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
J. Kaplunov, D. A. Prikazchikov, ab L. Prikazchikova
Summary: This paper concerns the comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. By studying an antiplane problem and considering a 1D exponential kernel, it is revealed that the solution to the differential model within Eringen's theory does not satisfy the equation of motion in nonlocal stresses. A more general differential setup is investigated, which shows that the transformation from the integral formulation to the differential one is only possible under certain conditions on nonlocal stresses. The proposed effective boundary condition supports an antiplane surface wave.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Michele Marino, Ferdinando Auricchio, Alessandro Reali, Elisabetta Rocca, Ulisse Stefanelli
Summary: The paper introduces a variational principle that combines phase-field and mixed Hu-Washizu functionals to derive traditional and novel topology optimization formulations, where material distribution quantity is either predetermined as a global constraint or minimized without constraint. Numerical solutions are obtained through mixed finite element schemes, avoiding global constraints and providing guidelines for phase-field parameter settings. The monolithic algorithm solution scheme is easily implemented, showcasing advantages in convergence studies and final design discussions in both two-dimensional and three-dimensional applications.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Artificial Intelligence
Hang Yu, Songwei Wu, Justin Dauwels
Summary: Estimating a sequence of dynamic undirected graphical models is crucial in various systems to spot trends, detect anomalies, predict vulnerability, and evaluate the impact of interventions. We propose a low-complexity tuning-free Bayesian approach, called BASS, for automatic structure learning from data.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2023)
Article
Mathematics, Applied
Lanhua Zhong, Dalong Dang, Wei Li, Zhanmei Ren, Qi Guo
Summary: The multi-peak solitons and their stability in the nonlocal nonlinear system with the sine-oscillation response were investigated. The Hermite-Gaussian-type multi-peak solitons and the ranges of the degree of nonlocality within which the solitons exist were obtained analytically using the variational approach. The stability of the multi-peak solitons was addressed by the linear stability analysis, and the upper thresholds of the peak-number of the stable solitons were determined for different Kerr coefficients.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Engineering, Mechanical
Shizhe Feng, Zhiping Xu
Summary: This study investigates the size dependence of superlubricity between single-crystal graphite flakes. Molecular dynamics simulations show that the friction force is reduced by one order of magnitude through the nucleation and propagation of dislocations and solitons. Theoretical models are developed to illustrate and predict the interfacial elastoplastic behaviors.
Article
Engineering, Civil
Jean Macedo, Jean-Michel Bergheau, Stephane Chapuliot, Eric Feulvarch, Olivier Ancelet, Antoine Martin
Summary: This article evaluates the performance of conventional constitutive models in modeling the structural ratcheting of an austenitic stainless steel structure under thermomechanical loading. The study highlights the influence of monotonic and cyclic behavior on ratcheting responses and proposes suggestions for determining constitutive models that can reproduce ratcheting responses. It is found that models employing only a few kinematic hardening are inadequate in predicting structural ratcheting. The results predicted by a simplified version of the Chaboche model proposed in this article show good agreement with experimental measurements.
THIN-WALLED STRUCTURES
(2023)
Article
Engineering, Mechanical
Shuang Shen, Zhen-Jun Yang, Hui Wang, Zhao-Guang Pang
Summary: This work theoretically studies the propagation characteristics of the tripolar breather trial solution in nonlocal nonlinear media with loss. The approximate equations of the tripolar breather parameters are obtained analytically and verified by numerical simulation. It is found that tripolar loss soliton and tripolar loss breather can be formed under suitable incident conditions. By analogy with Newton's laws of motion in classical mechanics and by studying the evolution law of the equivalent force and potential energy, the physical reasons for the periodic evolution of the tripolar breather are analyzed in depth.
NONLINEAR DYNAMICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yongzheng Zhang
Summary: In this study, a nonlocal operator method (NOM) is proposed for the dynamic analysis of (thin) Kirchhoff plates. The NOM simplifies the analysis process for thin plates and derives the dynamic governing formulation and operator energy functional using a variational principle. The Verlet-velocity algorithm is used for time discretization.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mechanics
A. Ricoeur, M. Wingen
Summary: Weak formulations of boundary value problems are derived using the method of weighted residuals or variational principles. Variational approaches are not straightforward for electrodynamical and caloric problems. This paper presents an energy-based approach for combined electrodynamic-thermomechanical problems.
Article
Mathematics, Applied
Annamaria Canino, Luigi Montoro, Berardino Sciunzi, Alessandro Trombetta
Summary: This article discusses a general class of nonlocal problems involving the fractional Laplacian and singular nonlinearities, and addresses the variational characterization of the solutions. Despite the lack of fractional Sobolev regularity in general solutions, a variational characterization of the solutions is provided through a suitable action functional.
