Article
Engineering, Multidisciplinary
Paulina Stempin, Tomasz P. Pawlak, Wojciech Sumelka
Summary: Designing nano/micro-devices is challenging due to their small size and precise engineering tolerances. Existing mathematical models are not accurate enough to capture all the properties of materials at the nano/micro-scale. In this study, a new mathematical model called the space-Fractional Kirchhoff-Love Plate (s-FKLP) is proposed for composite nano/micro-plates in bending. The s-FKLP model shows closer mapping to experimental results compared to previous formulations. The research findings have implications for the design and optimization of micro-sized devices.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This article discusses the scale invariance in nonlinear fractional dynamics in continuous and discrete time approaches. It uses non-integer-order integro-differential operators and considers nonlinear integro-differential equations with Hadamard type operators of non-integer orders and periodic sequence of kicks. Exact solutions are derived without using approximations, and mappings with non-local scaling in time are obtained from proposed equations for discrete time points.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Energy & Fuels
Krzysztof Szajek, Wojciech Sumelka, Krzysztof Bekus, Tomasz Blaszczyk
Summary: This paper discusses the applicability of the space-fractional non-local formulation (sFCM) in designing one-dimensional material bodies with specific dynamic eigenvalue spectra, highlighting the importance of proper spatial distribution of material length scale and the use of an inverse optimization procedure to find adequate length scale distribution. The analysis considers an objective function reduced to a single value based on Kreisselmeier-Steinhauser formula, with the total number of eigenvalues considered being smaller than the limit derived from the ratio of the sFCM length scale to the length of the material body.
Article
Physics, Multidisciplinary
Vasily E. Tarasov
Summary: The article proposes a formulation of nonlocal electrodynamics using the integral and integro-differential operators in the Luchko form. It suggests some basic concepts and effects of general nonlocal electrodynamics, including the concept of general nonlocal charged medium (GNCM) described by Sonin kernels. The general fractional vector calculus (GFVC) is used as mathematical tools to account for nonlocality in space. It also proposes the general fractional integral and differential equations of nonlocal electrodynamics as a generalization of Maxwell's equations. The article discusses nonlocal effects caused by nonlocality in space and time and provides examples of calculating electric and magnetic fields in nonlocal media using the general nonlocal Gauss's and Ampere's circuital laws.
Article
Mathematics
Vasily E. Tarasov
Summary: This paper discusses the mechanics of continuum with general form of nonlocality in space and time. It introduces some basic concepts of nonlocal continuum mechanics. General fractional calculus (GFC) and general fractional vector calculus (GFVC) are used as mathematical tools to construct the mechanics of media with general form of nonlocality. The balance equations for mass, momentum, and energy, which describe the conservation laws for nonlocal continuum, are derived using the fundamental theorems of GFC.
Article
Mathematics, Interdisciplinary Applications
Kinda Abuasbeh, Azmat Ullah Khan Niazi, Hafiza Maria Arshad, Muath Awadalla, Salma Trabelsi
Summary: This article investigates the approximate controllability of non-linear fractional stochastic differential inclusions with non-local conditions. We establish a set of sufficient conditions for their approximate controllability and provide results in terms of controllability for the fractional stochastic control system. Our approach relies on using fractional calculus and the fixed-point theorem for multiple-valued operators. Finally, we present an illustrative example to support our findings.
FRACTAL AND FRACTIONAL
(2023)
Article
Engineering, Mechanical
Sansit Patnaik, Sai Sidhardh, Fabio Semperlotti
Summary: This study introduces a fractional-order continuum mechanics approach that can capture stiffening and softening effects in a stable manner. The method is suitable for static and free vibration analysis, able to simulate the response of Timoshenko beams or Mindlin plates.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Mathematics, Applied
Edoardo Mainini, Danilo Percivale
Summary: We investigate the Gamma-limit relationship between finite elasticity and linear elasticity under the assumption of incompressibility and Dirichlet boundary conditions. The result is applicable to a wide range of energy densities for rubber-like materials.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mechanics
Gery De Saxce
Summary: The paper proposes a paradigm shift for the variational approach to brittle fracture. It addresses both dynamics and the limit case of statics within the same framework, using a space-time principle. The focus is on modeling crack extension using the internal variable formalism and a dissipation potential, rather than Griffith's original approach based on surface area. The new formulation appears to be more adaptable and generalizable than the standard theory.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Mathematics, Applied
Marco Berardi, Giovanni Girardi
Summary: This paper presents a novel approach to mathematically frame the concept of ecological memory of plant water stress in the context of root water uptake. A non-local sink term is used to model water absorption by roots, taking into account the memory effect. An integral equation is defined to model this memory effect, with the main objective of providing conditions for the existence and uniqueness of its solution. Tailored numerical methods are implemented and numerical simulations are provided.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Engineering, Multidisciplinary
Juan Bory-Reyes, Marco Antonio Perez-de la Rosa, Yudier Pena-Perez
