEM; WFEM; IGA; SFIGA; WFIGA; advanced composite materials; functionally graded materials; nanomaterials and nanotechnology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Conducting experiments is generally quite complicated and expensive; therefore, the development of appropriate mathematical models and their solutions for the study of the static and dynamic behavior of civil, mechanical, and other engineering structures is significant concerning their applications. These problems are generally governed by linear/nonlinear differential equations which are not always possible to solve analytically. This deficiency compels us to search for various numerical/computational/artificial intelligence methods for understanding the behaviors of the said structural systems.

In view of the above, the purpose of this Special Issue is to provide computationally efficient methods to investigate the static (bending) and dynamical behaviors (vibration, buckling) of various structures in general. The Special Issue will cover various advanced problems arising in the study of the static and dynamical behaviors of the nano, FG, and nano-FG structures considering various boundary conditions, existing and new higher-order shear deformation theories, complicating effects, non-classical continuum theories, as well as with material or geometrical uncertainties.

Dr. Subrat Kumar Jena
Prof. Dr. Snehashish Chakraverty
Prof. Dr. Dineshkumar Harursampath
Dr. Francesco Tornabene
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

  • vibration
  • bending
  • buckling
  • linear elasticity
  • finite elasticity
  • computational plasticity
  • nano and FG structures
  • numerical and semi-analytical methods
  • Rayleigh–Ritz method
  • differential quadrature method
  • differential transform method
  • Galerkin’s method
  • Haar wavelet method
  • finite element method
  • boundary element method
  • artificial intelligence methods (ANN, GA, SVM)
  • uncertainty modeling

Published Papers (6 papers)

