Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
A Modified Couple Stress Theory for Postbuckling Analysis of Timoshenko and Reddy-Levinson Single-Walled Carbon Nanobeams
364
373
EN
M
Akbarzadeh Khorshidi
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
M
Shariati
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
mshariati44@um.ac.ir
The novelty of this study is presentation of an exact solution for prediction of postbuckling behavior of shear deformable micro- and nano-scale beams based on modified couple stress theory and using principle of minimum potential energy. Timoshenko and Reddy-Levinson beam theories are applied to consider the shear deformation effect and Von Karman nonlinear kinematics is used to describe the nonlinear behavior of the postbuckling, and the Poisson's effect is also considered in stress-strain relation. Also, the size effect is exposed by introducing a material length scale parameter. Finally, the influences of shear deformation, Poisson's ratio and variations of length and thickness are investigated. The results indicate that the classical theory exaggerates the postbuckling amplitude of the nanobeam and overstates the effect of shear deformation on the postbuckling response of the nanobeam.
Postbuckling,Single-walled carbon nanobeam,Timoshenko and Reddy-Levinson beam theories
http://jsm.iau-arak.ac.ir/article_516395.html
http://jsm.iau-arak.ac.ir/article_516395_faac6e48e23ec4b0d41539d7dff64fe4.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
A Simple and Systematic Approach for Implementing Boundary Conditions in the Differential Quadrature Free and Forced Vibration Analysis of Beams and Rectangular Plates
374
399
EN
S.A
Eftekhari
Young Researchers and Elite Club, Karaj Branch, Islamic Azad University
aboozar.eftekhari@yahoo.com
This paper presents a simple and systematic way for imposing boundary conditions in the differential quadrature free and forced vibration analysis of beams and rectangular plates. First, the Dirichlet- and Neumann-type boundary conditions of the beam (or plate) are expressed as differential quadrature analog equations at the grid points on or near the boundaries. Then, similar to CBCGE (direct Coupling the Boundary Conditions with the discrete Governing Equations) approach, the resulting analog equations are used to replace the differential quadrature analog equations of the governing differential equations at these points in order to solve the problem. But, unlike the CBCGE approach, the grid points near the boundaries are not treated as boundary points in the proposed approach. In other words, the degrees of freedom related to Dirichlet-type boundary conditions are only eliminated from the original discrete equations. This simplifies significantly the solution procedure and its programming. A comparison of the proposed approach with other existing methodologies such as the CBCGE approach and MWCM (modifying weighting coefficient matrices) method is presented by their application to the vibration analysis of beams and rectangular plates with general boundary conditions to highlight the advantages of the new approach.
Simple and systematic approach,Implementation of boundary conditions,Differential quadrature method,Dirichlet-type boundary conditions,Neumann-type boundary conditions,Free and forced vibration analysis,Beams,Rectangular plates
http://jsm.iau-arak.ac.ir/article_516397.html
http://jsm.iau-arak.ac.ir/article_516397_42a653b020be9c44307583c8e993352c.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
Thermo-Viscoelastic Interaction Subjected to Fractional Fourier law with Three-Phase-Lag Effects
400
415
EN
P
Pal
Department of Applied Mathematics, University of Calcutta
A
Sur
Department of Applied Mathematics, University of Calcutta
abhiksur4@gmail.com
M
Kanoria
Department of Applied Mathematics, University of Calcutta
k_mri@yahoo.com
In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts thermoelasticity without energy dissipation (TEWOED) and with energy dissipation (TEWED)) are employed to study the thermo-mechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in complex domain by using Laguerre's method and the inversion of the Laplace transform is done numerically using a method based on Fourier series expansion technique. Some comparisons have been shown in the form of the graphical representations to estimate the effect of the non-local fractional parameter and the effect of viscosity is also shown.
Generalized thermoelasticity,Three-phase-lag model,Kelvin-Voigt model,Modified riemann-liouville fractional derivatives,Fractional Taylor’s series
http://jsm.iau-arak.ac.ir/article_516398.html
http://jsm.iau-arak.ac.ir/article_516398_c7391dc69170df69f5684140bb95d459.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
Magnetic Stability of Functionally Graded Soft Ferromagnetic Porous Rectangular Plate
416
428
EN
M
Jabbari
Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University
mohsen.jabbari@gmail.com
M
Haghi Choobar
Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University
A
Mojahedin
Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University
E
Farzaneh Joubaneh
Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University
This study presents critical buckling of functionally graded soft ferromagnetic porous (FGFP) rectangular plates, under magnetic field with simply supported boundary condition. Equilibrium and stability equations of a porous rectangular plate in transverse magnetic field are derived. The geometrical nonlinearities are considered in the Love-Kirchhoff hypothesis sense. The formulations are compared to those of homogeneous isotropic plates were given in the literature. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are studied.
Buckling analysis,Rectangular plate,Functionally graded plate,Porous material,Magnetic Field
http://jsm.iau-arak.ac.ir/article_516400.html
http://jsm.iau-arak.ac.ir/article_516400_f0192d2163d9cd368829633c0cadda74.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
Analysis of Axisymmetric Extrusion Process through Dies of any Shape with General Shear Boundaries
429
441
EN
H
Haghighat
Mechanical Engineering Department, Razi University
hhaghighat@razi.ac.ir
G.R
Asgari
Faculty of Mechanical Engineering , Shahid Rajaee Training University
In this paper, a generalized expression for the flow field in axisymmetric extrusion process is suggested to be valid for any dies and the boundary shapes of the plastic deformation zone. The general power terms are derived and the extrusion force is calculated by applying upper bound technique for a streamlined die shape and exponential functions for shear boundaries. It is shown that assuming exponential boundaries for deformation zone yields a die shape with smaller extrusion force than that of by assuming spherical shape boundaries is in agreement with the results obtained by the finite element method.