Article
Mathematics, Interdisciplinary Applications
M. Velasco-Juan, J. Fujioka
Summary: This paper investigates two new nonlocal NLS equations, demonstrating that these models possess Lagrangian structures, with solitary wave solutions trapped near the origin and others able to escape. The collisions of breathers obeying LN2 equation are studied numerically, showing these breathers are robust solutions.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Chemistry, Physical
Zachary Pierce Bansingh, Tzu-Ching Yen, Peter D. Johnson, Artur F. Izmaylov
Summary: Measuring quantum observables by grouping terms that can be rotated to sums of Pauli z operators has been proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary transformations to rotate the state of interest, allowing for a fewer number of measurements by grouping more terms into measurable fragments. However, previous estimations did not take into account the nonunit fidelity of quantum gates implementing the additional transformations. Through a simple error model, it is confirmed that the number of measurements in schemes using nonlocal qubit rotations are still lower than those using local qubit rotations, even after accounting for uncertainties introduced by additional gates.
JOURNAL OF PHYSICAL CHEMISTRY A
(2022)
Article
Mathematics, Applied
Elisa Davoli, Rita Ferreira, Carolin Kreisbeck, Hidde Schoenberger
Summary: We propose a unified framework for parameter learning in image processing, using bi-level optimization schemes. The framework deals with identifying the optimal regularizer within a family depending on a parameter in a general topological space. We extend the upper-level functional to the closure of the parameter domain via Gamma-convergence to overcome the lack of compactness in non-compact parameter domains. The extension coincides with the relaxation and allows for minimizers related to the parameter optimization problem.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Pei-Liang Bian, Hai Qing
Summary: In this study, a new FEM framework was developed to simulate the mechanical responses of the Euler-Bernoulli beam with a two-phase local/nonlocal mixed model. The model showed efficient convergence, simplicity of expressions, and flexibility in handling various boundary conditions and external loads.
ENGINEERING WITH COMPUTERS
(2023)
Article
Materials Science, Multidisciplinary
R. Barretta, F. Fabbrocino, R. Luciano, F. Marotti de Sciarra, G. Ruta
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2020)
Article
Mechanics
R. Barretta, S. Ali Faghidian, Francesco de Sciarra, M. S. Vaccaro
ARCHIVE OF APPLIED MECHANICS
(2020)
Article
Thermodynamics
R. Barretta, S. Ali Faghidian, F. Marotti de Sciarra
CONTINUUM MECHANICS AND THERMODYNAMICS
(2020)
Article
Materials Science, Multidisciplinary
R. Barretta, S. Ali Faghidian, F. Marotti de Sciarra, F. P. Pinnola
Summary: In the study of carbon nanotubes (CNTs), a nonlocal strain gradient approach was used to model CNTs and predict their reduced Young elastic modulus, which was validated through molecular dynamics simulations.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2021)
Article
Mechanics
R. Barretta, S. Ali Faghidian, Francesco Marotti de Sciarra, R. Penna, F. P. Pinnola
COMPOSITE STRUCTURES
(2020)
Article
Engineering, Multidisciplinary
F. P. Pinnola, S. Ali Faghidian, R. Barretta, F. Marotti de Sciarra
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(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
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
Mathematics, Applied
Raffaele Barretta, Marko Canadija, Francesco Marotti de Sciarra, Ante Skoblar, Roberto Zigulic
Summary: This article assesses eigenfrequencies of nanobeams under axial loads using stress-driven nonlocal model (SDM) and strain-driven two-phase local/nonlocal model (StrainTPM) of elasticity and Bernoulli-Euler kinematics. The study compares eigenfrequencies calculated using SDM with those obtained by StrainTPM and other nonlocal outcomes, while analyzing the influence of nonlocal thermoelastic effects and initial axial force on dynamic responses.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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
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
Mathematics
Francesco Paolo Pinnola, Raffaele Barretta, Francesco Marotti de Sciarra, Antonina Pirrotta
Summary: This paper proposes a consistent nonlocal viscoelastic beam model and investigates a Timoshenko bending problem considering size- and time-dependent effects. A stress-driven nonlocal formulation is used to inspect scale phenomena, and fractional linear viscoelasticity is considered to simulate time-dependent effects. Analytical solutions and application samples are presented, and parametric analyses are provided to show influences of viscoelastic and size effects on mechanical response.
Article
Chemistry, Multidisciplinary
Raffaele Barretta, Marko Canadija, Francesco Marotti de Sciarra, Ante Skoblar
Summary: Eigenfrequencies of a nanobeam interacting with a heavy fluid and point mass were calculated using Bernoulli-Euler kinematics and nonlocal elasticity model. The study compared the frequencies with local theory, analyzed the influence of nonlocal effects, heavy fluid interaction, and added point mass on dynamic responses, and discussed size phenomena.
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)
Article
Engineering, Multidisciplinary
R. Barretta, S. Ali Faghidian, F. Marotti de Sciarra, F. P. Pinnola
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
(2020)
