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: closed (15 June 2023) | Viewed by 36759

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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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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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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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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)
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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

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Department of Civil Engineering, University of Porto, 4200-465 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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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

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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
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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 (18 papers)

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Research

16 pages, 754 KiB  
Article
Asymptotic Consideration of Rayleigh Waves on a Coated Orthorhombic Elastic Half-Space Reinforced Using an Elastic Winkler Foundation
by Ali M. Mubaraki
Math. Comput. Appl. 2023, 28(6), 109; https://doi.org/10.3390/mca28060109 - 15 Nov 2023
Viewed by 1107
Abstract
This article derives approximate formulations for Rayleigh waves on a coated orthorhombic elastic half-space with a prescribed vertical load acting as an elastic Winkler foundation. In addition, perfect continuity conditions are imposed between the coating layer and the substrate, while suitable decaying conditions [...] Read more.
This article derives approximate formulations for Rayleigh waves on a coated orthorhombic elastic half-space with a prescribed vertical load acting as an elastic Winkler foundation. In addition, perfect continuity conditions are imposed between the coating layer and the substrate, while suitable decaying conditions are slated along the infinite depth of the half-space. The effect of the thin layer is modeled using appropriate effective boundary conditions within the long-wave limit. By applying the Radon transform and using the perturbation method, the derived model successfully captures the physical characteristics of elastic surface waves in coated half-spaces. The model consists of a pesudo-static elliptic equation decaying over the interior of the half-space and a singularly perturbed hyperbolic equation with a pseudo-differential operator. The pseudo-differential equation gives the approximate dispersion of surface waves on the coated half-space structure and is analyzed numerically at the end. Full article
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17 pages, 10059 KiB  
Article
Finite Element Analysis of Hierarchical Metamaterial-Based Patterns for Generating High Expansion in Skin Grafting
by Vivek Gupta and Arnab Chanda
Math. Comput. Appl. 2023, 28(4), 89; https://doi.org/10.3390/mca28040089 - 01 Aug 2023
Viewed by 942
Abstract
Burn injuries are very common due to heat, accidents, and fire. Split-thickness skin grafting technique is majorly used to recover the burn sites. In this technique, the complete epidermis and partial dermis layer of the skin are used to make grafts. A small [...] Read more.
Burn injuries are very common due to heat, accidents, and fire. Split-thickness skin grafting technique is majorly used to recover the burn sites. In this technique, the complete epidermis and partial dermis layer of the skin are used to make grafts. A small amount of skin is passed into the mesher to create an incision pattern for higher expansion. These grafts are transplanted into the burn sites with the help of sutures for recovering large burn areas. Presently, the maximum expansion possible with skin grafting is very less (<3), which is insufficient for covering larger burn area with a small amount of healthy skin. This study aimed to determine the possibility of employing innovative auxetic skin graft patterns and traditional skin graft patterns with three levels of hierarchy. Six different hierarchical skin graft designs were tested to describe the biomechanical properties. The meshing ratio, Poisson’s ratio, expansion, and induced stresses were quantified for each graft model. The computational results indicated that the expansion potential of the 3rd order auxetic skin graft was highest across all the models. These results are expected to improve burn surgeries and promote skin transplantation research. Full article
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19 pages, 12377 KiB  
Article
Effect of Adhesive Materials in Re-Attachment of Crown and Crown–Root Fractures of Permanent Maxillary Anterior Tooth: A Computational Study
by Anshika Garg, Shubham Gupta, Nitesh Tewari, Sukeshana Srivastav and Arnab Chanda
Math. Comput. Appl. 2023, 28(2), 41; https://doi.org/10.3390/mca28020041 - 10 Mar 2023
Cited by 3 | Viewed by 1704
Abstract
Traumatic dental injuries (TDI) are frequent among individuals of all ages, with a prevalence ranging from 12–22%, with crown and crown–root fractures being the most common. Fragment reattachment using light-cured nanocomposites is the recommended method for the management of these fractures. Though there [...] Read more.
