Review
Computer Science, Interdisciplinary Applications
Shengli Kong
Summary: The article discusses the size-dependent material deformation behaviors of certain metals and polymers at micro scale experiments and how the modified couple stress theory (MCST) can capture these size dependences. It reviews available size-dependent models for micro-beam and micro-plate based on MCST, and establishes relevant mechanical models and solutions for static bending, vibration, buckling, and pull-in instability of representative micro-structures. The results indicate significant size effects on the mechanical properties of micro-structures, suggesting potential further research on size-dependent behaviors.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2022)
Article
Physics, Multidisciplinary
Hamid M. Sedighi, Ahmed E. Abouelregal, S. Ali Faghidian
Summary: This study investigates the deficiency of the modified couple stress theory in accurately describing the material response of continua with nano-structural features. By reassessing the flexure mechanics of nano-scale beams within this theory, physically motivated constitutive laws are introduced and the effects of symmetric rotation gradients and transverse shear deformation are examined. Additionally, closed-form analytical formulae for the elastic modulus of Carbon Nanotubes are derived and the applicability of the modified couple stress beam model in accurately capturing size-effects in nano-materials is rigorously examined.
Article
Engineering, Civil
Cancan Liu, Jiangong Yu, Weijiang Xu, Xiaoming Zhang, Xianhui Wang
Summary: This paper studies the acoustic wave motion characteristics of Lamb and SH waves in FG anisotropic micro/nano-plates based on the modified couple stress theory, using the efficient LOPM method for solving process and examining the effects of size and material gradient. The research indicates that size effect causes wrinkles in Lamb wave dispersion curves, material gradient changes the amplitude and range of wrinkles, and length scale parameter influences the cut-off frequency of SH waves.
THIN-WALLED STRUCTURES
(2021)
Article
Mechanics
Zanhang He, Jianghong Xue, Sishi Yao, Yongfu Wu, Fei Xia
Summary: A modified first order shear deformation theory is proposed for laminated micro-nano plates with couple stress components involved, based on mechanics of composite materials and Koiter's theory. Governing equations with size-dependent effect are derived and applied to investigate the buckling and free vibration of laminated micro-nano plates. The proposed theory is validated and shown to be efficient and accurate through comparisons with existing models and ABAQUS analysis.
COMPOSITE STRUCTURES
(2021)
Article
Materials Science, Multidisciplinary
Jae-Hoon Choi, Hojang Kim, Ji-Young Kim, Kwang-Hyeok Lim, Byung-Chai Lee, Gi-Dong Sim
Summary: In this study, the additional length scale parameter in the couple stress theory was measured experimentally, and the physical origin of this parameter was discussed. The results showed that both the elastic modulus and bending rigidity increased as the material thickness decreased.
MATERIALS & DESIGN
(2022)
Article
Materials Science, Multidisciplinary
Junling Si, Shujuan Yi
Summary: This study develops a quasi-3D model based on a new modified couple stress theory as a benchmark for analyzing thermal size effects of composite laminated micro plate. Two simplified quasi-3D models are also proposed. Several conclusions can be drawn from numerical results obtained from a classical example of simply-supported micro laminated square plate.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Mechanics
Richa Priyanka, Jeyaraj Pitchaimani
Summary: This paper investigates the buckling and free vibration behaviors of micro laminated composite beams under varying axial loads using the modified couple stress theory, capturing the size effect by considering material length scale parameters and exploring different boundary conditions and layups. The observed size effect is more significant when the beam thickness is similar to the material length scale parameter and diminishes as the thickness increases. Different boundary conditions result in varying small size effect variations, with the fundamental frequency decreasing more rapidly under parabolic loading compared to other loading types.
COMPOSITE STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Yu-Hao Mao, Yan Shang, Song Cen, Chen-Feng Li
Summary: A novel nonconforming 3-node triangular plate element is proposed within the modified couple stress elasticity to simulate the size-dependent static and dynamic bending behaviors of thin microplates and study the effects of micro-inertia. The element exhibits satisfying numerical accuracy and captures size dependences effectively, with higher order modes being more influenced by micro-inertia.
ENGINEERING WITH COMPUTERS
(2023)
Article
Acoustics
Z. X. Xia, G. Y. Zhang, Y. Cong, S. T. Gu
Summary: The paper proposes a numerical model based on the modified couple stress theory of elasto-dynamics and a non-classical Mindlin plate finite element to consider the size effects of elastic wave band gaps in microscopic composite plates. The model offers flexibility in discretizing complex microstructures and sensitivity to size effects of microscopic problems.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Quoc-Hoa Pham, Phu-Cuong Nguyen, Van Ke Tran, Qui X. Lieu, Trung Thanh Tran
Summary: In this article, the isogeometric analysis based on the modified nonlocal couple stress theory is used to study the bending and free vibration characteristics of functionally graded nanoplates placed on an elastic foundation. A higher order refined plate theory is adapted, and several comparison studies are conducted to verify the proposed model and analyze the influence of various parameters.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mechanics
Jiangsen Liu, Yijiang Peng
Summary: The complementary energy principle associated with the modified couple stress theory (MCST) is proposed and proved for analyzing the size effects of Euler micro-beams considering support movements and negative Poisson's ratio. The main reason is that the influence of negative Poisson's ratio on the size effects is larger than that of positive Poisson's ratio in the theoretical analysis. The analytical solutions agree with the published data for the deflections and rotations without the support movements.
