20200707T15:57:23Z
http://jsm.iauarak.ac.ir/?_action=export&rf=summon&issue=116482
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Effect of Follower Force on Vibration Frequency of MagnetoStrictiveFaced Sandwich Plate with CNTR Composite Core
M.R
Ghorbanpour Arani
Z
Khoddami Maraghi
This study deals with the vibration response of sandwich plate with nanocomposite core and smart magnetostrictive face sheets. Composite core is reinforced by carbon nanotubes (CNTs) and its effective elastic properties are obtained by the rule of Mixture. TerfenolD films are used as the face sheets of sandwich due to magnetomechanical coupling in magnetostrictive material (MsM). In order to investigate the magnetization effect on the vibration characteristics of sandwich plate, a feedback control system is utilized. Also the sandwich plate undergoes the follower forces in opposite direction of x. Based on energy method, equations of motions are derived using Reddy’s third order shear deformation theory, and Hamilton’s principle and solved by differential quadrature method (DQM). A detailed numerical study is carried out based on thirdorder shear deformation theory to indicate the significant effect of follower forces, volume fraction of CNTs, temperature change, coretoface sheet thickness ratio and controller effect of velocity feedback gain on dimensionless frequency of sandwich plate. These finding can be used to automotive industry, aerospace and building industries.
Sandwich plate
Follower force
Feedback control system
NanoComposite
Magnetostrictive sheets
2018
12
30
688
701
http://jsm.iauarak.ac.ir/article_545713_284dbbab68338eb09b90612246f5b9ba.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
QuasiStatic Deformation of a Uniform Thermoelastic Half –Space Due to Seismic Sources and Heat Source
A.K
Vashishth
K
Rani
This paper investigates the quasistatic plane deformation of an isotropic thermoelastic halfspace due to buried seismic sources and heat source. Governing equations of thermoelasticity are solved to obtain solutions for seismic sources in a thermoelastic halfspace. The general solutions are acquired with the aid of Laplace and Fourier transforms and with the use of boundary conditions. The case of dipslip line dislocation is studied in detail along with line heat source. Analytical solutions for two limiting cases: adiabatic and isothermal, are obtained. The solutions for displacement, stresses and temperature in spacetime domain are obtained by using a numerical inversion procedure. The accuracy of the proposed method is verified through a comparison of the results obtained with the existing solutions for elastic medium. In addition, numerical results for displacements, stresses and temperature function, induced by a vertical dipslip dislocation and line heat source, are presented graphically to illustrate the effect of inclusion of thermal effect in simulation of the problem.
Thermoelastic
Seismic source
Dipslip dislocation
Plane deformation
Heat source
2018
12
30
702
718
http://jsm.iauarak.ac.ir/article_545714_ea4baa2981a32dcee431ab74e5561bdb.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
TwoDimensional Elasticity Solution for Arbitrarily Supported Axially Functionally Graded Beams
A
Singh
P
Kumari
<span>First</span><span> time, an analytical twodimensional (2D) elasticity solution for arbitrarily supported axially functionally graded (FG) beam is developed. Linear gradation of the material property along the axis of the beam is considered. Using the strain displacement and constitutive relations, governing partial differential equations (PDEs) is obtained by employing Ressiner mixed variational principle. Then PDEs are reduced to two set of ordinary differential equations (ODEs) by using recently developed extended Kantorovich method. The set of 4<em>n</em> ODEs along the <em>z</em>direction has constant coefficients. But, the set of 4<em>n</em> nonhomogeneous ODEs along <em>x</em>direction has variable coefficients which is solved using modified power series method. Efficacy and accuracy of the present methodology are verified thoroughly with existing literature and 2D finite element solution. Effect of axial gradation, boundary conditions and configuration layups are investigated. It is found that axial gradation influence vary with boundary conditions. These benchmark results can be used for assessing 1D beam theories and further present formulation can be extended to develop solutions for 2D micro or Nanobeams. </span>
Axially functionally graded
TwoDimensional elasticity
Arbitrary supported
Extended Kantorovich method
2018
12
30
719
733
http://jsm.iauarak.ac.ir/article_545715_c4a2ed8ed7838886bc9aff06688c8347.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
OneDimensional Transient Thermal and Mechanical Stresses in FGM Hollow Cylinder with Piezoelectric Layers
S.M
Mousavi
M
Jabbari
M.A
Kiani
In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient temperature distribution, as a function of radial direction and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler equation and complex Fourier series. This method of solution does not have the limitations of the potential function or numerical methods as to handle more general types of the mechanical and thermal boundary conditions.