Traumatic dental injuries (TDI) are frequent among individuals of all ages, with a prevalence ranging from 12–22%, with crown and crown–root fractures being the most common. Fragment reattachment using light-cured nanocomposites is the recommended method for the management of these fractures. Though there are several clinical studies that have assessed the efficacy of such materials, an in-silico characterization of the effects of traumatic forces on the re-attached fragments has never been performed. Hence, this study aimed to evaluate the efficacy of various adhesive materials in crown and crown–root reattachments through computational modelling. A full-scale permanent maxillary anterior tooth model was developed by segmenting 3D scanned cone beam computed tomography (CBCT) images of the pulp, root, and enamel precisely. The full-scale 3D tooth model was then subjected to a novel numerical cutting operation to describe the crown and crown–root fractures. The fractured tooth models were then filled computationally with three commonly used filler (or adhesive) materials, namely flowable composite, resin cement, and resin adhesive, and subjected to masticatory and traumatic loading conditions. The flowable composite demonstrated a statistically significant difference and the lowest produced stresses when subjected to masticatory loading. Resin cement demonstrated reduced stress values for crown–root fractures that were masticatory loaded after being reattached using adhesive materials. During traumatic loading, resin cement demonstrated lower displacements and stress values across both fractures. The novel findings reported in this study are anticipated to assist dentists in selecting the most appropriate adhesive materials that induce the least stress on the reattached tooth when subjected to second trauma, for both crown and crown–root fractures. Full article
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18 pages, 2006 KiB  
Article
Temperature Patterns in TSA for Different Frequencies and Material Properties: A FEM Approach
by Guilherme Duarte, Ana Neves and António Ramos Silva
Math. Comput. Appl. 2023, 28(1), 8; https://doi.org/10.3390/mca28010008 - 06 Jan 2023
Viewed by 1612
Abstract
Thermography techniques are gaining popularity in structural integrity monitoring and analysis of mechanical systems’ behavior because they are contactless, non-intrusive, rapidly deployable, applicable to structures under harsh environments, and can be performed on-site. More so, the use of image optical techniques has grown [...] Read more.
Thermography techniques are gaining popularity in structural integrity monitoring and analysis of mechanical systems’ behavior because they are contactless, non-intrusive, rapidly deployable, applicable to structures under harsh environments, and can be performed on-site. More so, the use of image optical techniques has grown quickly over the past several decades due to the progress in the digital camera, infrared camera, and computational power. This work focuses on thermoelastic stress analysis (TSA), and its main goal was to create a computational model based on the finite element method that simulates this technique, to evaluate and quantify how the changes in material properties, including orthotropic, affect the results of the stresses obtained with TSA. The numeric simulations were performed for two samples, compact and single lap joints. when comparing the numeric model developed with previous laboratory tests, the results showed a good representation of the stress test for both samples. The created model is applicable to various materials, including fiber-reinforced composites. This work also highlights the need to perform laboratory tests using anisotropic materials to better understand the TSA potential and improve the developed models. Full article
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7 pages, 283 KiB  
Article
Modeling of Perforated Piezoelectric Plates
by Houari Mechkour
Math. Comput. Appl. 2022, 27(6), 100; https://doi.org/10.3390/mca27060100 - 22 Nov 2022
Cited by 1 | Viewed by 1086
Abstract
In this article, we are interested in the behavior of a three-dimensional model of periodic perforated piezoelectric plate, when the thickness h of the plate and the size ε of the holes are small. We study the dependence of displacements and electric potential [...] Read more.
In this article, we are interested in the behavior of a three-dimensional model of periodic perforated piezoelectric plate, when the thickness h of the plate and the size ε of the holes are small. We study the dependence of displacements and electric potential on h and ε, and give equivalent limits when h and ε tend towards zero. We compute analytical formulae for all effective properties of the periodic perforated piezoelectric plate. Full article
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27 pages, 2770 KiB  
Article
On the Use of High-Order Shape Functions in the SAFE Method and Their Performance in Wave Propagation Problems
by Elyas Mirzaee Kakhki, Jalil Rezaeepazhand, Fabian Duvigneau, Lotfollah Pahlavan, Resam Makvandi, Daniel Juhre, Majid Moavenian and Sascha Eisenträger
Math. Comput. Appl. 2022, 27(4), 63; https://doi.org/10.3390/mca27040063 - 25 Jul 2022
Viewed by 2587
Abstract
In this research, high-order shape functions commonly used in different finite element implementations are investigated with a special focus on their applicability in the semi-analytical finite element (SAFE) method being applied to wave propagation problems. Hierarchical shape functions (p-version of the [...] Read more.
