Article
Engineering, Multidisciplinary
Francesco Paolo Pinnola, Marzia Sara Vaccaro, Raffaele Barretta, Francesco Marotti de Sciarra
Summary: The bending behavior of systems of straight elastic beams at different scales is investigated using stress-driven nonlocal continuum mechanics, and an effective computational methodology is developed to accurately account for long-range interactions.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Computer Science, Interdisciplinary Applications
S. Ali Faghidian
Summary: The nonlocal modified gradient theory combines the frameworks of nonlocal integral elasticity and modified strain gradient theory, applied to a beam model. Nanoscopic effects are accommodated, and well-posedness of problems on bounded structural domains is confirmed. Analytical solutions and numerical illustrations are provided for flexural wave behavior in nano-sized beams, and wave propagation in carbon nanotubes is validated through molecular dynamics simulations.
JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING
(2021)
Article
Mechanics
Sai Sidhardh, Sansit Patnaik, Fabio Semperlotti
Summary: This study presents a comprehensive framework for constitutive modeling of nonlocal thermoelasticity in solids using a fractional-order approach, showing that the fractional-order model allows for the rigorous application of localized thermodynamic balance principles. Additionally, the mechanical governing equations for fractional-order solids involve self-adjoint operators and have unique solutions.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Mathematics, Applied
Aurora Angela Pisano, Paolo Fuschi, Castrenze Polizzotto
Summary: Eringen's fully nonlocal elasticity model leads to ill-posed boundary-value problems and boundary effects, but an enhanced model with a regularizing non-homogeneous local phase provides well-posed boundary-value problems without paradoxes. The enhanced model applied to beam bending is equivalent to a sixth order differential equation with variable coefficients and predicts softening size effects consistently. The influence of the length scale parameter on the beam's response is highlighted, showing a wave pattern in the response function delta(lambda) as the parameter increases.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Mechanics
Francesco P. Pinnola, Marzia S. Vaccaro, Raffaele Barretta, Francesco Marotti de Sciarra
Summary: This study investigates the stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping using stress-driven nonlocal mechanics. Damping effects are simulated by considering viscous interactions between the beam and its surrounding environment. Loadings are modeled by accounting for their random nature, providing a comprehensive description of the beam's dynamic behavior.
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
Thermodynamics
Hooman Danesh, Mahdi Javanbakht, Mohammad Mohammadi Aghdam
Summary: In this study, the bending behavior of nanoscale beams was investigated using the 1D nonlocal integral Timoshenko beam theory and the 2D nonlocal integral elasticity theory. Two types of nonlocal kernels were utilized, and the governing equations were solved using the finite element method and the COMSOL code. The results revealed the main differences and similarities between the two theories at the nanoscale. The findings can be applied to the modeling of beam problems with nonlocal effects at the nanoscale.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Materials Science, Multidisciplinary
Mahdad Fazlali, Saeed H. Moghtaderi, S. Ali Faghidian
Summary: The study investigates the softening structural behavior of stress gradient and nonlocal beams at the nanoscale, revealing that smaller-sized nano-beams exhibit a greater tendency to soften. The use of nonlocal integral elasticity model and stress gradient theory proves to be effective in describing the bending response of nano-beams.
MATERIALS RESEARCH EXPRESS
(2021)
Article
Engineering, Multidisciplinary
Zhu XiaoWu, Li Li
Summary: This study demonstrates how both cross-sectional nonlocal interactions and axial nonlocality affect the tensile behaviors of nanobars. When the length-to-height ratio is small, nonlocal interactions become significant, while in slender bars, the main nonlocal effect stems from the nonlocal cross-sectional effect. Overcoming the ill-posed problem of pure nonlocal integral elasticity can be achieved by employing both pure nonlocal integral elasticity and surface elasticity.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2021)
Article
Mechanics
R. Ansari, M. Faraji Oskouie, M. Roghani, H. Rouhi
Summary: This paper presents a nonlinear formulation for beam-type structures using stress-driven nonlocal theory within different boundary conditions. The study investigates the bending response of beams under various conditions and compares the linear and nonlinear results using a numerical method. The influences of factors such as volume fraction/distribution pattern of graphene platelets, nonlocality, elastic foundation, and geometrical parameters are examined.
Article
Mechanics
H. M. Numanoglu, H. Ersoy, O. Civalek, A. J. M. Ferreira
Summary: This article examines the free thermal vibration analysis of nanobeams surrounded by an elastic matrix using nonlocal elasticity and Timoshenko beam theories. The equation of motion for free vibration is solved by analytical method, and a weighted residue-based finite element formulation is developed for boundary conditions other than simply supported nano beams. Numerical results show the high accuracy of the nonlocal finite element formulation and the effects of size dependency and environmental factors on the dynamic behavior of nanobeams are discussed in detail.