Transient
Symmetric thermal stress
Hollow cylinder
Functionally graded material
Piezoelectric
2018
12
30
734
752
http://jsm.iauarak.ac.ir/article_545716_2fec8bf49c3416c8383be6369424f803.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Dynamic Behavior of Anisotropic Protein Microtubules Immersed in Cytosol Via Cooper–Naghdi Thick Shell Theory
M.R
Ghorbanpour Arani
Z
Khoddami Maraghi
E
Haghparast
In the present research, vibrational behavior of anisotropic protein microtubules (MTs) immersed in cytosol via Cooper–Naghdi shell model is investigated. MTs are hollow cylindrical structures in the eukaryotic cytoskeleton which surrounded by filament network. The temperature effect on vibration frequency is also taken into account by assuming temperaturedependent material properties for MTs. To enhance the accuracy of results, strain gradient theory is utilized and the motion equations are derived based on Hamilton’s principle. Effects of various parameters such as environmental conditions by considering the surface traction of cytosol, length scale, thickness and aspect ratio on vibration characteristics of anisotropic MTs are studied. Results indicate that vibrational behavior of anisotropic MTs is strongly dependent on longitudinal Young’s modulus and length scale parameters. The results of this investigation can be utilized in the ultrasonic examine of MT organization in medical applications particularly in the treatment of cancers.
Anisotropic protein MT
Cooper–Naghdi thick shell model
Strain gradient theory
Viscoelastic biomedium
2018
12
30
753
765
http://jsm.iauarak.ac.ir/article_545717_af2e1aa3c9a349a9c840635095696b69.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Estimation of Thermoelastic State of a Thermally Sensitive Functionally Graded Thick Hollow Cylinder: A Mathematical Model
V. K
Manthena
N.K
Lamba
G.D
Kedar
The object of the present paper is to study temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature. The nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity is reduced to linear form by applying Kirchhoff’s variable transformation. Solution for the two dimensional heat conduction equation with internal heat source is obtained in the transient state. The influence of thermosensitivity on the thermal and mechanical behavior is examined. For theoretical treatment all physical and mechanical quantities are taken as dimensional, whereas for numerical computations we have considered nondimensional parameters. A mathematical model is constructed for both homogeneous and nonhomogeneous case. Numerical computations are carried out for ceramicmetalbased functionally graded material (FGM), in which alumina is selected as ceramic and nickel as metal. The results are illustrated graphically.
Functionally graded hollow cylinder
Temperature distribution
Thermal stresses
Thermosensitivity
2018
12
30
766
778
http://jsm.iauarak.ac.ir/article_545718_605f67f4cfd6308acbdfad4eca2ed342.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Influence of Temperature Change on Modal Analysis of Rotary Functionally Graded Nanobeam in Thermal Environment
E
Shahabinejad
N
Shafiei
M
Ghadiri
The free vibration analysis of rotating functionally graded (FG) nanobeams under an inplane thermal loading is provided for the first time in this paper. The formulation used is based on EulerBernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature method (GDQM). It is supposed that, according to the powerlaw form (PFGM), the thermal distribution is nonlinear and material properties are dependent to temperature and are changing continuously through the thickness. Free vibration frequencies are obtained for two types of boundary conditions; cantilever and propped cantilever. The novelty of this work is related to vibration analysis of rotating FG nanobeam under different distributions of temperature with different boundary conditions using nonlocal EulerBernoulli beam theory. Presented theoretical results are validated by comparing the obtained results with literature. Numerical results are presented in both cantilever and propped cantilever nanobeams and the influences of the thermal, nonlocal smallscale, angular velocity, hub radius, FG index and higher modes number on the natural frequencies of the FG nanobeams are investigated in detail.
