Loading...

**Search for:**strain-gradient-theory

0.007 seconds

Total 94 records

#### Comment on "A micro scale Timoshenko beam model based on strain gradient elasticity theory

, Article European Journal of Mechanics, A/Solids ; 2014 ; ISSN: 09977538 ; Salarieh, H ; Sharif University of Technology
Abstract

A micro scale Timoshenko beam was modeled with strain gradient theory in "A micro scale Timoshenko beam model based on strain gradient elasticity theory" by Wang et al., European Journal of Mechanics - A/Solids, vol. 29, pp. 591-599, 7//2010. Looking at the modeling of the beam, a mistake in deriving the effect of classical moment has occurred. The classical boundary conditions of a Timoshenko beam could not be derived going backward from the strain gradient Timoshenko beam theory which has been presented in aforementioned paper. In this comment, the contradiction has been shown and the correct form of the boundary conditions and final equations has been derived

#### Non-linear behaviors of carbon nanotubes under electrostatic actuation based on strain gradient theory

, Article International Journal of Non-Linear Mechanics ; Vol. 67, issue , 2014 , p. 236-244 ; Rastgoo, A ; Ahmadian, M. T ; Sharif University of Technology
Abstract

The paper deals with studying the deflection and pull-in voltages of the carbon nanotubes under electrostatic actuation with various dimensions and boundary conditions. The size-dependent behaviors of the carbon nanotubes (CNTs) are considered via application of the strain gradient theory. The results obtained from the strain gradient theory are compared to those estimated using the classical elasticity. The outcomes reveal that the classical elasticity theory underestimates the pull-in voltages of the carbon nanotubes and strain gradient theorem results in stiffer nano-structures with higher pull-in voltages. Increasing of the deflection due to the higher voltages increases the differences...

#### Comment on “A micro scale Timoshenko beam model based on strain gradient elasticity theory”

, Article European Journal of Mechanics, A/Solids ; Volume 60 , 2016 , Pages 361-362 ; 09977538 (ISSN) ; Salarieh, H ; Sharif University of Technology
Elsevier Ltd

Abstract

A micro scale Timoshenko beam was modeled with strain gradient theory in “A micro scale Timoshenko beam model based on strain gradient elasticity theory” by Wang et al., European Journal of Mechanics – A/Solids, vol. 29, pp. 591–599, 7//2010. Looking at the modeling of the beam, a mistake in deriving the effect of classical moment has occurred. The classical boundary conditions of a Timoshenko beam could not be derived going backward from the strain gradient Timoshenko beam theory which has been presented in aforementioned paper. In this comment, the contradiction has been shown and the correct form of the boundary conditions and final equations has been derived

#### Carbon nanotube-based nano-fluidic devices

, Article Journal of Physics D: Applied Physics ; Vol. 47, issue. 8 , 2014 ; ISSN: 00223727 ; Rastgoo, A ; Ahmadian, M. T ; Sharif University of Technology
Abstract

The paper investigates the influences of fluid flow on static and dynamic behaviours of electrostatically actuated carbon nanotubes (CNTs) using strain gradient theory. This nonclassical elasticity theory is applied in order to obtain more accurate results possessing higher agreement with the experimental data. The effects of various fluid parameters such as the fluid viscosity, velocity, mass and temperature on the pull-in properties of the CNTs with two cantilever and doubly clamped boundary conditions are studied. The results reveal the applicability of the proposed nano-system as nano-valves or nano-fluidic sensors

#### Second strain gradient theory in orthogonal curvilinear coordinates: Prediction of the relaxation of a solid nanosphere and embedded spherical nanocavity

, Article Applied Mathematical Modelling ; Volume 76 , 2019 , Pages 669-698 ; 0307904X (ISSN) ; Shodja, H. M ; Sharif University of Technology
Elsevier Inc
2019

Abstract

In this paper, Mindlin's second strain gradient theory is formulated and presented in an arbitrary orthogonal curvilinear coordinate system. Equilibrium equations, generalized stress-strain constitutive relations, components of the strain tensor and their first and second gradients, and the expressions for three different types of traction boundary conditions are derived in any orthogonal curvilinear coordinate system. Subsequently, for demonstration, Mindlin's second strain gradient theory is represented in the spherical coordinate system as a highly-practical coordinate system in nanomechanics. Second strain gradient elasticity have been developed mainly for its ability to capture the...

