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
Computer Science, Interdisciplinary Applications
Mahmood Fakher, Shahrokh Hosseini-Hashemi
Summary: Considering the size effects of nanostructures, employing the two-phase local/nonlocal elasticity has recently gained attention in nano-mechanics research. This study provides the exact solution for the vibrations of two-phase Timoshenko nanobeams and investigates the shear-locking problem in the case of two-phase finite-element method (FEM). It aims to create an efficient locking-free local/nonlocal FEM with a simple and efficient beam element.
ENGINEERING WITH COMPUTERS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mahsa Najafi, Isa Ahmadi
Summary: In this paper, an efficient method based on nonlocal elasticity theory and Layerwise theory is proposed for the analysis of bending, buckling, and vibration of functionally graded nanobeam. The method takes into account the transverse shear and normal strains of nanobeam and the small-scale effect. The proposed theory is validated by comparing with other theories and shows accurate results in predicting vibration, buckling, and bending of nanobeams.
ENGINEERING WITH COMPUTERS
(2023)
Article
Engineering, Civil
Moustafa S. Taima, Tamer A. El-Sayed, Michael I. Friswell
Summary: This study presents a novel approach to investigate the thermal lateral vibration of cracked nanobeams using Reddy beam analysis-based solutions. The effects of various factors on the natural frequencies are explored, and the outcomes are compared with prior findings, showing a strong level of agreement.
THIN-WALLED STRUCTURES
(2023)
Article
Mechanics
Mohamed-Ouejdi Belarbi, Mohammed-Sid-Ahmed Houari, Ahmed Amine Daikh, Aman Garg, Tarek Merzouki, H. D. Chalak, Hicham Hirane
Summary: An efficient nonlocal finite element model was developed to study the bending and buckling behavior of functionally graded nanobeams. The new theory provides accurate transverse shear stress distribution without the need for correction factors, showing high accuracy and convergence rate. Detailed numerical studies validated the performance and reliability of the proposed model.
COMPOSITE STRUCTURES
(2021)
Article
Construction & Building Technology
Mahsa Najafi, Isa Ahmadi
Summary: A nonlocal Layerwise theory is proposed for free vibration analysis of nanobeams resting on an elastic foundation, considering small-scale effects and predicting more accurate results. Effects of nonlocal parameter, Pasternak shear coefficient, Winkler spring coefficient, and boundary conditions on the vibration of nanobeams are studied. The theory can be applied to analyze the mechanical behavior of various nanostructures with different loading and boundary conditions.
STEEL AND COMPOSITE STRUCTURES
(2021)
Article
Physics, Multidisciplinary
Chinika Dangi, Roshan Lal
Summary: A nonlocal model has been proposed to study the vibration behavior of bi-directional functionally graded nanobeam, considering surface and size effects. The results show that the surface effect plays an important role in such material.
Article
Mathematics, Applied
Roshan Lal, Chinika Dangi
Summary: This article introduces a nonlocal model based on the Timoshenko beam theory for vibration response of bi-directional functionally graded moderately thick nanobeam under surface effect. The study considers surface and nonlocal effects using the Gurtin-Murdoch surface elasticity theory and Eringen's nonlocal theory, and numerical results are obtained using the differential quadrature method.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
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
Pejman Ayoubi, Habib Ahmadi
Summary: For the first time, the mixed local/nonlocal elasticity theory is used to study the free axisymmetric vibration of an annular single-layer graphene sheet. The imperfections on the sheet are considered as centric perforations. Dynamic equilibrium equations are derived and solved analytically. The influence of mixture parameter, nonlocal parameter, and imperfection radius on the natural frequency is examined and it is found that increasing the mixture parameter leads to an increase in the natural frequency.
Article
Mathematics, Applied
Hayri Metin Numanoglu, Hakan Ersoy, Bekir Akgoz, Omer Civalek
Summary: This study investigates the size-dependent thermo-mechanical vibration analysis of nanobeams by implementing Hamilton's principle and the stress equation of nonlocal elasticity theory. The finite element method is used to solve the eigenvalue problem and derive stiffness and mass matrices. Nonlocal finite element method is emphasized for analyzing the vibration behavior of nanobeams under different boundary conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Thermodynamics
Quoc-Hoa Pham, Van Ke Tran, Trung Thanh Tran, Trung Nguyen-Thoi, Phu-Cuong Nguyen, Van Dong Pham
Summary: This article presents a finite element method based on a quasi-3D nonlocal theory to study the free vibration of functionally graded material nanoplates on an elastic foundation in a thermal environment. The study compares numerical results with previous research to verify accuracy and investigates the effects of various parameters on the free vibration of nanoplates.
CASE STUDIES IN THERMAL ENGINEERING
(2021)
Article
Materials Science, Multidisciplinary
Xuesong Yan
Summary: This study uncovers the inconsistencies among different kernel functions by using two special cases of Eringen's nonlocal theory. The integral form of the theory is employed to avoid potential paradoxes. The Timoshenko beam theory is used to model rotating nanobeams, and numerical solutions are developed using the element-free Galerkin method.