COMPOSITE STRUCTURES
(2021)
Article
Mechanics
Lidiya Kurpa, Jan Awrejcewicz, Olga Mazur, Iryna Morachkovska
Summary: Free vibrations of orthotropic micro/nanoplates with nonclassical shape are investigated using the nonlocal elasticity theory. The Ritz method and R-function theory are used for constructing the system of coordinate functions. Linear frequencies are obtained for rectangular plates with two cutouts on opposite sides, considering different types of boundary conditions. The study also discusses the small-scale effects for various sizes of cutouts.
Article
Mathematics, Applied
Abdukomil Risbekovich Khashimov, Dana Smetanova
Summary: The article discusses third-order equations with multiple characteristics and general boundary value conditions, constructing a regular solution with known methods and proving the uniqueness of the solution using energy integrals. The existence of a solution is proved by reducing the problem to Fredholm integral equations of the second kind, utilizing Green's function and potential methods.
Article
Chemistry, Multidisciplinary
Marzia Sara Vaccaro, Francesco Paolo Pinnola, Francesco Marotti de Sciarra, Raffaele Barretta
Summary: The study introduces a new nonlocal approach by swapping the input and output fields involved in the original formulation of Wieghardt, using a displacement-driven nonlocal integral strategy to overcome inherent difficulties and issues. This new approach simplifies the integrodifferential equations governing the elastostatic problem of an inflected elastic slender beam, and involves kinematic, static, and new constitutive boundary conditions.
Article
Engineering, Multidisciplinary
Hao Dong
Summary: In this work, an innovative higher-order three-scale computational approach is developed for analyzing and simulating the nonlocal strain-stress gradient elasticity model of heterogeneous structures with multiple spatial scales. The approach decouples the fourth-order nonlocal gradient elasticity equations into new multi-scale second-order equations, and provides a unified computational framework for accurately analyzing and efficiently simulating the behavior of these structures.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mechanics
R. Barretta, S. Ali Faghidian, Francesco de Sciarra, M. S. Vaccaro
ARCHIVE OF APPLIED MECHANICS
(2020)
Article
Mechanics
Francesco P. Pinnola, Marzia S. Vaccaro, Raffaele Barretta, Francesco Marotti de Sciarra
Summary: This study investigates the stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping using stress-driven nonlocal mechanics. Damping effects are simulated by considering viscous interactions between the beam and its surrounding environment. Loadings are modeled by accounting for their random nature, providing a comprehensive description of the beam's dynamic behavior.
Article
Chemistry, Multidisciplinary
Marzia Sara Vaccaro, Francesco Paolo Pinnola, Francesco Marotti de Sciarra, Raffaele Barretta
Summary: The study introduces a new nonlocal approach by swapping the input and output fields involved in the original formulation of Wieghardt, using a displacement-driven nonlocal integral strategy to overcome inherent difficulties and issues. This new approach simplifies the integrodifferential equations governing the elastostatic problem of an inflected elastic slender beam, and involves kinematic, static, and new constitutive boundary conditions.
Article
Mechanics
Marzia Sara Vaccaro, Francesco Marotti de Sciarra, Raffaele Barretta
Summary: In this study, elastostatic problems of Bernoulli-Euler nanobeams were investigated using the stress-driven nonlocal elasticity model, resulting in the output of elastic curvature fields. It was shown that fields of elastic curvature associated with piecewise smooth source fields and bi-exponential kernels are continuously differentiable in the whole domain. The effectiveness of interface conditions was demonstrated through the solution of an exemplar assemblage of beams subjected to discontinuous and concentrated loadings and to thermal curvatures nonlocally associated with discontinuous thermal gradients.
Article
Chemistry, Multidisciplinary
Marzia Sara Vaccaro, Francesco Paolo Pinnola, Francesco Marotti de Sciarra, Raffaele Barretta
Summary: The dynamic behavior of micro- and nano-beams is investigated using nonlocal continuum mechanics, with size effects modeled by expressing elastic curvatures in terms of stress-driven local and nonlocal phases. Relevant nonlocal equations of motion for slender beams are formulated and integrated using an analytical approach. The presented strategy is applied to simple case problems of nanotechnological interest, and the validation of the proposed nonlocal methodology is provided by comparing natural frequencies with those obtained by the classical strain gradient model of elasticity. Overall, the outcomes obtained can be useful for the design and optimization of micro- and nano-electro-mechanical systems (M/NEMS).