In this research, high-order shape functions commonly used in different finite element implementations are investigated with a special focus on their applicability in the semi-analytical finite element (SAFE) method being applied to wave propagation problems. Hierarchical shape functions (p-version of the finite element method), Lagrange polynomials defined over non-equidistant nodes (spectral element method), and non-uniform rational B-splines (isogeometric analysis) are implemented in an in-house SAFE code, along with different refinement strategies such as h-, p-, and k-refinement. Since the numerical analysis of wave propagation is computationally quite challenging, high-order shape functions and local mesh refinement techniques are required to increase the accuracy of the solution, while at the same time decreasing the computational costs. The obtained results reveal that employing a suitable high-order basis in combination with one of the mentioned mesh refinement techniques has a notable effect on the performance of the SAFE method. This point becomes especially beneficial when dealing with applications in the areas of structural health monitoring or material property identification, where a model problem has to be solved repeatedly. Full article
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21 pages, 3847 KiB  
Article
An Efficient Orthogonal Polynomial Method for Auxetic Structure Analysis with Epistemic Uncertainties
by Shengwen Yin, Haogang Qin and Qiang Gao
Math. Comput. Appl. 2022, 27(3), 49; https://doi.org/10.3390/mca27030049 - 02 Jun 2022
Cited by 1 | Viewed by 1798
Abstract
Traditional approaches used for analyzing the mechanical properties of auxetic structures are commonly based on deterministic techniques, where the effects of uncertainties are neglected. However, uncertainty is widely presented in auxetic structures, which may affect their mechanical properties greatly. The evidence theory has [...] Read more.
Traditional approaches used for analyzing the mechanical properties of auxetic structures are commonly based on deterministic techniques, where the effects of uncertainties are neglected. However, uncertainty is widely presented in auxetic structures, which may affect their mechanical properties greatly. The evidence theory has a strong ability to deal with uncertainties; thus, it is introduced for the modelling of epistemic uncertainties in auxetic structures. For the response analysis of a typical double-V negative Poisson’s ratio (NPR) structure with epistemic uncertainty, a new sequence-sampling-based arbitrary orthogonal polynomial (SS-AOP) expansion is proposed by introducing arbitrary orthogonal polynomial theory and the sequential sampling strategy. In SS-AOP, a sampling technique is developed to calculate the coefficient of AOP expansion. In particular, the candidate points for sampling are generated using the Gauss points associated with the optimal Gauss weight function for each evidence variable, and the sequential-sampling technique is introduced to select the sampling points from candidate points. By using the SS-AOP, the number of sampling points needed for establishing AOP expansion can be effectively reduced; thus, the efficiency of the AOP expansion method can be improved without sacrificing accuracy. The proposed SS-AOP is thoroughly investigated through comparison to the Gaussian quadrature-based AOP method, the Latin-hypercube-sampling-based AOP (LHS-AOP) method and the optimal Latin-hypercube-sampling-based AOP (OLHS-AOP) method. Full article
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22 pages, 12258 KiB  
Article
Integrated Finite Strip Computation for Modelling and Frequency Analysis of Hybrid Laminated FRP Structures
by Hamidreza Naderian, Moe M. S. Cheung, Elena Dragomirescu and Abdolmajid Mohammadian
Math. Comput. Appl. 2022, 27(3), 47; https://doi.org/10.3390/mca27030047 - 27 May 2022
Viewed by 1739
Abstract
This paper proposes an efficient numerical technique for simulating hybrid fiber-reinforced polymer (FRP) bridge systems. An integrated finite strip method (IFSM) is proposed to evaluate the free vibration performance of cable-stayed FRP bridges. The structural performance of the ultra-long span cable-stayed bridge (ULSCSB) [...] Read more.