Axisymmetric extrusion,Velocity field,Upper bound method
http://jsm.iau-arak.ac.ir/article_516402.html
http://jsm.iau-arak.ac.ir/article_516402_a3f475afc6b15ddb3b8971d0758b4f06.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
The Effect of Fiber Breakage on Transient Stress Distribution in a Single-Lap Joint Composite Material
442
457
EN
M
Shishehsaz
Department of Mechanical Engineering, Shahid Chamran University
mshishehsaz@scu.ac.ir
S
Yaghoubi
Department of Mechanical Engineering, Bu-Ali Sina University
In the present study, the transient stress distribution caused by a break in the fibers of an adhesive bonding is investigated. Transient stress is a dynamic response of the system to any discontinuity in the fibers from detachment time till their equilibrium state (or steady state). To derive the governing dynamic equilibrium equations shear lag model is used. Here, it is assumed that the tensile load is supported only by the fibers. Employing dimensionless equations, initial conditions and proper boundary conditions, the differential-difference equations are solved using explicit finite difference method and the transient stress distribution is obtained in the presence of discontinuities. The present work aims to investigate the transient stress distribution in a single-lap joint, caused by the fiber breakage in a single layer of the adhesive joint. For this purpose, the effect of different number of broken fibers (including mid fiber) in the adherend on load distribution in other intact filaments, the location of fiber breaks in the adherend, and the effect of adhesive length is studied on the overall joint behavior. The results show that a the fiber is broken away, the amount of initial shock (maximum load) into the fiber and thus the dynamic overshoot is reduced. Maximum amount of shock in the lateral fibers is broken at this point due to breakage in the thirteenth fiber maximum axial load and shock are introduce to the fourteenth fiber.
Composite,Fibers,Adhesive joints,Stress concentration,Transient stress
http://jsm.iau-arak.ac.ir/article_516404.html
http://jsm.iau-arak.ac.ir/article_516404_a96fcfb9fb3da96dc50e5f28ba30d423.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
Modified Couple Stress Theory for Vibration of Embedded Bioliquid-Filled Microtubules under Walking a Motor Protein Including Surface Effects
458
476
EN
A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan---
Institute of Nanoscience & Nanotechnology, University of Kashan
aghorban@kashanu.ac.ir
M
Abdollahian
Faculty of Mechanical Engineering, University of Kashan
A.H
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Microtubules (MTs) are fibrous and tube-like cell substructures exist in cytoplasm of cells which play a vital role in many cellular processes. Surface effects on the vibration of bioliquid MTs surrounded by cytoplasm is investigated in this study. The emphasis is placed on the effect of the motor protein motion on the MTs. The MT is modeled as an orthotropic beam and the surrounded cytoplasm is assumed as an elastic media which is simulated by Pasternak foundation. In order to consider the small scale effects, the modified couple stress theory (MCST) is taken into account. An analytical method is employed to solve the motion equations obtained by energy method and Hamilton’s principle. The influence of surface layers, bioliquid, surrounding elastic medium, motor proteins motion, and small scale parameter are shown graphically. Results demonstrate that the speed of motor proteins is an effective parameter on the vibration characteristics of MTs. It is interesting that increasing the motor proteins speed does not change the maximum and minimum values of MTs dynamic deflection. The presented results might be useful in biomedical and biomechanical principles and applications.
Dynamic deflection,Motor protein movement,Bioliquid-filled microtubules,Cytoplasm,Modified couple stress theory
http://jsm.iau-arak.ac.ir/article_516405.html
http://jsm.iau-arak.ac.ir/article_516405_64cbfe4f0fd06fb028d60a0835c4d521.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
7
4
2015
12
30
Effect of Thermal Gradient on Vibration of Non-Homogeneous Square Plate with Exponentially Varying Thickness
477
484
EN
A
Khanna
Department of Mathematics, DAV College Sadhaura, Yamuna Nagar, Haryana
rajieanupam@gmail.com
R
Deep
Department of Mathematics, Maharishi Markandeshwar University- Mullana
D
Kumar
Department of Mathematics, Maharishi Markandeshwar University- Mullana
Vibrations of plate and plate type structures made up of composite materials have a significant role in various industrial mechanical structures, aerospace industries and other engineering applications. The main aim of the present paper is to study the two dimensional thermal effect on the vibration of non-homogeneous square plate of variable thickness having clamped boundary. It is assumed that temperature varies bi-parabolic i.e. parabolic in x-direction & parabolic in y-direction and thickness is considered to vary exponentially in x direction. Also, density is taken as the function of “x” due to non-homogeneity present in the plate’s material. Rayleigh Ritz technique is used to calculate the natural frequency for both the modes of vibration for the various values of taper parameter, non-homogeneity constant and thermal gradient. All the calculations are carried out for an alloy of Aluminum, Duralumin<em>,</em> by using mathematica.
Vibration,Frequency,Thermal gradient,Taper constant,Non-homogeneity constant
http://jsm.iau-arak.ac.ir/article_516406.html
http://jsm.iau-arak.ac.ir/article_516406_4b712a6cca3fb3b2c4e86f55410656a6.pdf