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Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue...
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Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: 31 December 2024 | Viewed by 10140

Special Issue Editors

Dr. Nicholas Fantuzzi

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Department of Civil, Chemical, Environmental, and Materials Engineering, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy
Interests: modeling of offshore structures and offshore structural components; structural theories of plates and applied mathematical modeling; mechanics of solids and structures; study of composite laminated structures and advanced composite materials; fracture mechanics and crack propagation and initiation; applied numerical methods such as finite element method and mesh-free element method
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Prof. Dr. Michele Bacciocchi

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Guest Editor
DESD Department, University of San Marino, Via Consiglio dei Sessanta, 99, 47891 Dogana, Repubblica Di San Marino
Interests: finite element methods; structural mechanics; plates and beams; numerical analysis; laminated composites; multiphase composites; innovative composite materials; functionally graded materials; carbon nanotubes; non-local theories
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Eugenio Ruocco

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Guest Editor
Dipartimento di Ingegneria, University of Campania ”L. Vanvitelli”, Via Roma 28, 81031 Caserta, Italy
Interests: boundary element method; domain boundary elements
Dr. Maria Amélia Ramos Loja

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Guest Editor
1. CIMOSM—Centro de Investigação em Modelação e Otimização de Sistemas Multifuncionais, ISEL, IPL—Instituto Politécnico de Lisboa, Av. Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
2. IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenue Rovisco Pais, 1, 1049-001 Lisboa, Portugal
Interests: computational mechanics of solids; composite materials; adaptive structures; optimization; reverse engineering
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Prof. Dr. Jose Antonio Loya

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Guest Editor
Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, Avda. de la Universidad, 30, Leganés, 28911 Madrid, Spain
Interests: fracture mechanics; composite and multifunctional materials; impact engineering; shock; micro- and nanomechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is difficult to talk about mechanics without mentioning at least one contribution made by Prof. J.N. Reddy, who embraced all aspects of applied mechanics, from continuums to engineering theories.

Prof. J.N. Reddy is best known for his research on the shear deformation theories of beams, plates, and shells (which bear his name—Reddy third-order theory) that have been extended to layer-wise models also (known as Reddy layer-wise theory).

He not only worked on solid mechanics but also in other fields such as the flows of viscous fluids and non-Newtonian fluids.

Most of his research was developed using finite element method in several fields, and it has since been incorporated into well-known and extremely powerful commercial codes.

Without doubt we can say that he is a legend in applied mechanics research and at the same time his teaching methods have been recognized worldwide as outstanding.

All this has been driven by a profound passion and love that he can naturally transfer to his students and collaborators.

An enormous contribution to this wide and interesting field has been made by the research of Prof. J.N. Reddy.

Prof. J.N. Reddy is a Distinguished Professor and a Regents' Professor and has been the inaugural holder of the Oscar S. Wyatt Endowed Chair in Mechanical Engineering at Texas A&M University, College Station, Texas, USA since 1992.

He is a highly cited researcher with a Google Scholar h-index of 100, the author of 21 textbooks and over 620 journal papers, and has been a leader in engineering research and education for more than 42 years. He has delivered over 160 plenary, keynote lectures, or general invited lectures at international conferences; taught over 110 short courses on linear and nonlinear finite elements, composite materials, and nonlocal structural theories; and advised 36 postdoctoral fellows and research visitors, along with 115 graduate students.

Mathematical and Computational Applications is highly pleased to host a Special Issue honoring Prof. J.N. Reddy for his outstanding achievements in mathematical and computational approaches in applied mechanics, recognizing him as a great researcher, teacher, and person.

Prof. Dr. Nicholas Fantuzzi
Dr. Michele Bacciocchi
Prof. Dr. Eugenio Ruocco
Dr. Maria Amélia Ramos Loja
Prof. Dr. Jose Antonio Loya
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. Mathematical and Computational Applications 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 1400 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.

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Published Papers (5 papers)