Rotating EulerBernoulli beam
FG Nanobeam
Eringen elasticity theory
GDQM
Thermal vibration
2018
12
30
779
803
http://jsm.iauarak.ac.ir/article_545719_a53490ca1a23c70a7a3fa3fcf095c7e5.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Delamination of TwoDimensional Functionally Graded Multilayered NonLinear Elastic Beam  an Analytical Approach
V
Rizov
Delamination fracture of a twodimensional functionally graded multilayered fourpoint bending beam that exhibits nonlinear behaviour of the material is analyzed. The fracture is studied analytically in terms of the strain energy release rate. The beam under consideration has an arbitrary number of layers. Each layer has individual thickness and material properties. A delamination crack is located arbitrary between layers. The material is twodimensional functionally graded in the crosssection of each layer. The beam mechanical behaviour is described by a powerlaw stressstrain relation. The fracture is analyzed also by applying the <em>J</em>integral approach in order to verify the solution derived for the strain energy release rate. The effects of crack location, material gradient and nonlinear behaviour of material on the delamination fracture are evaluated. It is found that the material nonlinearity leads to increase of the strain energy release rate. Therefore, the material nonlinearity should be taken into account in fracture mechanics based safety design of twodimensional functionally graded multilayered structural members. It is found also that the delamination behaviour can be effectively regulated by using appropriate material gradients in the design stage of functionally graded multilayered structural members and components.
Twodimensional functionally graded material
Multilayered structure
Delamination
Material nonlinearity
Analytical approach
2018
12
30
804
815
http://jsm.iauarak.ac.ir/article_545720_4aa05ccc009b12f8c0bd197ee6375322.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Investigation of Prebuckling Stress Effect on Buckling Load Determination of Finite Rectangular Plates with Circular Cutout
S
Abolghasemi
H.R
Eipakchi
M
Shariati
This paper investigates the buckling of finite isotropic rectangular plates with circular cutout under uniaxial and biaxial loading. The complex potential method is used to calculate the prebuckling stress distribution around the cutout in the plate with finite dimensions. To satisfy the inplane boundary conditions, the generalized complexpotential functions are introduced and a new method based on the boundary integral which has been obtained from the principle of virtual work is used to apply the boundary conditions at the plate edges. The potential energy of the plate is calculated by considering the first order shear deformation theory and the Ritz method is used to calculate the buckling load. The effects of cutout size, type of loading and different boundary conditions on the buckling load are investigated. Comparing of the calculated buckling loads with the finite element results shows the accuracy of the presented method for buckling analysis of the plates.
Circular cutout
Complex potential functions
Ritz method
Buckling
Finite rectangular plate
Shear deformation
2018
12
30
816
830
http://jsm.iauarak.ac.ir/article_545721_83958eeb7b3da9dcce0b16d0c67f20f0.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Inquisitive Analysis of the Point Source Effect on Propagation of SH Wave Through an Orthotropic Crustal Layer
S
Gupta
S
Pramanik

Smita
A
Pramanik
The occurrence of SH wave propagation under the effect of a point source in an orthotropic substratum lying over a heterogeneous orthotropic half space is deliberated in the prospect of a devastating earthquake. The quadratic alteration is acknowledged for density and shear modulus which is hypothesized to be a function of depth. The method of Green's function and transformation technique contributes to obtain the dispersion equation and dispersion curves. An effort has been accomplished to demonstrate the classical equation of Love wave followed from dispersion equation. “Mathematica” software is applied to depict the graphics. Graphics are designed to show the effect of heterogeneous parameters corresponding to density and shear modulus. Dispersion equation is obtained considering the case that the displacement and stress are continuous at the interface. The present work is an attempt to express the behavior of SH wave in an orthotropic medium under the effect of point source.