Article
Mechanics
Marzia Sara Vaccaro, Francesco Paolo Pinnola, Francesco Marotti de Sciarra, Raffaele Barretta
Summary: This paper investigates the bending behavior of small-scale Bernoulli-Euler beams using Eringen's two-phase local/nonlocal theory of elasticity. It finds that some obtained solutions do not meet equilibrium requirements and kinematic boundary conditions, therefore cannot be assumed as solutions of the purely nonlocal theory of beam elasticity. This conclusion aligns with the known result that the elastic equilibrium problem of beams formulated by Eringen's purely nonlocal theory admits no solution.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2021)
Article
Mechanics
Raffaele Barretta, Francesco Marotti de Sciarra, Francesco P. Pinnola, Marzia S. Vaccaro
Summary: This paper investigates nonlocal hereditariness in Bernoulli-Euler beam and proposes an approach to solve the problem using non-integer order operators of fractional linear viscoelasticity for time-dependent hereditary behavior and integral stress-driven formulation for space-dependent nonlocal phenomena. The combined approaches provide a new model for simulating nonlocal viscoelastic bending problems, with application samples and parametric study showing the influences of hereditariness and nonlocal effects on mechanical bending response. The proposed formulation can be useful for designing and optimizing structures in advanced applications where local elastic theory is not applicable.
Article
Engineering, Multidisciplinary
Francesco Paolo Pinnola, Marzia Sara Vaccaro, Raffaele Barretta, Francesco Marotti de Sciarra
Summary: The bending behavior of systems of straight elastic beams at different scales is investigated using stress-driven nonlocal continuum mechanics, and an effective computational methodology is developed to accurately account for long-range interactions.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Mechanics
Francesco Paolo Pinnola, Marzia Sara Vaccaro, Raffaele Barretta, Francesco Marotti de Sciarra, Giuseppe Ruta
Summary: A challenging task in nonlocal continuum mechanics is to formulate constitutive relations for well-posed structural problems. Strategies such as using local/nonlocal mixtures of elasticity and integral models have been adopted to overcome the limitations of Eringen's pure nonlocal theory in nanostructures. This paper proposes a consistent formulation of a nonlocal elastic foundation for a Bernoulli-Euler beam, where the transverse displacements are a convex combination of reaction-driven local and nonlocal phases governed by Winkler and Wieghardt laws, respectively. The proposed integral mixture is proven to be equivalent to a more convenient differential problem with nonlocal boundary conditions, which can effectively solve nonlocal problems of beams on mixture reaction-driven continuous foundation.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Marzia Sara Vaccaro
Summary: This paper provides a consistent methodology of integral elasticity to address applicative problems of nanocomposite beams undergoing large configuration changes. The constitutive properties of nanofillers are experimentally validated and the effects of nanofillers on size-dependent structural responses are numerically investigated.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2022)
Article
Computer Science, Interdisciplinary Applications
Marzia Sara Vaccaro, Hamid M. Sedighi
Summary: In this work, the two-phase integral theory of elasticity for nano-beams is extended to model two-dimensional nano-continua. A mixture local/stress-driven nonlocal elasticity is proposed to accurately predict size effects in Kirchhoff axisymmetric nanoplates. The structural problem is governed by integro-differential equations, and the Helmholtz's averaging kernel is adopted for explicit inversion of the integral constitutive law. The presented methodology is applicable in designing and optimizing nano-electro-mechanical systems (NEMS) based on plates.
ENGINEERING WITH COMPUTERS
(2023)
Article
Engineering, Mechanical
Francesco Paolo Pinnola, Marzia Sara Vaccaro
Summary: The paper investigates the random flexural vibrations of small-scale Bernoulli-Euler beams with internal and external damping. The study is relevant in the design and optimization of structural components for smart miniaturized electromechanical systems. The proposed formulation incorporates Boltzmann superposition integral, fractional-order viscoelasticity, and an integral nonlocal formulation to account for non-conventional phenomena and size effects. The methodology is suitable for modeling and capturing the effective behavior of miniaturized devices.
PROBABILISTIC ENGINEERING MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Raffaele Barretta, Andrea Caporale, Raimondo Luciano, Marzia Sara Vaccaro
Summary: Nonlocal continuum theories are applied to investigate the mechanics of nanobeams under non-smooth fields. The study starts with the general formulation of elasticity in nanobeams based on the abstract form of nonlocal gradient theory. The equivalent differential problem is derived to determine the constitutive law, and the simplest constitutive interface conditions not involving spatial convolutions are established.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Nanoscience & Nanotechnology
Marzia S. Vaccaro, Francesco P. Pinnola, Francesco Marotti de Sciarra, Marko Canadija, Raffaele Barretta
Summary: This research investigates the size-dependent static behavior of elastic curved stubby beams using Timoshenko kinematics and stress-driven two-phase integral elasticity. The corresponding governing equations of nonlocal elasticity are established, non-classical boundary conditions are detected, and an effective coordinate-free solution procedure is proposed. The presented mixture approach is elucidated by solving simple curved small-scale beams, contributing to the design and optimization of modern sensors and actuators.
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART N-JOURNAL OF NANOMATERIALS NANOENGINEERING AND NANOSYSTEMS
(2021)
