Special Issue "Mathematical and Computational Modelling in Mechanics of Materials and Structures"

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 15 June 2023 | Viewed by 7608

Special Issue Editors

Prof. Dr. Nicholas Fantuzzi
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Guest Editor
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. Francesco Fabbrocino
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Guest Editor
Department of Engineering, Telematic University Pegaso, Piazza Trieste e Trento, 48, 80132 Naples, Italy
Interests: composite materials; masonry structures; numerical modeling; mechanical engineering; bridge engineering; modal analysis; dynamics; civil engineering; materials engineering; experimental characterization; concrete durability
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Prof. Dr. Marco Montemurro
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Guest Editor
Arts et Métiers ParisTech, Institut de Mécanique et d’Ingénierie (I2M) de Bordeaux CNRS UMR 5295, F-33400 Talence, France
Interests: composite materials; composite structures; anisotropy; mechanics of solid; optimization; genetic algorithms; topology optimization; NURBS curves and surfaces; reverse engineering; curve and surface fitting; inverse problems; homogenisation
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Prof. Dr. Francesca Nanni
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Guest Editor
Department of Enterprise Engineering “Mario Lucertini”, University of Rome “Tor Vergata”, and INSTM RU Roma-Tor Vergata, via del Politecnico 1, 00133 Rome, Italy
Interests: materials engineering; composite materials and nanocomposites; nanofibers and nanofillers in polymer matrices; self-aiding materials; electro-magnetic materials (shielding, absorbing)
Dr. Qun Huang
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Guest Editor
School of Civil Engineering, Wuhan University, 8 South, Road of East Lake, Wuchang, Wuhan 430072, China
Interests: multi-scale modelling; thin-walled composite structures; data-driven mechanics; finite element method; composite structures; computational methods
Dr. José A.F.O. Correia
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Guest Editor
Department of Civil Engineering, University of Porto, 4200465 Porto, Portugal
Interests: numerical modeling of engineering structures and structural components (offshore applications, steel bridges, pressure vessels, pipelines, wind turbine towers, etc.); mathematical problems in fatigue and fracture; mechanics of solids and structures; metals materials and structures; numerical fracture mechanics and crack growth; local approaches; finite element methods in structural mechanics applications; computer-aided structural integrity
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Dr. Leonardo Dassatti
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Guest Editor
Institute of Dentistry and Maxillofacial Surgery, Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Università Cattolica del Sacro Cuore, Largo Francesco Vito, 1, 00168 Rome, Italy
Interests: oral surgery; periodontology; guided bone regeneration (GBR); work-flow in implant digital dentistry; expert in design of cad-cam devices for GBR; mucogengival plastic surgery; implant dentistry
Dr. Michele Bacciocchi
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Guest Editor
Dipartimento di Economia, Scienze e Diritto (DESD), University of San Marino, Via Consiglio dei Sessanta, 47891 Dogana, 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; numerical analysis; non-local theories
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Structural design in any engineering field is led by iterative optimization processes that traditionally involve operational experience, and at the same time rely on the mathematical behavior of structural theories. In recent years, the characterization and analysis of advanced materials has become fundamental for predicting structural behavior. This is mainly due to the fact that composites and lattice structures are spreading more and more in the industry, pushing researchers towards analyzing and modeling the anisotropic and nonlocal behaviors, as well as the multi-fields, of materials and structures.

The present Special Issue focuses on two main aspects: first, the material, with its design and characterization; second, the structure, with its modelling and solution. As far as materials are concerned, lattice, anisotropic, nonlocal and multi-physics behaviors are considered. On the structures side, the Special Issue aims to attract contributions on the topics of multi-scale modeling, 3D-printed components and computer-aided structural engineering.

The guest editors of this Special Issue hope to attract and obtain the contributions of engineers, mathematicians and material scientists, among others, allowing for creating a multidisciplinary collection of innovative works and stimulating further discussions on these ground-breaking topics. Participants of the "1st International Conference on Computations for Science and Engineering" are encouraged submit their extended conference papers to this Special Issue.

Dr. Nicholas Fantuzzi
Prof. Dr. Francesco Fabbrocino
Prof. Dr. Marco Montemurro
Prof. Dr. Francesca Nanni
Dr. Qun Huang
Dr. José A.F.O. Correia
Dr. Leonardo Dassatti
Dr. Michele Bacciocchi
Guest Editors

The article processing charge (APC) is waived for well-prepared manuscripts submitted to this issue.

