Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials

Mohammad Zamani Nejad,Amin Hadi,Ali Farajpour 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.63 No.2

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler- Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory

Nejad, Mohammad Zamani,Hadi, Amin,Omidvari, Arash,Rastgoo, Abbas Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.67 No.4

The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen's non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers' knowledge, in the literature, there is no study carried out into integral form of Eringen's non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen's non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen's model. For all boundary conditions, it is clearly seen that the integral form of Eringen's model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied.

Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen’s non-local elasticity theory

Mohammad Zamani Nejad,Amin Hadi,Arash Omidvari,Abbas Rastgoo 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.67 No.4

The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen‟s non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers‟ knowledge, in the literature, there is no study carried out into integral form of Eringen‟s non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen‟s non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen‟s model. For all boundary conditions, it is clearly seen that the integral form of Eringen‟s model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied.

An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties

Mohammad Zamani Nejad,Majid Abedi,Mohammad Hassan Lotfian,Mehdi Ghannad 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.12

Exact closed-form solutions have been derived for stresses and the displacements in thick spherical shells made of functionally graded materials with exponential-varying properties subjected to internal and external pressure. Poisson’s ratio is assumed to be constant. The obtained results show that the inhomogeneity properties of FGMs have a significant influence on the displacement and stresses distribution along the radial direction. A numerical solution using finite element method is also presented and good agreement was found between the analytical solutions and the solutions carried out through the FEM. The values used in this study are arbitrarily chosen to demonstrate the effect of inhomogeneity on displacements and stresses distributions.

Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates

Dehshahri, Kasra,Nejad, Mohammad Zamani,Ziaee, Sima,Niknejad, Abbas,Hadi, Amin Techno-Press 2020 Advances in nano research Vol.8 No.2

In this paper, the free vibrations analysis of the nanoplates made of three-directional functionally graded material (TDFGM) with small scale effects is presented. To study the small-scale effects on natural frequency, modified strain gradient theory (MSGT) has been used. Material properties of the nanoplate follow an arbitrary function that changes in three directions along the length, width and thickness of the plate. The equilibrium equations and boundary conditions of nanoplate are obtained using the Hamilton's principle. The generalized differential quadrature method (GDQM) is used to solve the governing equations and different boundary conditions for obtaining the natural frequency of nanoplate made of three-directional functionally graded material. The present model can be transformed into a couple stress plate model or a classic plate model if two or all parameters of the length scales set to zero. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants and the aspect ratio with different boundary conditions on the free vibrations of nanoplates. To the best of the researchers' knowledge, in the literature, there is no study carried out into MSGT for free vibration analysis of FGM nanoplate with arbitrary functions.

Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels

Tayebeh Ebrahimi,Mohammad Zamani Nejad,Hamid Jahankohan,Amin Hadi 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.38 No.2

An analytical solution is presented to analyze the thermoelastoplastic response of a rotating thick-walled cylindrical pressure vessel made of functionally graded material (FGM). The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening material behaviour. The uncoupled theory of thermoelasticity is used, and the plane strain condition is assumed. The material properties except for Poisson's ratio, are assumed to vary nonlinearly in the radial direction. Elastic, partially plastic, fully plastic, and residual stress states are investigated. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the vessel. It is assumed that‏ the inner surface is exposed to an airstream and that the outer surface is exposed to a uniform heat flux. Tresca's yield criterion and its associated flow rule are used to formulate six different plastic regions for a linearly hardening‏ condition. All these stages are studied in detail. It is shown that the thermoelastoplastic stress response of a rotating FGM pressure vessel is affected significantly by the nonhomogeneity of the material and temperature gradient. The results are validated with those of other researchers for appropriate values of the system parameters and excellent agreement is observed.

Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory

Amin Hadi,Mohammad Zamani Nejad,Abbas Rastgoo,Mohammad Hosseini 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.26 No.6

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

Buckling analysis of arbitrary two-directional functionally graded nano-plate based on nonlocal elasticity theory using generalized differential quadrature method

Maryam Emadi,Mohammad Zamani Nejad,Sima Ziaee,Amin Hadi 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.39 No.5

In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen’s nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson’s ratio boundary condition and side to thickness ratio on size dependent Frequency.

Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells

Mosayeb Davoudi Kashkoli,Mohammad Zamani Nejad 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.28 No.3

This paper presents a semi-analytical solution for the creep analysis and life assessment of 304L austenitic stainless steel thick truncated conical shells using multilayered method based on the first order shear deformation theory (FSDT). The cone is subjected to the non-uniform internal pressure and temperature gradient. Damages are obtained in thick truncated conical shell using Robinson's linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson-Miller Parameter (LMP). The creep response of the material is described by Norton's law. In the multilayer method, the truncated cone is divided into <i>n</i> homogeneous disks, and <i>n</i> sets of differential equations with constant coefficients. This set of equations is solved analytically by applying boundary and continuity conditions between the layers. The results obtained analytically have been compared with the numerical results of the finite element method. The results show that the multilayered method based on FSDT has an acceptable amount of accuracy when one wants to obtain radial displacement, radial, circumferential and shear stresses. It is shown that non-uniform pressure has significant influences on the creep damages and remaining life of the truncated cone.

Creep damage and life assessment of thick cylindrical pressure vessels with variable thickness made of 304L austenitic stainless steel

Mosayeb Davoudi Kashkoli,Khosro Naderan Tahan,Mohammad Zamani Nejad 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.6

Using firstfirst-order shear deformation theory (FSDT), a semi semi-analytical solution is employed to analyze creep damage and remaining life assessment of 304L austenitic stainless steel thick (304L ASS) cylindrical pressure vessels with variable thickness subjected to the temperature gradient and internal non non-uniform pressure. Damages are obtained in thick cylinder using RobinsonRobinson’s linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson Larson-Miller Parameter (LMP). The thermo-elastic creep response of the material is described by Norton Norton’s law. The novelty of the present work is that it seeks to investigate creep damage and life assessment of the vessels with variable thickness made of 304L ASS using LMP based on first first-order shear deformation theory. A numerical solution using finite element method (FEM) is also presented and good agreement is found. It is shown that temperature gradient and non non-uniform pressure have significant influences on the creep damages and remaining li fe of the vessel vessel.