Article
Chemistry, Multidisciplinary
Xiaoyan Yang, Chaozhe Wang, Sheng Cao, Fengxi Wang, Wenbing Wu, Angelo Luongo, Yanlin Zhao, Yixian Wang, Hang Lin, Panpan Guo
Summary: This article systematically studies the lateral vibration of a helical pile embedded in a viscoelastic foundation. The helical pile is transformed into a cylindrical pile of special diameter using the equivalent stiffness method, and the lateral vibration model considering shear deformation is established based on the Winkler foundation model and the Timoshenko beam theory. The analytical solutions for the lateral dynamic displacement, bending moment, and shear force of the helical pile are derived, and the influence of pile and soil properties on the lateral dynamic response is investigated.
APPLIED SCIENCES-BASEL
(2023)
Article
Construction & Building Technology
Hongzhan Cheng, Renpeng Chen, Huaina Wu, Fanyan Meng, Yaolin Yi
Summary: This paper proposes a new approach to evaluate the longitudinal deformation of shield tunnels by taking into account multiple discontinuities in strata, using a Timoshenko beam on a Winkler foundation to model soil-tunnel interaction, and presenting new analytical solutions for predicting tunnel deformation characteristics.
TUNNELLING AND UNDERGROUND SPACE TECHNOLOGY
(2021)
Article
Engineering, Mechanical
Andras Szekrenyes
Summary: In this work, the stability of the DCB and 4ENF fracture specimens is analyzed using beam theories and the compliance calibration method. The main goal is to investigate the influence of linear springs on crack propagation stability. A large number of experiments were carried out, including crack initiation tests, compliance datasets, and qualitative observations. The results indicate that the stability of the DCB specimen is worse with smaller spring stiffness, while the 4ENF test cannot be destabilized regardless of additional spring stiffness.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2023)
Article
Engineering, Civil
Camilo J. Fernandez-Escobar, Carlos A. Vega-Posada, Edwin F. Garcia-Aristizabal
Summary: This article focuses on investigating the influence of shear deformation and its interaction with the surrounding soil in short, rigid, and large-diameter piles. Through a parametric study using SAP2000 software, it is found that the deflection and rotation of the pile head significantly increase when considering shear deformation, with the most significant effect observed at low values of the pile/soil stiffness ratio.
ENGINEERING STRUCTURES
(2023)
Article
Engineering, Mechanical
Isaac Elishakoff, Marco Amato
Summary: This paper discusses flutter in a uniform and homogeneous beam under gas flow, considering shear deformation and rotary inertia effects with a truncated Timoshenko-Ehrenfest beam model. It compares the simplified equations with the original Timoshenko-Ehrenfest equations, showing that the former is more consistent and significantly simplifies analytical and numerical analyses. The critical flutter velocities obtained from the simplified equations are compared with those from the original set, highlighting the benefits of the simpler and more consistent approach.
INTERNATIONAL JOURNAL OF MECHANICS AND MATERIALS IN DESIGN
(2021)
Article
Engineering, Civil
Arash Sahraei, Payam Pezeshky, Siriwut Sasibut, Feng Rong, Magdi Mohareb
Summary: This study develops a theory for the static analysis of thin-walled members with general asymmetric cross-sections, capturing global and through-thickness warping, as well as shear deformation effects. Closed-form solutions are formulated for beams with asymmetric, monosymmetric, point symmetric, and doubly symmetric cross-sections, and comparisons with previous theories verify the validity of the present theory and quantify the effects of shear deformation and warping.
THIN-WALLED STRUCTURES
(2021)
Article
Engineering, Civil
Angelo Luongo, Francesco D'Annibale, Manuel Ferretti
Summary: This work introduces one-dimensional equivalent beam models embedded in a two-dimensional space for static analysis of beam-like structures. The extensible shear and Timoshenko beam models are formulated under the assumption of rigid cross-sections, with constitutive laws determined through a homogenization procedure. The linear constitutive equation accounts for axial and shear forces coupled with bending, with the warping of the cross-section considered through the concept of shear and flexural factors.