APPLIED PHYSICS A-MATERIALS SCIENCE & PROCESSING
(2022)
Article
Mechanics
Busra Uzun, Omer Civalek, Mustafa Ozgur Yayli
Summary: This study presents an efficient solution method based on the Stokes' transformation to investigate the effects of deformable boundary conditions and axial point load on the transverse vibration of a nanobeam. The eigenvalue problem obtained by using Fourier sine series and Stokes' transform can be used to analyze the frequencies of nanobeam applications subjected to vibration and axial force at both rigid and non-rigid boundaries. This analytical method can be applicable to various nanotechnology structures and machines.
Article
Mechanics
S. El-Borgi, P. Rajendran, M. Trabelssi
Summary: This paper investigates the free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported by a nonlinear foundation. By combining nonlocal and surface elasticity and using the physical neutral axis method, a new formulation for the dynamic response of the beam is proposed. The effects of various parameters on the vibration response are thoroughly studied.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Mechanics
Ismail Esen, Mohamed A. Eltaher, Alaa A. Abdelrahman
Summary: This article investigates the dynamic responses of symmetric and sigmoid FG Timoshenko beam subjected to moving mass. The study explores the influences of gradation type, gradation index, elastic foundation stiffnesses, inertia, and variable velocity of the moving mass on the dynamic response. The Hamilton principle and finite element method are used for modeling and solving the system.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mechanics
Alaa A. Abdelrahman, Ismail Esen, Ahmed Amin Daikh, Mohamed A. Eltaher
Summary: In this study, a nonclassical size dependent model was developed to investigate the dynamic behavior of CNTs reinforced composite beams under moving load. The effects of various parameters such as elastic foundation parameters, volume fraction, CNTs configuration, nonclassical parameters, and moving load velocity were analyzed. The obtained results provide valuable insights for the design and manufacturing of composite CNTs beams.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mechanics
M. A. Eltaher, R. A. Shanab, N. A. Mohamed
Summary: This article presents an enhanced mathematical model and closed-form solutions to explore the dynamic vibration response of perforated viscoelastic nanostructure thin/thick nanobeams with a size-dependent continuum model and different boundary conditions. The influences of viscoelastic parameter, nonlocal softening coefficient, supporting conditions, and filling/spacing ratio on the vibration response are analyzed.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Mathematics
Ammar Melaibari, Salwa A. A. Mohamed, Amr E. E. Assie, Rabab A. A. Shanab, Mohamed A. A. Eltaher
Summary: This manuscript presents a mathematical formulation of the dynamical behavior of bi-directional functionally graded porous plates (BDFGPP) using unified higher-order plate theories (UHOPT) on a Winkler-Pasternak foundation. The kinematic displacement fields are utilized to satisfy the shear strain/stress conditions without correction factors. The material gradation is proposed in both axial and transverse directions using power-law distribution, and porosity distribution is defined using cosine functions in the transverse direction. The derived equations of motion and boundary conditions are solved using the two-dimensional differential integral quadrature method (2D-DIQM). A parametric analysis is conducted to investigate the effects of various factors on the natural frequencies and mode shapes of BDFGPP.
Article
Mathematics
Gamal S. S. Abdelhaffez, Ahmed Amine Daikh, Hussein A. A. Saleem, Mohamed A. A. Eltaher
Summary: A mathematical model of tricoated functionally graded materials (FGMs) is proposed in this paper to analyze analytically the buckling problem of coated FG spherical nanoshells resting on an orthotropic elastic foundation subjected to biaxial loads. The study considers the size-dependent and microstructure effects using the nonlocal strain gradient theory and applies the principle of virtual work to obtain equilibrium equations. The Galerkin technique is used to solve the obtained differential equations under various boundary conditions. A detailed parametric analysis is conducted to investigate the influence of different schemes of coated FGMs, gradient material distribution, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and orthotropic elastic foundation on the critical buckling loads.
Article
Mathematics
Ammar Melaibari, Salwa A. Mohamed, Amr E. Assie, Rabab A. Shanab, Mohamed A. Eltaher
Summary: This study analyzes the responses of beams and plates using middle surface (MS) and neutral surface (NS) formulations. It derives the relations between the displacement field variables on NS and MS, and defines modified boundary conditions for immovable simply supported plates. The study shows that the responses of BDFG plates based on MS and NS formulations are identical for clamped and movable simply supported boundary conditions. However, there are differences in the responses for immovable simply supported boundary conditions if fixation constraints at different planes are not properly treated.
Article
Mathematics
Alaa A. Abdelrahman, Hussein A. Saleem, Gamal S. Abdelhaffez, Mohamed A. Eltaher
Summary: The electromechanical-size-dependent bending of piezoelectric composite structural components with flexoelectricity has been studied using nonlocal strain gradient elasticity theory. The accuracy of the proposed methodology is verified by comparing the results with existing literature. Parametric studies are conducted to explore the effects on the bending behavior and it is found that controlling the parameters can improve the electromechanical and mechanical behaviors.