Summary: This work introduces a fractional generalization of the classical Moisil-Teodorescu operator, providing a concise mathematical formulation for physical systems in various branches of science and engineering. The Stillinger's formalism is combined with quaternionic analysis in a novel way, and a quaternionic reformulation of a fractional time-harmonic Maxwell system is established, demonstrating a deep relation between its solutions and those of the perturbed fractional Moisil-Teodorescu operator. Furthermore, the fractional constructions here will have further applications in areas such as hydrodynamics and magneto hydrodynamics.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Predrag Vukovic
Summary: The main objective of this paper is to prove new local fractional Hilbert-type inequalities. The general results obtained are applicable to homogeneous kernels. Furthermore, the best possible constants in terms of local fractional hypergeometric function are derived. The obtained results demonstrate that the employed method is simple and effective for solving various types of local fractional Hilbert-type inequalities.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Sansit Patnaik, Sai Sidhardh, Fabio Semperlotti
Summary: This study introduces analytical formulations and finite element solutions for a fractional-order nonlocal plate under both Mindlin and Kirchhoff formulations. By using consistent definitions for fractional-order kinematic relationships, governing equations and boundary conditions are derived based on variational principles. The fractional-order nonlocal model results in a self-adjoint and positive definite system that accepts a unique solution, with a 2D finite element model presented for solving the governing equations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Mechanics
Rafael C. Deptulski, Magdalena Dymitrowska, Djimedo Kondo
Summary: This study evaluates the use of the Corrected Smoothed Particle Hydrodynamics (CSPH) method in predicting non-local elastic effects in finite deformations. The numerical simulations show that CSPH method can capture non-local effects in dynamic conditions and have good agreement with available analytical solutions. Additionally, strain-based and stress-based formulations in CSPH lead to similar responses, and the study discusses the influence of finite and infinite support kernel functions.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2022)
Article
Mechanics
Sai Sidhardh, Sansit Patnaik, Fabio Semperlotti
Summary: This study presents a theoretical and computational framework based on fractional calculus for analyzing the nonlocal static response of cylindrical shell panels, exploring both linear and geometrically nonlinear static responses. Using the fractional finite element method, the impact of long-range interactions in curved structures is efficiently and accurately considered.
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2022)
Article
Engineering, Multidisciplinary
Andrea Francesco Russillo, Giuseppe Failla, Gioacchino Alotta, Francesco Marotti de Sciarra, Raffaele Barretta
Summary: Size-dependent dynamic responses of small-size frames are modeled and evaluated using stress-driven non-local elasticity and a consistent finite-element methodology. The exact dynamic stiffness matrix is evaluated for a two-node stress-driven nonlocal beam element, and a global dynamic stiffness matrix for an arbitrarily-shaped small-size frame is built using standard finite-element assembly procedures. The methodology is suitable for investigating free vibrations of small-size systems in Nano-Engineering.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2021)
Article
Engineering, Mechanical
Gioacchino Alotta, Giuseppe Failla
Summary: This paper introduces improved inerter-based absorbers for vibration mitigation in structural systems. By incorporating standard inerter-based devices within a rhombus truss, a significant amplification of inertance can be achieved. The design of the improved inerter-based devices is straightforward and they can be retuned by changing the geometry of the rhombus truss.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Mechanics
Roberta Santoro, Giuseppe Failla
Summary: This paper discusses the frequency response of beams in the presence of interval parameters and proposes a two-step method to calculate the bounds of all response variables. Each crack is modeled as a linearly-elastic rotational spring with uncertain-but-bounded stiffness and position parameters using the standard Euler-Bernoulli beam theory. The method relies on analytical forms for all response variables and their sensitivity functions, showing potential and accuracy in applications focusing on the frequency response of multi-cracked beams with tuned mass dampers.
Article
Mechanics
Andrea Burlon, Gioacchino Alotta, Mario Di Paola, Giuseppe Failla
Summary: This work deals with viscoelastic constitutive models involving variable-order fractional operators. Two main fractional models in the literature represent the stress-strain relation of viscoelastic materials with time-varying mechanical properties, with one of them appearing to be more meaningful. A novel formulation is proposed to effectively compute the strain response of a viscoelastic material with time-dependent mechanical properties due to any stress input, showing a clear physical meaning and a consistent application of the Boltzmann superposition principle. The paper's main contribution is to establish the relationship between the proposed formulation and the existing meaningful fractional model in the literature.
Article
Engineering, Civil
Andrea Burlon, Giuseppe Failla
Summary: In this study, a comprehensive framework is introduced to address the triply-coupled bending-torsion problem in beams with asymmetric cross section, considering warping effects and obtaining responses in frequency and time domains under arbitrary loads. The proposed approach utilizes Laplace Transform and the theory of generalized functions to derive exact solutions under proportional damping, which are easy to implement. This framework is also extended to beams with in-span transversal stiffeners, external supports, and non-proportional damping scenarios, providing a versatile tool for dynamic analysis.