ENGINEERING STRUCTURES
(2021)
Article
Materials Science, Multidisciplinary
Hart Honickman, Stefan Kloppenborg
Summary: This article introduces a new higher-order beam model that accurately represents the deformation shapes and stress distributions of beams, particularly suitable for laminated beams. The model is considered a finite approximation of a one-dimensional beam model, and its accuracy is verified through calculations and comparisons.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Materials Science, Multidisciplinary
Giulio Maria Tonzani, Isaac Elishakoff
Summary: This paper analyzes the free vibration frequencies of a beam on a Winkler-Pasternak foundation using three different models, comparing the results under different sets of boundary conditions and revealing interesting phenomena.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Engineering, Multidisciplinary
Said Mesmoudi, Omar Askour, Mohammed Rammane, Oussama Bourihane, Abdeljalil Tri, Bouazza Braikat
Summary: This study couples the spectral Chebyshev differential quadrature method with the high order continuation method for analyzing the nonlinear bending and buckling behavior of functionally graded sandwich beams. It investigates the influence of different parameters on the performance of FG sandwich beams.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Yiming Huang, Mi Zhao, Piguang Wang, Haibin Xu, Xiuli Du
Summary: An analytical solution is developed to study the horizontal SV wave responses of end-bearing pile considering shear deformation of Timoshenko beam and soil free-field shear stress. The Timoshenko beam model is used to account for additional deflection caused by pile bending and shear deformation. The impedance of the soil to the pile under horizontal SV wave is obtained, and the closed solution of the problem is obtained based on the governing equation of Timoshenko beam, the interaction between pile and soil, and the fixed bottom and free top boundaries of the end-bearing pile. The influence of soil free-field shear stress and pile shear deformation are analyzed, providing guidance for engineering structure design.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Engineering, Mechanical
M. C. Ray
Summary: This paper derives benchmark three-dimensional exact solutions for the static analysis of rectangular antisymmetric angle ply plates, showing that these solutions can be used for numerical results for any fiber orientation angle, but not for other angle-ply plates. It is also found that the first order shear deformation theory (FSDT) can be efficiently used for thin and two layered thick antisymmetric angle-ply plates, as compared to exact solutions.
INTERNATIONAL JOURNAL OF MECHANICS AND MATERIALS IN DESIGN
(2021)
Article
Engineering, Multidisciplinary
Guozhe Shen, Yang Xia, Weidong Li, Guojun Zheng, Ping Hu
Summary: Peridynamics is a nonlocal theory that can handle easily discontinuities such as cracks, even though it is computationally more expensive. The study introduces new PD beam and shell models based on micro-beam bond and Timoshenko beam theory, with interpolation method used for describing various deformations and strain energy densities. The high precision of PD beam and shell models is proven through simulation results.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Acoustics
W. Rodriguez-Cruz, J. C. Torres-Guzman, A. Diaz-de-Anda
Summary: In this study, it is demonstrated analytically and numerically that degenerate states of a beam with free ends tend asymptotically to the thickness-shear mode in the infinitely long beam limit, occurring in the first degeneracy points above the cutoff frequency. The accuracy of the results is validated by comparing them with those obtained using the Finite Element method and plane stress elastodynamics theory. It is also shown that the anti-symmetric states closely resemble the thickness-shear mode but for a finite beam with free ends under flexural vibrations.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Mechanics
Samir Emam, Walter Lacarbonara
Summary: This paper presents exact solutions for the buckling loads and postbuckling states of extensible, shear deformable beams. The dependence of the buckling load on the length-to-radius of gyration is discussed, as well as the significant effects of extensibility and shear deformation on the buckling loads and the postbuckling response.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2021)
Article
Computer Science, Interdisciplinary Applications
S. Ali Faghidian, Hamid Mohammad-Sedighi
Summary: The thick bar model is a comprehensive structural theory that considers lateral deformation, shear stiffness, and lateral inertia effect to study the axial deformation of carbon nanotubes. By applying a consistent variational framework, the physically motivated definition of the axial force field and higher order boundary conditions are determined. The nonlocal integral elasticity is used to properly account for long-range interactions, and the established size-dependent thick bar model is exempt from the drawbacks of the nonlocal differential formulation.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mechanics
S. Ali Faghidian, Esmaeal Ghavanloo
Summary: The unified higher-order theory of two-phase nonlocal gradient elasticity is proposed by introducing higher-order nonlocality to the higher-order gradient theory of elasticity. Nonlocal approaches are used to simulate long-range interactions at the nano-scale, with equivalence between the constitutive law's integral convolutions and the nonlocal gradient differential formulation confirmed through non-classical boundary conditions.
Article
Mechanics
Saeed H. Moghtaderi, S. Ali Faghidian, Mohsen Asghari
Summary: This study examines the nonlinear vibration characteristics of elastic nano-bars with large vibration amplitudes and proposes an effective analytical method. By applying the nonlocal elasticity theory and strain gradient elasticity theory, the method considers the nano-scale effects and non-classical boundary conditions. This analytical approach can be used for optimized design of vibration-based nano-devices and addressing nonlinear dynamic phenomena.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Mechanics
S. Ali Faghidian, Krzysztof Kamil Zur, J. N. Reddy, A. J. M. Ferreira
Summary: In this study, the dispersion characteristics of flexural waves in functionally graded porous nanobeams were analyzed using higher-order nonlocal gradient elasticity theory. The results reveal that the size-dependent response of the symmetric FG porous nanobeam and the closed-form solution of the phase velocity can be effectively utilized in the design and optimization of composite nano-structural elements.