Keywords

  • Computational structural modeling
  • Mathematical theories for beams, plates and shells
  • Mathematical and computational approches to composites
  • Nonlocal and non-standard mathematical models in continuum mechanics
  • Mathematical formulation of materials
  • Smart and multi-field materials and structures
  • Multi-scale mathematical and computational modeling
  • Mathematical modeling of 3D-printed materials and structures
  • Applied numerical methods
  • Finite element methods
  • Mesh-free based methods
  • Mathematical modeling of bridges and large structures
  • Dynamics of materials and structures
  • Material characterization
  • Material and structural optimization
  • Lattice materials and structures
  • Computer-aided structural engineering

Published Papers (10 papers)

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Research

Article
Microwave Characterization and Modelling of PA6/GNPs Composites
Math. Comput. Appl. 2022, 27(3), 41; https://doi.org/10.3390/mca27030041 - 11 May 2022
Viewed by 239
Abstract
The interest in composite materials has increased in the last decades since they have the advantages of combining intrinsic properties of each component and offer better performance with respect to the base constituents. In particular, these kinds of materials can have different electrical [...] Read more.
The interest in composite materials has increased in the last decades since they have the advantages of combining intrinsic properties of each component and offer better performance with respect to the base constituents. In particular, these kinds of materials can have different electrical characteristics by varying the filling percentage and, therefore, they can be used in diverse applications. Thus, a detailed study of the microwave response of these composite systems is of great practical importance. In fact, the dielectric constant and loss tangent are key factors in the design of microwave components. In this frame, the outstanding properties of graphene-like fillers may be exploited to develop new very interesting materials to study and characterize. In this paper, microwave characterization of compounds, based on nylon 6 containing different percentages of graphene nanoplatelets, is carried out taking the neat matrix sample processed under the same conditions as benchmark. The measurements were carried out using two microwave systems, operating at two different frequency bands, appropriate to characterize solid and compact material samples. The achieved results, in line with limited data from the literature and from material data sheets, highlight the possibility to use the present polymers as an excellent electromagnetic interference shielding, as confirmed by full wave electromagnetic numerical simulations that were conducted with a numerical electromagnetic software. Full article
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Article
Interval-Based Computation of the Uncertainty in the Mechanical Properties and the Failure Analysis of Unidirectional Composite Materials
Math. Comput. Appl. 2022, 27(3), 38; https://doi.org/10.3390/mca27030038 - 29 Apr 2022
Viewed by 360
Abstract
An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates. The method was applied to two composite laminates: a carbon/epoxy and a glass/epoxy. The mechanical properties of the UD lamina [...] Read more.
An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates. The method was applied to two composite laminates: a carbon/epoxy and a glass/epoxy. The mechanical properties of the UD lamina were derived using simplified micromechanical equations. An uncertainty level of ±5% was assumed for the input properties of the constituents. The global minimum and maximum values of the properties were computed using an interval branch-and-bound algorithm. Interval arithmetic operations were used to evaluate the uncertainty in the Hashin-type failure criteria in a closed form. Using the closed-form uncertainties of intervals and sets of stresses obtained by finite element analysis, the uncertainty in the failure assessment was quantified for the two composite laminates. For the assumed uncertainty level of ±5%, the computed uncertainty for the mechanical properties ranges from 6.64% to 10.63% for the carbon/epoxy material and from 6.72% to 12.28% for the glass/epoxy material. For evaluating the uncertainty effect on the efficiency of failure criteria, a probability of failure function, which employs interval boundaries, was defined and proved capable of evaluating the whole spectrum of stresses. Full article
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Article
Theoretical and Computational Results of a Memory-Type Swelling Porous-Elastic System
Math. Comput. Appl. 2022, 27(2), 27; https://doi.org/10.3390/mca27020027 - 11 Mar 2022
Viewed by 551
Abstract
In this paper, we consider a memory-type swelling porous-elastic system. First, we use the multiplier method to prove explicit and general decay results to solutions of the system with sufficient regularities. These decay results are established under a very general assumption on the [...] Read more.
In this paper, we consider a memory-type swelling porous-elastic system. First, we use the multiplier method to prove explicit and general decay results to solutions of the system with sufficient regularities. These decay results are established under a very general assumption on the relaxation function and for suitable given data. We also perform several numerical tests to illustrate our theoretical decay results. Our results generalize and improve many earlier results in the literature. Full article
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Article
On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay
Math. Comput. Appl. 2022, 27(2), 20; https://doi.org/10.3390/mca27020020 - 24 Feb 2022
Viewed by 587
Abstract
The present paper aims to present the effects of late switching on (time delay) between two or three DC electrical machines characterized by limited power supplies on their fast or late self-synchronization when mounted on a rectangular plate with simply supported edges. The [...] Read more.
The present paper aims to present the effects of late switching on (time delay) between two or three DC electrical machines characterized by limited power supplies on their fast or late self-synchronization when mounted on a rectangular plate with simply supported edges. The DC electrical machines are considered here as non-ideal oscillators, rotating in the same direction and acting as an external excitation on a specific surface of the plate. The stability analysis of the whole studied system (with two machines) around the obtained fixed point is done through analytical and numerical approaches by using the generalized Lyapunov and Routh-Hurwitz criterion. The existence conditions of the fixed point and the stability conditions are derived and presented. Great attention is put on the incidence of such study on the vibrations amplitude of the plate, which are considerably reduced in some cases. It appears that the time delay induces a rapid or late synchronization observed between the DC sources. This has been observed by numerically exploring the dynamics of the system for various possibilities that could occur. Moreover, in the modelling of the system, the positions on the plate occupied by DC electrical machines are taken into account by using the Heaviside function. It is shown that, in the case of three DC electrical machines, these positions influence the time to obtain a synchronous state between the DC electrical machines. Full article