THIN-WALLED STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
Andrea Francesco Russillo, Giuseppe Failla, Gioacchino Alotta
Summary: A novel concept of locally-resonant inertant plate is proposed, which can create a very large band gap in the low-frequency range through periodic inerter-based resonator structures, and it is of significant importance to structural and mechanical engineering applications.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mechanics
Andrea Francesco Russillo, Giuseppe Failla
Summary: The study introduces a novel dynamic-stiffness formulation for analyzing the dynamics of locally resonant metamaterial plates. The method accurately calculates the natural frequencies and modal responses of the plates, providing closed analytical forms for modal responses under arbitrary loading conditions assuming classical damping. The comparison with finite-element results in ABAQUS demonstrates the accuracy and effectiveness of the proposed reduced-order dynamic-stiffness formulation.
COMPOSITE STRUCTURES
(2022)
Article
Engineering, Mechanical
Andrea Francesco Russillo, Giuseppe Failla
Summary: This paper focuses on the elastic wave propagation analysis of small-size planar beam lattices, proposing two novel computational approaches and comparing their advantages. Dispersion curves for a typical lattice are calculated to highlight the role of nonlocality.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Engineering, Mechanical
Andrea Burlon, Giuseppe Failla
Summary: This study introduces a theoretical framework for calculating the dispersive properties of locally-resonant beams with beam-like resonators, and suggests that coupled bending-torsion beam-like resonators may be more efficient than uncoupled ones.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Engineering, Biomedical
Fabiana Amiri, Emanuela Bologna, Gianmarco Nuzzo, Lorenzo Moroni, Massimiliano Zingales
Summary: This paper presents a three-axial model of linear hereditariness and fractional-order calculus to describe the constitutive behavior of fibrous tissues like the meniscus. It also introduces a novel model of fractional-order poromechanics to study the evolution of diffusion phenomenon in the meniscus. A numerical application involving a 1D confined compression test is conducted to demonstrate the influence of material hereditariness on pressure drop evolution.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2023)
Article
Engineering, Civil
Andrea Francesco Russillo, Giuseppe Failla
Summary: This paper proposes an exact reduced-order dynamic-stiffness model for studying the dynamics of two-dimensional hierarchical beam lattices. The model accurately condenses the nodal degrees of freedom of the lattice structure internal to the unit cell and connected to the primary nodes, and allows for the exact modal response to external loading in both time and frequency domains. The proposed model is validated through numerical comparisons with standard finite-element solutions in ABAQUS.
THIN-WALLED STRUCTURES
(2023)
Article
Chemistry, Multidisciplinary
Emanuela Bologna, Ettore Dinoto, Francesco Di Simone, Felice Pecoraro, Sara Ragusa, Katia Siciliano, Massimiliano Zingales
Summary: In this study, a fluid-structure interaction analysis was conducted on an aneurysmatic aorta. The results showed the benefits of personalized stents/grafts in terms of blood flow and wall stress, supporting the shift towards customized stents/grafts in vascular surgery.
APPLIED SCIENCES-BASEL
(2023)
Article
Medicine, General & Internal
Ettore Dinoto, Domenico Mirabella, Francesca Ferlito, Graziella Tortomasi, Davide Turchino, Salvatore Evola, Massimiliano Zingales, Emanuela Bologna, Felice Pecoraro
Summary: The intima-media thickness (IMT) and its irregularities or ulcerations in the common carotid artery (CCA) can serve as biomarkers for cardiovascular system integrity. Total homocysteine and lipoprotein levels are commonly used for cardiovascular risk stratification. Duplex ultrasound (DUS) combined with serum biomarkers can assess atherosclerotic disease and cardiovascular risk effectively.
Article
Engineering, Civil
Gioacchino Alotta, Chiara Biondo, Agathoklis Giaralis, Giuseppe Failla
Summary: The tuned inerter damper (TID) is a new resonant vibration absorber that reduces the requirement for large secondary mass in conventional tuned mass dampers (TMDs) for seismic protection of building structures. This paper extends the application of TID to the seismic response reduction of the supporting towers of land-based wind turbines (WTs). Numerical assessment shows that installing the TID closer to the tower top and increasing the inertance and/or distance of the attachment locations improves the TID vibration suppression performance. The TID achieves significant reductions in tower top displacement, acceleration, base shear, and bending moment, outperforming a conventional TMD.
Article
Engineering, Civil
Gioacchino Alotta, Valentina Laface, Giuseppe Failla, Carlo Ruzzo, Felice Arena
Summary: This paper proposes a innovative concept of floating absorber for motion mitigation in floating wind turbines on spar supports. Extensive time-domain numerical simulations are performed to validate the effectiveness of the floating absorber in reducing the pitch motion of the floating wind turbine. The results demonstrate the great potential of the proposed concept for motion mitigation in floating wind turbines.
ENGINEERING STRUCTURES
(2023)