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
Engineering, Multidisciplinary
Dhiraj S. Bombarde, Manish Agrawal, Sachin S. Gautam, Arup Nandy
Summary: In this work, stress-based hybrid solid elements are proposed for isogeometric analysis to alleviate locking issues. The elements are constructed based on a two-field Hellinger-Reissner variational statement and the stress interpolation functions are derived systematically. The results of benchmark problems demonstrate the efficacy and robustness of the proposed elements.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
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
Chemistry, Physical
Qian Feng, Peng Wei, Junbin Lou, Daiwei Wang, Jinbiao Cai, Rongqiao Xu
Summary: The Hellinger-Reissner method is applied in this study to analyze the deformation and force of a cable-stayed suspension bridge. The results show good agreement with test results and finite element analysis, highlighting the efficiency of this method in selecting key parameters for cable-stayed suspension bridges.
Article
Engineering, Multidisciplinary
Junchao Wu, Xinyu Wu, Yaobing Zhao, Dongdong Wang
Summary: A rotation-free Hellinger-Reissner meshfree thin plate formulation is proposed to naturally accommodate the essential boundary conditions in a variationally consistent way. In this approach, the bending moment is expressed as the second order smoothed gradients which inherently embed the integration constraint and fulfill the variational consistency condition. The enforcement of essential boundary conditions has a similar form as that of the Nitsche's method, but with replaced derivatives and without artificial parameters.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Jialin Wang, Junbo Zhang, Zhuo Chen, Lin He
Summary: This paper investigates the application of the Hellinger-Reissner (H-R) variational principle to the specified stress condition problem in a structure. By introducing the unknown non-elastic strain as an additional unknown quantity, a variational functional satisfying the specified stress conditions is established. The use of non-elastic strain as an independent variable expands the capabilities of the existing variational principle and finite element method.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
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
Mechanics
Rosa Penna, Luciano Feo, Antonio Fortunato, Raimondo Luciano
Summary: The study investigates the size-dependent flexural nonlinear free vibrations of geometrically imperfect functionally graded nano-beams using the stress-driven nonlocal integral model (SDM). The Galerkin method is applied to derive a nonlinear ordinary differential equation, and the closed form analytical solution of the nonlinear natural flexural frequency for different boundary conditions is established using the Hamiltonian approach. The effects of nonlocal scale parameter and initial axial tension force on fundamental frequencies are examined and compared with results obtained from Eringen's nonlocal model. The study demonstrates that the nonlinear approach based on nonlocal stress model is effective in capturing the dynamical responses of nano-beams and is advantageous for the design and optimization of nano-scaled components in NEMS.
COMPOSITE STRUCTURES
(2021)
Article
Computer Science, Interdisciplinary Applications
Dhiraj S. Bombarde, Manish Agrawal, Sachin S. Gautam, Arup Nandy
Summary: The study introduces a novel twenty-seven node quadratic EAS element, addressing the underutilization of quadratic elements in existing 3D EAS elements. Additionally, a six-node wedge and an eighteen-node wedge EAS element are presented in the manuscript.
COMPUTERS & STRUCTURES
(2024)
Article
Engineering, Civil
Qian Feng, Peng Wei, Junbin Lou, Jinbiao Cai, Rongqiao Xu
Summary: This article introduces an improved analysis method, the Hellinger-Reissner variational principle, for the early design stage of tied-arch bridges. This method has high accuracy and efficiency in analyzing the deformation and forces of tied-arch bridges.
Article
Engineering, Multidisciplinary
Andrea Caporale, Hossein Darban, Raimondo Luciano
Summary: In this study, a unified approach is used to determine the strain-driven and stress-driven differential equations of Timoshenko nano-beams with loading discontinuities. The proposed models can simulate small scale effects with different types of constitutive laws and consider points of discontinuities for generalized internal forces. Novel constitutive continuity conditions are imposed at the beam interior points of loading discontinuities, providing an alternative to Dirac delta function. Closed-form solutions to practical cases are obtained using the proposed models.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2022)
Article
Engineering, Geological
Junhong Yu, Xinchun Shang, Gang Wang
Summary: The contact pressure in the Brazilian disc test is investigated through theoretical analysis and experiment, where a new theoretical approach is presented to obtain a semi-analytical solution of the contact pressure and calculate the contact angle through variational techniques. The distribution of contact pressure is found to be a semi-ellipse curve, with minor effects of elastic modulus and Poisson ratio on contact angle. The applicability of the proposed theoretical approach is validated through experimental data and finite element analysis, showing good agreement with the variational solutions and indirectly determining the elastic modulus of natural sandstone samples.
ROCK MECHANICS AND ROCK ENGINEERING
(2022)
Article
Mathematics, Applied
Fleurianne Bertrand, Daniele Boffi, Rui Ma
Summary: This paper examines the approximation of eigenvalues in the mixed Hellinger-Reissner elasticity problem using a recently introduced simple finite element method. The method is proven to converge with a residual type error estimator and the estimator shows optimal decay with increasing degrees of freedom. A postprocessing technique is discussed and numerically tested, originally proposed in a different context.
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Yufei Rong, Feng Sun, Qin Sun, Ke Liang
Summary: In this paper, a solution framework for solid element based on co-rotational formulation is developed for geometrically nonlinear analysis. A novel eight-node solid element embedded in the framework is developed using a modified Hellinger-Reissner variational principle, and the stiffness matrix is derived by compatible displacement and the most desirable stress fields, as well as a penalty function. Additionally, an accelerated modified Newton method is proposed to improve the efficiency of the solution of nonlinear equations, and a hybrid load-controlled/arc-length algorithm is used to compute the equilibrium path of structures exhibiting instability.
COMPUTATIONAL MECHANICS
(2023)
Article
Mechanics
M. E. Fares, M. G. Salem, Doaa Atta, M. Kh. Elmarghany
Summary: A mixed variational principle is established for the micropolar elasticity theory, treating displacements, microrotations, force stresses, and couple stresses as independent fields. This principle helps to overcome inconsistencies between simple kinematic assumptions and boundary conditions and presents an improved 2D model for micropolar plates. Bending and free vibration applications are studied, considering different edge conditions and assessing the importance of normal strain and microrotation effects.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
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)