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Research

19 pages, 2491 KiB  
Article
Variability on Functionally Graded Plates’ Deflection Due to Uncertainty on Carbon Nanotubes’ Properties
by Alda Carvalho, Ana Martins, Ana F. Mota and Maria A. R. Loja
Math. Comput. Appl. 2024, 29(2), 22; https://doi.org/10.3390/mca29020022 - 16 Mar 2024
Cited by 1 | Viewed by 1195
Abstract
Carbon nanotubes are widely used as material reinforcement in diverse fields of engineering. Being that their contribution is significant to improving the mean properties of the resulting materials, it is important to assess the influence of the variability on carbon nanotubes’ material and [...] Read more.
Carbon nanotubes are widely used as material reinforcement in diverse fields of engineering. Being that their contribution is significant to improving the mean properties of the resulting materials, it is important to assess the influence of the variability on carbon nanotubes’ material and geometrical properties to structures’ responses. This work considers functionally graded plates constituted by an aluminum continuous phase reinforced with single-walled or multi-walled carbon. The nanotubes' weight fraction evolution through the thickness is responsible for the plates’ functional gradient. The plates’ samples are simulated considering that only the nanotubes’ material and geometrical characteristics are affected by uncertainty. The results obtained from the multiple regression models developed allow us to conclude that the length of the nanotubes has no impact on the maximum transverse displacement of the plates in opposition to the carbon nanotubes’ weight fraction evolution, their internal and external diameters, and the Young’s modulus. The multiple regression models developed can be used as alternative prediction tools within the domain of the study. Full article
(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)
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17 pages, 2762 KiB  
Article
Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method
by Lidiya Kurpa, Francesco Pellicano, Tetyana Shmatko and Antonio Zippo
Math. Comput. Appl. 2024, 29(1), 10; https://doi.org/10.3390/mca29010010 - 29 Jan 2024
Cited by 2 | Viewed by 1919
Abstract
Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are [...] Read more.
Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz’s method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied. Full article
(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)
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13 pages, 2393 KiB  
Article
Buckling of Cracked Euler–Bernoulli Columns Embedded in a Winkler Elastic Medium
by José Antonio Loya, Carlos Santiuste, Josué Aranda-Ruiz and Ramón Zaera
Math. Comput. Appl. 2023, 28(4), 87; https://doi.org/10.3390/mca28040087 - 28 Jul 2023
Viewed by 1446
Abstract
This work analyses the buckling behaviour of cracked Euler–Bernoulli columns immersed in a Winkler elastic medium, obtaining their buckling loads. For this purpose, the beam is modelled as two segments connected in the cracked section by a mass-less rotational spring. Its rotation is [...] Read more.
This work analyses the buckling behaviour of cracked Euler–Bernoulli columns immersed in a Winkler elastic medium, obtaining their buckling loads. For this purpose, the beam is modelled as two segments connected in the cracked section by a mass-less rotational spring. Its rotation is proportional to the bending moment transmitted through the cracked section, considering the discontinuity of the rotation due to bending. The differential equations for the buckling behaviour are solved by applying the corresponding boundary conditions, as well as the compatibility and jump conditions of the cracked section. The proposed methodology allows calculating the buckling load as a function of the type of support, the parameter defining the elastic soil, the crack position and the initial length of the crack. The results obtained are compared with those published by other authors in works that deal with the problem in a partial way, showing the interaction and importance of the parameters considered in the buckling loads of the system. Full article
(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)
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18 pages, 450 KiB  
Article
Thermal–Structural Linear Static Analysis of Functionally Graded Beams Using Reddy Beam Theory
by Carlos Enrique Valencia Murillo, Miguel Ernesto Gutierrez Rivera and Luis David Celaya Garcia
Math. Comput. Appl. 2023, 28(4), 84; https://doi.org/10.3390/mca28040084 - 23 Jul 2023
Cited by 2 | Viewed by 1563
Abstract
In this work, a finite element model to perform the thermal–structural analysis of beams made of functionally graded material (FGM) is presented. The formulation is based on the third-order shear deformation theory. The constituents of the FGM are considered to vary only in [...] Read more.
In this work, a finite element model to perform the thermal–structural analysis of beams made of functionally graded material (FGM) is presented. The formulation is based on the third-order shear deformation theory. The constituents of the FGM are considered to vary only in the thickness direction, and the effective material properties are evaluated by means of the rule of mixtures. The volume distribution of the top constituent is modeled using the power law form. A comparison of the present finite element model with the numerical results available in the literature reveals that they are in good agreement. In addition, a routine to study functionally graded plane models in a commercial finite element code is used to verify the performance of the proposed model. In the present work, displacements for different values of the power law exponent and surface temperatures are presented. Furthermore, the normal stress variation along the thickness is shown for several power law exponents of functionally graded beams subjected to thermal and mechanical loads. Full article
(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)
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27 pages, 8536 KiB  
Article
Thermal Stress Formation in a Functionally Graded Al2O3-Adhesive Single Lap Joint Subjected to a Uniform Temperature Field
by Mustafa Kemal Apalak and Junuthula N. Reddy
Math. Comput. Appl. 2023, 28(4), 82; https://doi.org/10.3390/mca28040082 - 11 Jul 2023
Viewed by 1751
Abstract
This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al2O3 micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering [...] Read more.
This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al2O3 micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering the spatial derivatives of Lamé constants and the coefficient of thermal expansion for local material composition. The set of partial differential equations and mechanical boundary conditions for a two-dimensional model was reduced to a set of linear equations by means of the central finite difference approximation at each grid point of a discretized joint. The through-thickness Al2O3-adhesive composition was tailored by the functional grading concept, and the mechanical and thermal properties of local adhesive composition were predicted by Mori–Tanaka’s homogenization approach. The adherend–adhesive interfaces exhibited sharp discontinuous thermal stresses, whereas the discontinuous nature of thermal strains along bi-material interfaces can be moderated by the gradient power index, which controls the through-thickness variation of particle amount in the local adhesive composition. The free edges of the adhesive layer were also critical due to the occurrence of high normal and shear strains and stresses. The gradient power index can influence the distribution and levels of strain and stress components only for a sufficiently high volume fraction of particles. The grading direction of particles in the adhesive layer was not influential because the temperature field is uniform; namely, it can only upturn the low and high strain and stress regions so that the neat adhesive–adherend interface and the particle-rich adhesive–adherend interface can be relocated. Full article
(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)
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