ARCHIVE OF APPLIED MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Maryam Lori Dehsaraji, Mohammad Arefi, Abbas Loghman
Summary: This paper employs higher-order shear and normal deformation theory to analyze the free vibration of cylindrical micro/nano shells, taking into account thickness stretching effect and size dependency. Numerical results are used to investigate the impact of geometric parameters, material properties, applied voltages, and temperature rising on the free vibration responses.
DEFENCE TECHNOLOGY
(2021)
Article
Mechanics
Pham Hong Cong, Do Van Thom, Doan Hong Duc
Summary: This paper investigates the crack propagation behavior of plane strain micro-plates using the modified couple stress theory and the phase-field theory. A phase-field formulation for fracture mechanics based on the framework of the modified couple stress is established for the first time. The results highlight the difference in mechanical properties during crack propagation when considering size-effect based on modified couple stress. This work is important for scientists studying the fracture development process in microstructures.
ENGINEERING FRACTURE MECHANICS
(2022)
Article
Acoustics
J. Ranjan Banerjee, Stanislav O. Papkov, Thuc P. Vo, Isaac Elishakoff
Summary: Several models based on continuum mechanics have been proposed to solve the free vibration problem of micro beams. This paper focuses on the modified couple stress theory in conjunction with the Timoshenko-Ehrenfest theory to study the free vibration characteristics of micro beams. The main advantage of the modified couple stress theory is its use of only one material length scale parameter. The results demonstrate the effects of the length scale parameter on the free vibration characteristics of Timoshenko-Ehrenfest micro beams.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Mechanics
H. Golbakhshi, M. R. Dashtbayazi, A. R. Saidi
Summary: In this paper, a new couple stress model is proposed for the analysis of micro-beams, which allows for the modification of governing equations and boundary conditions into a more convenient form. The validity of the model is demonstrated through investigations on the static bending and free vibration of isotropic and FG porous micro-beams subjected to a concentrated load at the mid-span.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2022)
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
Materials Science, Multidisciplinary
Mohammad Amin Shahmohammadi, Sayed Mohamad Mirfatah, Hamzeh Salehipour, Fatemeh Azhari, Omer Civalek
Summary: This article investigates the dynamic instability of hybrid fiber/nanocomposite-reinforced toroidal shells, achieving a semi-analytical solution through the approximation of Fourier series and Galerkin method. By comparing the results and performing a parametric study, the accuracy and effects of geometrical and mechanical specifications on the dynamic instability are evaluated.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Shahriar Dastjerdi, Amin Alibakhshi, Bekir Akgoz, Omer Civalek
Summary: This paper applies a semi-analytical polynomial method (SAPM) to solve the mechanical governing equations of nano-sized spherical functionally graded structures. The SAPM is based on polynomial functions and assumes the spherical coordinate system. The results obtained are compared with those in other articles to examine the accuracy of the solution method.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Engineering, Multidisciplinary
Mohammad Amin Shahmohammadi, Sayed Mohamad Mirfatah, Hamzeh Salehipour, Omer Civalek
Summary: The objective of this paper is to evaluate the geometrically nonlinear and size-dependent response of shallow sandwich curved micro-panels. The governing equations are developed using modified couple stress theory based on the first-order shear deformation theory. The equations are analytically solved using the Galerkin method and numerically solved using the forth-order Runge-Kutta method. The accuracy of the method is validated and the effects of various properties on the forced vibration of the micro-panels are evaluated through a parametric study.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Engineering, Aerospace
Sayed Mohamad Mirfatah, Saman Tayebikhorami, Mohammad Amin Shahmohammadi, Hamzeh Salehipour, Omer Civalek
Summary: This paper investigates the geometric nonlinear dynamic behavior of shallow sandwich panels made of nanocomposite enriched face-sheets and auxetic honeycomb core with negative Poisson's ratio. An analytical approach based on the Galerkin method is used to solve the governing nonlinear differential equations, resulting in a closed form equation of motion solved by the fourth-order Runge-Kutta method. The proposed method is verified and shown to yield results with less than 2% error compared to previously published papers. Numerical studies show that the proposed method allows for efficient nonlinear dynamic analysis of the panels.
AEROSPACE SCIENCE AND TECHNOLOGY
(2023)
Article
Engineering, Civil
Emad Sobhani, Amir R. Masoodi, Omer Civalek, Amir Reza Ahmadi-Pari
Summary: This article investigates the frequencies of tangential waves in Functionally Graded (FG) sandwich Merged Hemispherical-Cylindrical Shells (MHCS) with free-damped vibration characteristics. The three-layered MHCS contains Functionally Graded Material (FGM) with functional variation along the thickness. The mechanical features of the materials are determined using Equivalent Single Layer (ESL) and Rule of Mixture (RM). Eight sandwich types are examined, assuming flexible merging and support conditions. The article utilizes Donnell's hypothesis and Hamilton's scheme to acquire the kinetic differential equations and applies the Generalized Differential Quadrature Method (GDQM) to discretize the equations and determine the tangential wave frequencies.