COMPOSITE STRUCTURES
(2022)
Article
Engineering, Multidisciplinary
S. Ali Faghidian, Krzysztof Kamil Zur, Ernian Pan, Jinseok Kim
Summary: The paper presents the mixture stress gradient theory of elasticity, which unifies classical elasticity theory and stress gradient theory, rigorously formulates the boundary-value problem of functionally graded nano-bars, and determines the constitutive law of the axial force field with proper non-standard boundary conditions. By using numerical and analytical methods, the effectiveness of the established theory in characterizing the size-dependent response of functionally graded structural elements is demonstrated.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
S. Ali Faghidian, Krzysztof Kamil Zur, J. N. Reddy
Summary: The proposed higher-order unified gradient elasticity theory effectively characterizes the nanoscopic response of advanced nano-materials, as demonstrated by its application to study the torsional behavior of elastic nano-bars and determine the shear modulus of nano-sized bars in closed-form analytical formula. Additionally, a practical approach to calibrate characteristic lengths is introduced.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2022)
Article
Materials Science, Multidisciplinary
S. Ali Faghidian, Krzysztof Kamil Zur, Timon Rabczuk
Summary: The mixture unified gradient theory of elasticity is utilized to assess the size-dependent behavior of materials with nano-structural features. Integrating the strain gradient theory and the stress gradient theory with the classical continuum theory, the study examines the dynamics and elastostatic response of nanobars. The established generalized continuum theory proves effective in accurately describing the size-effects at the ultra-small scale, as evidenced by electrostatic and elastodynamic analysis of nanobars.
APPLIED PHYSICS A-MATERIALS SCIENCE & PROCESSING
(2022)
Editorial Material
Engineering, Multidisciplinary
Krzysztof Kamil Zur, S. Ali Faghidian, J. N. Reddy, K. M. Liew, A. J. M. Ferreira
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics, Applied
S. Ali Faghidian, Krzysztof Kamil Zur, Isaac Elishakoff
Summary: This study utilizes the mixture unified gradient theory of elasticity to investigate the nanoscopic nonlinear flexure mechanics of nanobeams. Through a mixed variational framework and numerical approach, the size-effect phenomenon associated with stress gradient, strain gradient, and classical elasticity theories is realized and the nonlinear flexural characteristics of nano-sized beams are detected and compared.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Multidisciplinary
S. Ali Faghidian, Krzysztof Kamil Zur, Ernian Pan
Summary: The mixture unified gradient theory of elasticity integrates the stress gradient, strain gradient, and classical elasticity theory within a consistent variational framework. It incorporates all the governing equations into a single functional, making it a suitable counterpart for the two-phase local/nonlocal gradient theory. The theory can effectively examine various multi-dimensional structural problems in Engineering Science and has significant practical importance.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Mechanics
S. Ali Faghidian, Isaac Elishakoff
Summary: This paper highlights the importance of the shear coefficient in the Timoshenko-Ehrenfest beam theory and addresses the challenge of determining the appropriate formula for solid rectangular cross-sections. A variational framework is proposed to establish a consistent shear coefficient for prismatic beams, and the efficacy of the introduced coefficient is demonstrated through the discussion of intrinsic anomalies.
Article
Engineering, Mechanical
Seyed Ali Faghidian, Abdelouahed Tounsi
Summary: The dynamic characteristics of elastic nanobeams are rigorously analyzed using the mixture unified gradient theory of elasticity, with closed-form solutions and numerical evaluations. The study shows that the established elasticity model effectively describes the softening and stiffening responses of nanobeams, providing a practical approach to tackle dynamics of nano-structures.
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
S. Ali Faghidian, Isaac Elishakoff
Summary: This study investigates the random vibration of elastic beams at the ultra-small scale using the mixture unified gradient theory of elasticity. The closed-form solution of the space-time correlation function and the mean-square of the transverse displacements of the elastic nanobeam with simply supported ends is obtained. The spatial variation of the mean-square value of the transverse displacements is graphically illustrated and discussed in terms of gradient length-scale parameters.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Electrical & Electronic
Kabir Sadeghi, Amir Shamsi, S. Ali Faghidian
Summary: Carbon nanotubes are influential in advanced engineering systems, but classical continuum mechanics is inadequate for accurately describing their structural response. The mixture unified gradient theory of elasticity is applied to study the structural characteristics of nanobars in a nanoscopic scale. This study provides a new benchmark for the analysis and design of pioneering nanosystems.
MICROSYSTEM TECHNOLOGIES-MICRO-AND NANOSYSTEMS-INFORMATION STORAGE AND PROCESSING SYSTEMS
(2023)
Article
Acoustics
S. Ali Faghidian, Isaac Elishakoff
Summary: A size-dependent elasticity theory is developed to analyze wave propagation in nanosized beams. The theory integrates stress gradient theory, strain gradient model, and traditional elasticity theory to account for size effects. A stationary variational framework compatible with the kinematics of Timoshenko-Ehrenfest beam is established. Numerical simulations are performed to validate the proposed theory and a method for inverse determination of characteristic length-scale parameters is proposed.
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME
(2022)