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Research

22 pages, 2271 KiB  
Article
The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations
by Mahmure Avey, Francesco Tornabene, Nigar Mahar Aslanova and Abdullah H. Sofiyev
Mathematics 2024, 12(5), 749; https://doi.org/10.3390/math12050749 - 01 Mar 2024
Viewed by 551
Abstract
The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and [...] Read more.
The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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18 pages, 1922 KiB  
Article
Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model
by Yunhe Zou and Yaser Kiani
Mathematics 2023, 11(19), 4109; https://doi.org/10.3390/math11194109 - 28 Sep 2023
Viewed by 726
Abstract
An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount [...] Read more.
An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount of GPLs may be different between the layers, which results in functionally graded media. To establish the governing equations of the plate, a quasi-3D plate model is used, which takes the non-uniform shear strains as well as normal strain through the thickness into account. With the aid of the Hamilton principle, the governing equations of the plate are established. For the case of a plate that is simply supported all around, natural frequencies are obtained using the well-known Navier solution method. The results of this study are compared with the available data in the open literature, and, after that, novel numerical results are provided to explore the effects of different parameters. It is depicted that, with the introduction of GPLs in the matrix of the composite media, the natural frequencies of the plate enhance. Also, a proper graded pattern in GPL-reinforced composite plates, i.e., an FG-X pattern, results in the maximum frequencies of the plate. In addition, the introduced quasi-3D plate theory is accurate in the estimation of the natural frequencies of thick nanocomposite plates at nanoscale. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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21 pages, 5062 KiB  
Article
The Influence of GPL Reinforcements on the Post-Buckling Behavior of FG Porous Rings Subjected to an External Pressure
by Shaoping Bi, Enming Zhang, Masoud Babaei, Francesco Tornabene and Rossana Dimitri
Mathematics 2023, 11(11), 2421; https://doi.org/10.3390/math11112421 - 23 May 2023
Cited by 2 | Viewed by 1092
Abstract
The work focuses on the post- buckling behavior of functionally graded graphene platelet (FG-GPL)-reinforced porous thick rings with open-cell internal cavities under a uniform external pressure. The generalized rule of mixture and the modified Halpin–Tsai model are here used to evaluate the effective [...] Read more.
The work focuses on the post- buckling behavior of functionally graded graphene platelet (FG-GPL)-reinforced porous thick rings with open-cell internal cavities under a uniform external pressure. The generalized rule of mixture and the modified Halpin–Tsai model are here used to evaluate the effective mechanical properties of the ring. Three types of porosity patterns are assumed together with five different GPL distributions as reinforcement across the ring thickness. The theoretical formulation relies on a 2D-plane stress linear elasticity theory and Green strain field in conjunction a virtual work principle to derive the nonlinear governing equations of the post-buckling problem. Unlike the simple ring models, 2D elasticity considers the thickness stretching. The finite element model combined with an iterative Newton–Raphson algorithm is used to obtain the post-buckling path of the ring up to the collapse. A systematic investigation evaluates the effect of the weight fraction of nanofillers, the coefficient of porosity, porosity distribution, and the GPLs distribution on the deep post-buckling path of the ring. Based on the results, it is found that the buckling value and post-buckling strength increase considerably (by approximately 80%) by increasing the weight fraction of the nanofiller of about 1%. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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26 pages, 7875 KiB  
Article
A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium
by Emad E. Ghandourah, Ahmed Amine Daikh, Samir Khatir, Abdulsalam M. Alhawsawi, Essam M. Banoqitah and Mohamed A. Eltaher
Mathematics 2023, 11(10), 2407; https://doi.org/10.3390/math11102407 - 22 May 2023
Cited by 9 | Viewed by 1047
Abstract
Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to [...] Read more.
Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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13 pages, 2733 KiB  
Article
A Machine-Learning-Based Model for Buckling Analysis of Thermally Affected Covalently Functionalized Graphene/Epoxy Nanocomposite Beams
by Farzad Ebrahimi and Hosein Ezzati
Mathematics 2023, 11(6), 1496; https://doi.org/10.3390/math11061496 - 18 Mar 2023
Cited by 3 | Viewed by 1268
Abstract
In this paper, a machine-learning model is utilized to estimate the temperature-dependent moduli of neat, thermally reduced graphene and covalently functionalized graphene/epoxy nanocomposites. In addition, the governed mathematical expressions have been used to solve the buckling problem of beams fabricated from such nanocomposites [...] Read more.
In this paper, a machine-learning model is utilized to estimate the temperature-dependent moduli of neat, thermally reduced graphene and covalently functionalized graphene/epoxy nanocomposites. In addition, the governed mathematical expressions have been used to solve the buckling problem of beams fabricated from such nanocomposites in the presence of a thermal gradient. In order to do so, an energy-based method including the shear deformable beam hypothesis is used. The beam structure is rested on the Winkler–Pasternak substrate. The reported verifications demonstrate the impressive precision of the presented ML model, as well as the buckling response of the under-study structures. Finally, in the framework of some numerical case studies, the impact of several parameters on the buckling of nanocomposite beams is depicted. The results of this study delineate that temperature has a vital role in the determination of the critical buckling load that the nanocomposite structures can endure. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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31 pages, 11173 KiB  
Article
Investigation of Size-Dependent Vibration Behavior of Piezoelectric Composite Nanobeams Embedded in an Elastic Foundation Considering Flexoelectricity Effects
by Alaa A. Abdelrahman, Mohamed S. Abdelwahed, Hani M. Ahmed, Amin Hamdi and Mohamed A. Eltaher
Mathematics 2023, 11(5), 1180; https://doi.org/10.3390/math11051180 - 27 Feb 2023
Cited by 3 | Viewed by 1384
Abstract
This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regularly squared cut-out elastic core with two piezoelectric face sheet layers. [...] Read more.
This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regularly squared cut-out elastic core with two piezoelectric face sheet layers. An analytical geometrical model is adopted to obtain the equivalent geometrical variables of the perforated core. To capture the Poisson’s ratio effect, the three-dimensional continuum mechanics adopted to express the kinematics are kinetics relations in the framework of the Euler–Bernoulli beam theory (EBBT). The nonlocal strain gradient theory is utilized to incorporate the size-dependent electromechanical effects. The Hamilton principle is applied to derive the nonclassical electromechanical dynamic equation of motion with flexoelectricity impact. A closed form solution for resonant frequencies is obtained. Numerical results explored the impacts of geometrical and material characteristics on the nonclassical electromechanical behavior of nanobeams. Obtained results revealed the significant effects of the mechanical, electrical, and elastic foundation parameters on the dynamic behavior of piezoelectric composite nanobeams. The developed procedure and the obtained results are helpful for many industrial purposes and engineering applications, such as micro/nano-electromechanical systems (MEMS) and NEMS. Full article
(This article belongs to the Special Issue Advances in Computational Solid Mechanics and Scientific Computing)
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