Orthotropic
SH wave
Green's function
Transformation technique
Point source
2018
12
30
831
844
http://jsm.iauarak.ac.ir/article_545722_54002f09841488d3419965b12edcf205.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
NonAxisymmetric TimeDependent Creep Analysis in a ThickWalled Cylinder Due to the Thermomechanical loading
M
Moradi
A
Loghman
In this study, the nonlinear creep behaviour of a thickwalled cylinder made of stainless steel 316 is investigated using a semianalytical method. The thickwalled cylinder is under a uniform internal pressure and a nonaxisymmetric thermal field as a function of the radial and circumferential coordinates. For the high temperature and stress levels, creep phenomena play a major role in stress redistributions across the cylinder thickness. The BaileyNorton creep constitutive equation is used to model the uniaxial creep behaviour of the material. Creep strain increments are accumulated incrementally during the life of the vessel. Creep strain increments are related to the current stresses and the material uniaxial creep model by the wellknown PrandtlReuss relations. Considering the mentioned nonaxisymmetric boundary conditions, the heat conduction equation and the Navier partial differential equations has been solved using the separation of variables and the complex Fourier series methods. The corresponding displacement, strain and stress functions are obtained. Considering the nonaxisymmetric loadings, the distribution of the radial, circumferential and shear stresses are studied. Furthermore, the effects of internal pressure and external temperature distribution on the effective stress history are investigated. It has been found that the nonaxisymmetric thermal loading has a significant effect on stress redistributions.
Timedependent creep
Thickwalled cylinder
Stainless Steel 316
Thermal and mechanical loads
Nonaxisymmetric loading
2018
12
30
845
863
http://jsm.iauarak.ac.ir/article_545724_b4c3d3b091c2e52cc8bb01b76ac84e61.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Effect of the Interparticle Interactions on AdsorptionInduced Frequency Shift of NanobeamBased Nanoscale MassSensors: A Theoretical Study
K
Rajabi
Sh
HosseiniHashemi
<span>It is wellknown that the Interparticle interactions between adsorbates and surface of an adsorbent can affect the surface morphology. One of the consequences of this issue is that the resonant frequency of a nanoscale resonator can be changed due to adsorption. In this study we have chosen a cantileverbased nanoscale masssensor with a single nanoparticle at its tip. Using the classical continuum mechanics and the EulerBernoulli beam theory we have derived the governing equation of free vibration of the proposed sensor. By the assumption of physisorption, the weak van der Waals forces between the attached nanoparticle and the upper surface atoms have been taken into account. Effect of this interparticle interaction on the frequency response of the mass sensor is examined. Accordingly, the classical equation of motion has been modified by an additional term</span><span>on the dynamics behavior of the sensor</span><span> with a variable coefficient. It has been shown that the effect of this additional term is the same as that of an elastic foundation with variable modulus. Numerical results have shown that this additional term has significant effect on the frequency shift of a nanoscale masssensor in such a way that by approaching the nanoparticle towards the sensor, the frequency shift of the sensor will increase significantly. The smaller is the nanoparticle, the higher is the frequency shift. </span>
Nanoscale masssensors
Nanobeam resonators
Nanocantilever resonators
Physisorption effects
EulerBernoulli beam theory
2018
12
30
864
873
http://jsm.iauarak.ac.ir/article_545725_5a507543da20d1e7119facbe0e59f1d5.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Free Axisymmetric Bending Vibration Analysis of two Directional FGM Circular Nanoplate on the Elastic Foundation
M
Zarei
Gh
Rahimi
In the following paper, free vibration analysis of two directional FGM circular nanoplate on the elastic medium is investigated. The elastic modulus of plate varies in both radial and thickness directions. Eringen’s theory was employed to the analysis of circular nanoplate with variation in material properties. Simultaneous variations of the material properties in the radial and transverse directions are described by a general function. Ritz functions were utilized to obtain the frequency equations for simply supported and clamped boundary. Differential transform method also used to develop a semianalytical solution the sizedependent natural frequencies of nonhomogenous nanoplates. Both methods reported good results. The validity of solutions was performed by comparing present results with themselves and those of the literature for both classical plate and nanoplate. Effect of nonhomogeneity on the nonlocal parameter, geometries, boundary conditions and elastic foundation parameters is examined the paper treats some interesting problems, for the first time.