Article
Mathematics
Emad E. Ghandourah, Ahmed Amine Daikh, Samir Khatir, Abdulsalam M. Alhawsawi, Essam M. Banoqitah, Mohamed A. Eltaher
Summary: This study proposes a new model for functionally graded shell structures called Tri-coated FGM, which investigates the free vibration response by incorporating porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, and five distribution patterns are proposed. A novel modified field of displacement is proposed by considering the shear deformation effect. Extensive parametric analysis is conducted to investigate the influence of various factors on the fundamental frequencies.
Article
Engineering, Civil
Salwa A. Mohamed, Amr E. Assie, Mohamed A. Eltaher
Summary: The manuscript introduces a nonlinear mathematical model for investigating the nonlinear bending response of Bi-directional functionally graded plates resting on elastic foundations. A unified higher order shear plate theory is employed to account for the shear influence with parabolic distribution. The gradation of materials is described by a power law function. The developed model is solved using a novel incremental-iterative method and the differential/integral quadrature method to numerically discretize the governing equations with variable-coefficients.
THIN-WALLED STRUCTURES
(2023)
Article
Engineering, Aerospace
Ola A. Siam, Rabab A. Shanab, Mohamed A. Eltaner, Norhan A. Mohamed
Summary: This manuscript aims to derive the closed form solutions for the free vibration of a viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory. The kinematic displacements based on Euler-Bernoulli and Timoshenko theories are developed to consider the nanobeam's thin and moderate thickness structures. Kelvin/Voigt constitutive relation is proposed to consider the internal damping viscoelastic effect. The derived equations of motion and boundary conditions are evaluated to obtain closed form solutions for damped and natural frequencies.
ADVANCES IN AIRCRAFT AND SPACECRAFT SCIENCE
(2023)
Article
Engineering, Aerospace
Yousef A. Alessi, Ibrahim Ali, Mashhour A. Alazwari, Khalid Almitani, Alaa Abdelrahman, Mohamed A. Eltaher
Summary: This article presents a numerical analysis of the natural frequencies and harmonic response of a perforated cantilever beam connected to two layers of piezoelectric materials using the finite element method. The effects of perforation geometry, the number of rows, and resistance on natural frequencies, frequency response, and power are investigated. The study finds that thickness is positively correlated with natural frequency, and rectangular perforations produce higher voltage.
ADVANCES IN AIRCRAFT AND SPACECRAFT SCIENCE
(2023)
Article
Nanoscience & Nanotechnology
Ismail Esen, Mashhour A. Alazwari, Khalid H. Almitani, Mohamed A. Eltaher, A. Abdelrahman
Summary: This article investigates the free and forced responses of functionally graded material (FGM) porous nanoplates under thermal and magnetic fields using nonclassical nonlocal strain gradient elasticity. The mathematical model considers shear deformation, size-scale effects, and miscorstructure influences. Four different porosity models and their distribution across the thickness are studied. The derived equations of motion are solved analytically using the Navier method, and the effects of various factors such as nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. The study shows that a directed magnetic field can dampen the forced vibrations of FGM porous nanoplates under thermal and live loads.
ADVANCES IN NANO RESEARCH
(2023)
Article
Engineering, Multidisciplinary
Norhan A. Mohamed, Rabab A. Shanab, Mohamed A. Eltaher, Alaa A. Abdelrahman
Summary: This manuscript presents a mathematical model and numerical solution to predict the vibration responses of nonlocal strain gradient perforated viscoelastic nanobeam under dynamic moving loads. The effects of micro-structure, size length scales, and viscoelastic damping are considered. The proposed method provides insights into the dynamic behavior of viscoelastic perforated nanobeams under moving load.
RESULTS IN ENGINEERING
(2023)
Article
Mechanics
Amr E. Assie, Salwa A. Mohamed, Rabab A. Shanab, Rasha M. Abo-bakr, Mohamed A. Eltaher
Summary: This article develops a mathematical model to study the static stability of bi-directional functionally graded porous unified plate and discusses the significant factors affecting the static stability and buckling loads through parametric studies.
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS
(2023)
Article
Mechanics
H. M. Abo-Bakr, R. M. Abo-Bakr, S. A. Mohamed, M. A. Eltaher
Summary: This study investigates multiobjective shape optimization of nonuniform microbeams made of functionally graded materials. The goal is to discover optimal shape functions and volume fraction distribution to maximize critical buckling load and fundamental frequency while minimizing mass and material cost. The study presents the static and dynamic behavior of axially functionally graded material nonuniform microbeam based on Timoshenko beam theory with modified couple stress theory. Multiobjective particle swarm optimization is applied to search for Pareto optimal solutions, considering shape functions parameters, types, and FGM power index as design variables. Several cases are studied to demonstrate the effectiveness of multiobjective optimal shape design of axially functionally graded beams.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