This paper proposes an efficient numerical technique for simulating hybrid fiber-reinforced polymer (FRP) bridge systems. An integrated finite strip method (IFSM) is proposed to evaluate the free vibration performance of cable-stayed FRP bridges. The structural performance of the ultra-long span cable-stayed bridge (ULSCSB) is totally different than steel and concrete bridge structures due to the complexity of the mechanical behavior of the FRP deck. Herein, the anisotropic nature of the FRP laminated deck is considered in the analysis by introducing so-called laminate spline strips in the integrated finite strip solution. The structural interactions between all the components of the bridge can be handled using the proposed method. Column strips and cable strips are introduced and used to model the towers and cables, respectively. In addition, a straightforward scheme for modeling boundary conditions is developed. A case study is presented through which the accuracy and efficiency of the IFSM in modeling such structures, as well as in performing natural frequency analysis of long-span cable-stayed FRP bridges, are evaluated. The finite strip results are verified against the finite element analysis, and a significant enhancement in efficiency in terms of reduction in computational cost is demonstrated with the same level of accuracy. Full article
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14 pages, 3335 KiB  
Article
Microwave Characterization and Modelling of PA6/GNPs Composites
by Erika Pittella, Emanuele Piuzzi, Pietro Russo and Francesco Fabbrocino
Math. Comput. Appl. 2022, 27(3), 41; https://doi.org/10.3390/mca27030041 - 11 May 2022
Cited by 1 | Viewed by 1990
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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21 pages, 5051 KiB  
Article
Interval-Based Computation of the Uncertainty in the Mechanical Properties and the Failure Analysis of Unidirectional Composite Materials
by Dimitris G. Sotiropoulos and Konstantinos Tserpes
Math. Comput. Appl. 2022, 27(3), 38; https://doi.org/10.3390/mca27030038 - 29 Apr 2022
Cited by 3 | Viewed by 1980
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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17 pages, 691 KiB  
Article
Theoretical and Computational Results of a Memory-Type Swelling Porous-Elastic System
by Adel M. Al-Mahdi, Mohammad M. Al-Gharabli and Mohamed Alahyane
Math. Comput. Appl. 2022, 27(2), 27; https://doi.org/10.3390/mca27020027 - 11 Mar 2022
Cited by 5 | Viewed by 2010
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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19 pages, 1567 KiB  
Article
On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay
by Armand Anthelme Nanha Djanan, Steffen Marburg and Blaise Roméo Nana Nbendjo
Math. Comput. Appl. 2022, 27(2), 20; https://doi.org/10.3390/mca27020020 - 24 Feb 2022
Cited by 1 | Viewed by 1936
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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15 pages, 896 KiB  
Article
Meshless Computational Strategy for Higher Order Strain Gradient Plate Models
by Francesco Fabbrocino, Serena Saitta, Riccardo Vescovini, Nicholas Fantuzzi and Raimondo Luciano
Math. Comput. Appl. 2022, 27(2), 19; https://doi.org/10.3390/mca27020019 - 22 Feb 2022
Cited by 3 | Viewed by 2315
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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24 pages, 1326 KiB  
Article
Numerical and Theoretical Stability Study of a Viscoelastic Plate Equation with Nonlinear Frictional Damping Term and a Logarithmic Source Term
by Mohammad M. Al-Gharabli, Adel M. Almahdi, Maher Noor and Johnson D. Audu
Math. Comput. Appl. 2022, 27(1), 10; https://doi.org/10.3390/mca27010010 - 28 Jan 2022
Cited by 5 | Viewed by 2329
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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25 pages, 348 KiB  
Article
Well-Posedness and Stability Results for a Nonlinear Damped Porous–Elastic System with Infinite Memory and Distributed Delay Terms
by Abdelkader Moumen, Djamel Ouchenane, Keltoum Bouhali and Yousif Altayeb
Math. Comput. Appl. 2021, 26(4), 71; https://doi.org/10.3390/mca26040071 - 16 Oct 2021
Viewed by 2295
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
19 pages, 3482 KiB  
Article
Simple Algebraic Expressions for the Prediction and Control of High-Temperature Annealed Structures by Linear Perturbation Analysis
by Constantino Grau Turuelo and Cornelia Breitkopf
Math. Comput. Appl. 2021, 26(2), 43; https://doi.org/10.3390/mca26020043 - 01 Jun 2021
Cited by 2 | Viewed by 2129
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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12 pages, 1000 KiB  
Article
Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method
by Muhammad Usman, Shaaban Abdallah and Mudassar Imran
Math. Comput. Appl. 2021, 26(2), 33; https://doi.org/10.3390/mca26020033 - 20 Apr 2021
Viewed by 2119
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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14 pages, 4017 KiB  
Article
Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness
by Qi-Wen Jin, Zheng Liu and Shuan-Hai He
Math. Comput. Appl. 2021, 26(2), 26; https://doi.org/10.3390/mca26020026 - 28 Mar 2021
Viewed by 2034
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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