Eringen’s theory
Free vibration
FGM nanoplate
Ritz method
Differential transform method
2018
12
30
874
893
http://jsm.iauarak.ac.ir/article_545726_ffbad6cc73d1da6f9b7e9d2a061f019a.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
An Enhanced Viscoplastic Constitutive Model for SemiSolid Materials to Analyze Shear Localization
M.H
SheikhAnsari
M
AghaieKhafri
Semisolid materials undergo strain localization and shear band formation as a result of granular nature of semisolid deformation. In the present study, to analyze the shear localization, a unified viscoplastic constitutive model was developed for the homogeneous flow. Then, a linearized analysis of the stability performed by examining the necessary condition for the perturbation growth. For this purpose, a shear layer model was considered to analyze the perturbation growth and subsequent instability. The perturbation analysis revealed that the failure mode in semisolid materials is diffused with long wave length regime, rather than to be localized and exhibiting short wave length regime. Moreover, decreasing the solid skeleton has a retarding effect on the perturbation growth and localization at low and modest strain rates. The performed analysis showed that the localization analysis results in a new interpretation for the micromechanisms of the semisolid deformation. The constitutive model was fairly well correlated with the experimental results.
Viscoplastic model
Shear band
Perturbation growth
Dilatancy
SemiSolid
2018
12
30
894
901
http://jsm.iauarak.ac.ir/article_545727_16f4e37532d54d650f5a0faba3d702d4.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Extended Finite Element Method for Statics and Vibration Analyses on Cracked Bars and Beams
F
Mottaghian
A
Darvizeh
A
Alijani
In this paper, the extended finite element method (XFEM) is employed to investigate the statics and vibration problems of cracked isotropic bars and beams. Three kinds of elements namely the standard, the blended and the enriched elements are utilized to discretize the structure and model cracks. Two techniques referred as the increase of the number of Gauss integration points and the rectangle subgrid are applied to refine the integration within the blended and enriched elements of the beam in which the priority of the developed rectangle subgrid technique is identified. The stiffness and the mass matrices of the beam are extended by considering the Heaviside and the crack tip functions. In a plane stress analysis, the effects of various crack positions and depths, different boundary conditions and other geometric parameters on the displacement and the stress contours are detected. Moreover, in a free vibration analysis, changes of the natural frequencies and the mode shapes due to the aforementioned effects are determined.
Extended finite element method
Statics and vibration
Cracked bars and beams
Increasing Gauss integration points
Rectangle subgrid
2018
12
30
902
928
http://jsm.iauarak.ac.ir/article_545728_26368fe6ea9834e16fb29b4bc7d1b018.pdf
Journal of Solid Mechanics
JSM
20083505
20083505
2018
10
4
Finite Element Modeling of the Vibrational Behavior of SingleWalled Silicon Carbide Nanotube/Polymer Nanocomposites
S
Rouhi
R
Ansari
A
Nikkar
The multiscale finite element method is used to study the vibrational characteristics of polymer matrix reinforced by singlewalled silicon carbide nanotubes. For this purpose, the nanoscale finite element method is employed to simulate the nanotubes at the nanoscale. While, the polymer is considered as a continuum at the larger scale. The polymer nanotube interphase is simulated by spring elements. The natural frequencies of nanocomposites with different nanotube volume percentages are computed. Besides, the influences of nanotube geometrical parameters on the vibrational characteristics of the nanocomposites are evaluated. It is shown that reinforcing polymer matrix by singlewalled silicon carbide nanotubes leads to increasing the natural frequency compared to neat resin. Increasing the length of the nanotubes at the same diameter results in increasing the difference between the frequencies of nanocomposite and pure polymer. Besides, it is observed that clampedfree nanocomposites experience a larger increase in the presence of the nanotubes than clampedclamped nanotube reinforced polymers.
Finite Element Method
Vibrational behavior
Singlewalled silicon carbide nanotube
Polymer matrix
nanocomposites
2018
12
30
929
939
http://jsm.iauarak.ac.ir/article_545729_e3ed599535906089cf6190496e98c8d4.pdf