#### Calculation of the Additional Constants for Fcc Materials in Second Strain Gradient Elasticity: Behavior of a Nano-Size Bernouli--Euler Beam with Surface Effects

, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fcc metals are given in terms of the parameters of Sutten-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a...

#### Poly silicon nanobeam model based on strain gradient theory

, Article Mechanics Research Communications ; Vol. 62 , December , 2014 , pp. 83-88 ; ISSN: 00936413 ; Yousefi-Koma, A ; Pishkenari, H. N ; Sharif University of Technology
Abstract

Conventional continuum theory does not account for contributions from length scale effects. Failure to include size-dependent contributions can lead to underestimates of deflection and stresses of micro and nanobeams. This research aims to use strain gradient elasticity theory to model size-dependent behavior of small beams. In this regard, Young's modulus and length scale parameters of poly silicon are estimated by fitting the predicted static pull-in voltages to the reported experimental results in the literature. The results demonstrate that decreasing the beam thickness results in higher pull-in voltage, lower deflection and lower sensitivity to axial stress and mid-plane stretching in...

#### Forced Vibration Analysis of Rotating Micro-Shaft Based on the Non-local Strain Gradient Theory

, M.Sc. Thesis Sharif University of Technology ; Asghari, Mohsen (Supervisor)
Abstract

Nowadays, with progresses made in manufacturing technologies, it is possible to produce micro-scale products such as micro-electromechanical systems. Micro-motors are one type of these systems that can be used in such applications as power supply of electronic devices. To achieve a better performance, these systems must rotate at high rotational speeds (about one million revolutions per minute). At such a high rotational speed, vibrational analysis is highly crucial. The results of recent studies indicate the inability of classical theories of continuum mechanics to analyze the behavior of these micro systems. Therefore, in this research, the rotor of micro-motors are modeled using the...

#### Surface elasticity revisited in the context of second strain gradient theory

, Article Mechanics of Materials ; Volume 93 , 2016 , Pages 220-237 ; 01676636 (ISSN) ; Shodja, H. M ; Sharif University of Technology
Elsevier

Abstract

Surface/interface stresses, when notable, are closely associated with a surface/interface layer in which the interatomic bond lengths and charge density distribution differ remarkably from those of the bulk. The presence of such topographical defects as edges and corners amplifies the noted phenomena by large amounts. If the principal features of interest are such studies as the physics and mechanics of evolving microscopic-/nanoscopic-interfaces and the behavior of nano-sized structures which have a very large surface-to-volume ratio, traditional continuum theories cease to hold. It is for the treatment of such problems that augmented continuum approaches like second strain gradient and...

#### The second strain gradient theory-based Timoshenko beam model

, Article JVC/Journal of Vibration and Control ; Volume 23, Issue 13 , 2017 , Pages 2155-2166 ; 10775463 (ISSN) ; Momeni, S. A ; Vatankhah, R ; Sharif University of Technology
SAGE Publications Inc
2017

Abstract

The governing equations of motion, together with the associated boundary conditions, are derived for the second strain gradient Timoshenko micro- and nano-beams. The second strain gradient theory is a highly powerful nonclassical continuum theory, capable of capturing the size effects in micro- and nano-scale structures. In case studies, the static and free-vibration behaviors of a hinged-hinged beam are investigated utilizing the presented second strain gradient theory-based Timoshenko beam model. The obtained results are compared with those of the available models in the literature, which are based on the (first) strain gradient theory, the modified couple stress theory, and the classical...