ENGINEERING STRUCTURES
(2023)
Article
Mathematics, Applied
Omer Civalek, Busra Uzun, Mustafa Ozgur Yayli
Summary: This paper proposes a finite element model to investigate the size-dependent vibrational responses of guide-supported imperfect functionally graded nonlocal beams embedded in an elastic foundation. The nonlocal finite element solution considers nonlocal effect, power-law distribution function, sigmoid distribution function, even and uneven porosity models, elastic foundation parameter, and guide support condition for vibration analysis of imperfect FG nanobeams. Tables and figures are used to show the frequency values of perfect/imperfect FG power-law and sigmoid nanobeams obtained by using a nonlocal FE method.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Mathematics, Applied
Ahmed E. Abouelregal, Bekir Akgoz, Omer Civalek
Summary: The objective of this work is to improve a generalized thermoelastic heat transport framework, which is compatible with observable physical processes and allows speed reduction of heat waves within the solid. The proposed model can be used to derive alternative thermoelasticity models as special cases. The influence of Hall current on magneto-thermoelastic couplings in an infinite conducting viscoelastic medium with a cylindrical cavity under a strong magnetic field is also considered.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Civil
Sayed Mohamad Mirfatah, Mohammad Amin Shahmohammadi, Hamzeh Salehipour, Omer Civalek
Summary: The aim of this paper is to study the size-dependent geometrical nonlinear static characteristics of curved panels enriched by nano-additives incorporating thermal effects. The size-dependency is considered by developing the basic equations based on the modified couple stresses theory (MCST). An analytical approach based on the Galerkin method is used to find the response of the achieved set of nonlinear differential equations and obtain a closed-form pressure-deflection relationship representing the nonlinear equilibrium path of the curved micropanels. The closed-form relationship is examined and a parametric numerical study is conducted to investigate the effects of material length-scale parameter (MLSP) and the characteristics of geometry and material on the geometrical nonlinear path of equilibrium.
ENGINEERING STRUCTURES
(2023)
Article
Engineering, Multidisciplinary
Omer Civalek, Busra Uzun, Mustafa Ozgur Yayli
Summary: In this work, the nonlinear stability behaviors of saturated porous nanobeams embedded in an elastic foundation are investigated. The restrained nanobeam is modeled using geometric nonlinear equations and the constitutive law of saturation. Three patterns for saturation along the thickness of the nanobeam are considered. The effects of saturation and nonlinearity on buckling loads are studied, and the nonlinear results are validated.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Engineering, Multidisciplinary
Shahriar Dastjerdi, Omer Civalek, Mohammad Malikan, Bekir Akgoz
Summary: This research focuses on analyzing rotating truncated conical baskets reinforced by carbon nanotubes around two independent axes. A time-dependent analysis is used to extract the nonlinear dynamic governing equations for the structure. Carbon nanotubes are used to reinforce the conical basket, with different distributions impacting the mechanical properties. The resistance of a novel two-axis rotating conical basket as a centrifuge device is investigated at various rotational velocities. The results show that reinforcing the basket with carbon nanotubes increases its resistance against deformation caused by rotation.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2023)
Article
Mechanics
Shahriar Dastjerdi, Mohammad Malikan, Bekir Akgoz, Omer Civalek, Victor A. Eremeyev
Summary: The research simulates the motion of the Earth's layers caused by internal pressures using an efficient mathematical model. By considering the Earth's rotation, the model provides more accurate results regarding the shape and displacement of the internal layers and tectonic plates. It also solves the fully nonlinear and dynamic differential equations using a semi-analytical polynomial method, which is an innovative and efficient approach.
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS
(2023)
Article
Multidisciplinary Sciences
O. Ragb, Mohamed Salah, M. S. Matbuly, H. Ersoy, O. Civalek
Summary: In this study, polynomial, discrete singular convolution, and sinc quadrature techniques were utilized to derive accurate and efficient numerical solutions for reaction-diffusion equations. Three models were presented and reduced to nonlinear ordinary differential equations using different quadrature schemes. The Runge-Kutta fourth-order method was employed to solve these equations, and MATLAB program was used for computation. Comparisons and statistical errors showed the ease of implementation and efficiency of the new methods. Parametric analysis demonstrated the influence of diffusion and reaction parameters on the solution.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2023)
Article
Mechanics
Busra Uzun, Omer Civalek, Mustafa Ozgur Yayli
Summary: This study presents a vibration analysis of functionally graded nano-sized beams resting on an elastic foundation using a finite element method. The beams are modeled based on Euler-Bernoulli beam theory and Eringen's nonlocal elasticity theory under various boundary conditions. The material properties of the beams vary across the thickness direction. The paper emphasizes the use of shape functions and Eringen's nonlocal elasticity theory to establish stiffness matrices and mass matrices for free vibration analysis. Several numerical examples are provided to investigate the effects of different parameters on frequencies.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