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Article
Meshless Computational Strategy for Higher Order Strain Gradient Plate Models
Math. Comput. Appl. 2022, 27(2), 19; https://doi.org/10.3390/mca27020019 - 22 Feb 2022
Viewed by 609
Abstract
The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach [...] Read more.
The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach approximating functions at collocation nodes are obtained by using radial basis functions which depend on shape parameters. The selection of such parameters can strongly influences the accuracy of the numerical technique. Therefore the authors are presenting some numerical benchmarks which involve the solution of nanoplates by employing an optimization approach for the evaluation of the undetermined shape parameters. Stability is discussed as well as numerical reliability against solutions taken for the existing literature. Full article
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Article
Numerical and Theoretical Stability Study of a Viscoelastic Plate Equation with Nonlinear Frictional Damping Term and a Logarithmic Source Term
Math. Comput. Appl. 2022, 27(1), 10; https://doi.org/10.3390/mca27010010 - 28 Jan 2022
Viewed by 630
Abstract
This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies [...] Read more.
This paper is designed to explore the asymptotic behaviour of a two dimensional visco-elastic plate equation with a logarithmic nonlinearity under the influence of nonlinear frictional damping. Assuming that relaxation function g satisfies g(t)ξ(t)G(g(t)), we establish an explicit general decay rates without imposing a restrictive growth assumption on the damping term. This general condition allows us to recover the exponential and polynomial rates. Our results improve and extend some existing results in the literature. We preform some numerical experiments to illustrate our theoretical results. Full article
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Article
Well-Posedness and Stability Results for a Nonlinear Damped Porous–Elastic System with Infinite Memory and Distributed Delay Terms
Math. Comput. Appl. 2021, 26(4), 71; https://doi.org/10.3390/mca26040071 - 16 Oct 2021
Viewed by 715
Abstract
In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between [...] Read more.
In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation. Full article
Article
Simple Algebraic Expressions for the Prediction and Control of High-Temperature Annealed Structures by Linear Perturbation Analysis
Math. Comput. Appl. 2021, 26(2), 43; https://doi.org/10.3390/mca26020043 - 01 Jun 2021
Cited by 1 | Viewed by 834
Abstract
The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the calculation of final equilibrium structures [...] Read more.
The prediction and control of the transformation of void structures with high-temperature processing is a critical area in many engineering applications. In this work, focused on the void shape evolution of silicon, a novel algebraic model for the calculation of final equilibrium structures from initial void cylindrical trenches, driven by surface diffusion, is introduced. This algebraic model provides a simple and fast way to calculate expressions to predict the final geometrical characteristics, based on linear perturbation analysis. The obtained results are similar to most compared literature data, especially, to those in which a final transformation is reached. Additionally, the model can be applied in any materials affected by the surface diffusion. With such a model, the calculation of void structure design points is greatly simplified not only in the semiconductors field but in other engineering fields where surface diffusion phenomenon is studied. Full article
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Article
Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method
Math. Comput. Appl. 2021, 26(2), 33; https://doi.org/10.3390/mca26020033 - 20 Apr 2021
Viewed by 648
Abstract
In this work, the response of a ship rolling in regular beam waves is studied. The model is one degree of freedom model for nonlinear ship dynamics. The model consists of the terms containing inertia, damping, restoring forces, and external forces. The asymptotic [...] Read more.
In this work, the response of a ship rolling in regular beam waves is studied. The model is one degree of freedom model for nonlinear ship dynamics. The model consists of the terms containing inertia, damping, restoring forces, and external forces. The asymptotic perturbation method is used to study the primary resonance phenomena. The effects of various parameters are studied on the stability of steady states. It is shown that the variation of bifurcation parameters affects the bending of the bifurcation curve. The slope stability theorems are also presented. Full article
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Article
Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness
Math. Comput. Appl. 2021, 26(2), 26; https://doi.org/10.3390/mca26020026 - 28 Mar 2021
Viewed by 772
Abstract
Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several [...] Read more.
Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several dimensionless evaluation indexes have been defined for structural robustness so far, such as the structural reliability-based redundancy index. However, these different evaluation indexes are usually based on subjective definitions, and they are also difficult to put into engineering practice. The mathematical relational model between structural reliability and structural robustness has not been established yet. This paper is a quantitative study, focusing on the mathematical relation between structural reliability and structural robustness so as to further develop the theory of structural robustness. A strain energy evaluation index for structural robustness is introduced firstly by considering the energy principle. The mathematical relation model of structural reliability and structural robustness is then derived followed by a further comparative study on sensitivity, structural damage, and random variation factor. A cantilever beam and a truss beam are also presented as two case studies. In this study, a parabolic curve mathematical model between structural reliability and structural robustness is established. A significant variation trend for their sensitivities is also observed. The complex interaction mechanism of the joint effect of structural damage and random variation factor is also reflected. With consideration of the variation trend of the structural reliability index that is affected by different degrees of structural damage (mild impairment, moderate impairment, and severe impairment), a three-stage framework for structural life-cycle maintenance management is also proposed. This study can help us gain a better understanding of structural robustness and structural reliability. Some practical references are also provided for the better decision-making of maintenance and management departments. Full article
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