#### Modeling the coupled effects of surface layer and size effect on the static and dynamic instability of narrow nano-bridge structure

, Article Journal of the Brazilian Society of Mechanical Sciences and Engineering ; Volume 39, Issue 5 , 2017 , Pages 1735-1744 ; 16785878 (ISSN) ; Koochi, A ; Kanani, A ; Navazi, H. M ; Abadyan, M ; Sharif University of Technology
Springer Verlag
2017

Abstract

For modeling the electromechanical behavior of nano-bridge structures with slender narrow-width beam elements, not only the simultaneous effects of surface layer and size dependency should be taken into account but also corrected force models should be considered. In this paper, the instability of a narrow-width nano-bridge is studied based on strain gradient theory and Gurtin–Murdoch surface elasticity. The mid-plane stretching is incorporated in the governing equation as well as corrected force distribution. Using Rayleigh–Ritz method, a parametric analysis is conducted to examine the impacts of surface layer, size dependence, dispersion forces and structural damping on static and dynamic...

#### Exact solution for frequency response of sandwich microbeams with functionally graded cores

, Article JVC/Journal of Vibration and Control ; Volume 25, Issue 19-20 , 2019 , Pages 2641-2655 ; 10775463 (ISSN) ; Fallah, F ; Sharif University of Technology
SAGE Publications Inc
2019

Abstract

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton’s principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the...

#### Prediction of in-plane elastic properties of graphene in the framework of first strain gradient theory

, Article Meccanica ; Volume 54, Issue 1-2 , 2019 , Pages 299-310 ; 00256455 (ISSN) ; Mehralian, F ; Dehghani Firouz Abadi, R ; Borhan Panah, M. R ; Rahmanian, M ; Sharif University of Technology
Springer Netherlands
2019

Abstract

In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular mechanics model. To this end, a Wigner–Seitz primitive cell is adopted. Additionally, the first strain gradient theory for graphene with trigonal crystal system is formulated and the relation between elastic stiffness coefficients and molecular mechanics parameters are calculated. Thus, the ongoing research challenge on providing the accurate mechanical properties of graphene is addressed herein. Using results obtained, the in-plane free vibration of graphene is studied and a detailed numerical investigation is...

#### Prediction of in-plane elastic properties of graphene in the framework of first strain gradient theory

, Article Meccanica ; Volume 54, Issue 1-2 , 2019 , Pages 299-310 ; 00256455 (ISSN) ; Mehralian, F ; Dehghani Firouz-Abadi, R ; Borhan Panah, M. R ; Rahmanian, M ; Sharif University of Technology
Springer Netherlands
2019

Abstract

In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular mechanics model. To this end, a Wigner–Seitz primitive cell is adopted. Additionally, the first strain gradient theory for graphene with trigonal crystal system is formulated and the relation between elastic stiffness coefficients and molecular mechanics parameters are calculated. Thus, the ongoing research challenge on providing the accurate mechanical properties of graphene is addressed herein. Using results obtained, the in-plane free vibration of graphene is studied and a detailed numerical investigation is...

#### Nonlinear forced vibration of strain gradient microbeams

, Article Applied Mathematical Modelling ; Volume 37, Issue 18-19 , 1 October , 2013 , pp. 8363-8382 ; ISSN: 0307904X ; Kahrobaiyan, M. H ; Alasty, A ; Ahmadian, M. T ; Sharif University of Technology
Abstract

In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler-Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior...

#### Dynamic information of the time-dependent tobullian biomolecular structure using a high-accuracy size-dependent theory

, Article Journal of Biomolecular Structure and Dynamics ; 2020 ; Shamsodin, M ; Wang, H ; NoormohammadiArani, O ; Mashood Khan, A ; Habibi, M ; Al Furjan, M. S. H ; Sharif University of Technology
Taylor and Francis Ltd
2020

Abstract

As the most rigid cytoskeletal filaments, tubulin–labeled microtubules bear compressive forces in living cells, balancing the tensile forces within the cytoskeleton to maintain the cell shape. The current structure is often under several environmental conditions as well as various dynamic or static loads that can decrease the stability of the viscoelastic tubulin–labeled microtubules. For this issue, the dynamic stability analysis of size-dependent viscoelastic tubulin–labeled microtubules using modified strain gradient theory by considering the exact three-length scale parameter. Viscoelastic properties are modeled using Kelvin-Voight model to study the time-dependent tubulin–labeled...

#### Effect of Curved Micro-beam on Natural Frequency and Pull-In Voltage Considering Strain Gradient Theory

, M.Sc. Thesis Sharif University of Technology ; Ahmadiyan, Mohammad Taghi (Supervisor) ; Firoozbakhsh, Keikhosrow (Supervisor)
Abstract

A microbeam, actuated by electrostatic distributed force, is a flexible beam-shaped element attached to a fixed rigid substrate. Electrostatically actuated microbeams are extensively used in different applications such as signal filtering and mass sensing. When the input voltage exceeds a critical value, called pull-in voltage (V_pi), the flexible microbeam spontaneously deflects towards the rigid plate. Pull-in instability is a basic phenomenon considered in the design of the micro actuators. When the rate of voltage variation is low and consequently inertia has almost no influence on the microsystem behavior, the critical value of voltage is called static pull-in voltage (V_pi). However,...

#### The Analysis of Cracked Atomic Force Microscope Micro-Cantilever by Strain Gradient Theory

, M.Sc. Thesis Sharif University of Technology ; Asghari, Mohsen (Supervisor)
Abstract

The present study deals with the analysis of Atomic Microscope with crack by making use of Strain Gradient Elasticity theory. Empirical observations represent that in micro dimensions, materials show behaviors, which the classic continuum mechanics theories are not able to explain. Thus, taking advantage of non-classic theories, which are capable of explaining such phenomena or behaviors in analyzing materials in micro dimensions seems necessary and of much significance. In this direction, by applying an Euler-Bernoulli beam assumption and neglecting the shear effects, governing equations and boundary conditions of the problem were obtained via taking advantage of variations in Hamilton...

#### Post-Buckling Analysis of Microplates based on the Strain Gradient Elasticity Theory

, M.Sc. Thesis Sharif University of Technology ; Asghari, Mohsen (Supervisor)
Abstract

In recent years, the world has seen a great progress in micro electro-mechanical systems (MEMS). Small size, low weight, high accuracy and low energy consumption have made these devices applicable in a variety of usages. In MEMS devices, mechanical components are used for specific purposes among which one of the most widely used are micro plates. Microplates are used in the structure of many devices such as microswitchs and atomic force microscopes. Therefore, studying of static and dynamic behavior of microplates is important. As the object gets smaller (to the scale of micro and nano meters), the classic theory of mechanics of continuous media cannot predict the behavior due to its...

#### “Static and Dynamic Analysis of Vibrating Ring Gyroscopes based on the Strain Gradient Theory”

, Ph.D. Dissertation Sharif University of Technology ; Ahmadian, Mohammad Taghi (Supervisor) ; Firoozbakhsh, Kikhosro (Supervisor) ; Rahaeifard, Massuod (Co-Advisor)
Abstract

Vibrating ring gyroscopes (VRG) as MEMS devices are employed to micro scale systems for determination of the rotation rate and rotation speed of them. It is experimentally approved that micro scale structures behaves differently in comparison to macro scale systems, Therefore higher order continuum theories are required for modeling and analysis of these systems. In addition to that there is no comprehensive investigation on the dynamic performance of ring gyroscopes in the literature, In view of this in the present research the static and dynamic analysis of vibrating ring gyroscopes based on the strain gradient theory and the proposed finite element model of the gyroscope is performed. The...