Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Bending Analysis of Laminated Composite Plates with Arbitrary Boundary Conditions
1
13
EN
A.M
Naserian Nik
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
M
Tahani
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
mtahani@ferdowsi.um.ac.ir
It is well known that for laminated composite plates a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of laminated composite plates with arbitrary lamination and boundary conditions subjected to transverse loads. The method is based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation theory (FSDT), a laminated plate theory is developed. Two systems of coupled ordinary differential equations with constant coefficients are obtained by using the principle of minimum total potential energy. Since the procedure used is simple and straightforward it can, therefore, be adopted in developing higher-order shear deformation and layerwise laminated plate theories. The obtained equations are solved analytically using the state-space approach. The results obtained from the present method are compared with the Levy-type solutions of cross-ply and antisymmetric angle-ply laminates with various admissible boundary conditions to verify the validity and accuracy of the present theory. Also for other laminations and boundary conditions that there exist no Levy-type solutions the present results may be compared with those obtained from finite element method. It is seen that the present results have excellent agreements with those obtained by Levy-type method.
Laminated plates,Analytical solution,Arbitrary boundary conditions,First-order shear deformation theory
http://jsm.iau-arak.ac.ir/article_514232.html
http://jsm.iau-arak.ac.ir/article_514232_ca9273a6a843db9bd8473959baf90199.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
The Buckling of Non-Homogeneous Truncated Conical Shells under a Lateral Pressure and Resting on a Winkler Foundation
14
21
EN
A.H
Sofiyev
Department of Civil Engineering, Suleyman Demirel University, Isparta 32260, Turkey
asofiyev@mmf.sdu.edu.tr
A
Valiyev
Chair of Mathematics and General Technical Subjects of Odlar Yurdu University, Baku, Azerbaijan
P
Ozyigit
Department of Civil Engineering, Suleyman Demirel University, Isparta 32260, Turkey
In this paper, the buckling of non-homogeneous isotropic truncated conical shells under uniform lateral pressure and resting on a Winkler foundation is investigated. The basic relations and governing equations have been obtained for non-homogeneous truncated conical shells. The critical uniform lateral pressures of non-homogeneous isotropic truncated conical shells with or without a Winkler foundation are obtained. Finally, carrying out some computations, effects of the variations of truncated conical shell characteristics, the non-homogeneity and the Winkler foundation on the critical uniform lateral pressures have been studied. The results are compared with other works in open literature.
Buckling,Non-homogeneous material,Truncated conical shell,Winkler foundation,Critical uniform lateral pressure
http://jsm.iau-arak.ac.ir/article_514233.html
http://jsm.iau-arak.ac.ir/article_514233_b25ce19600f4c1585380e26c17dcc3e4.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Free Vibration of Functionally Graded Beams with Piezoelectric Layers Subjected to Axial Load
22
28
EN
M
Karami Khorramabadi
Faculty of Engineering, Islamic Azad University, Khorramabad Branch
mehdi_karami2001@yahoo.com
This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers subjected to axial compressive loads. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing equation is established. Resulting equation is solved using the Euler’s Equation. The effects of the constituent volume fractions, the influences of applied voltage and axial compressive loads on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.
Free vibration,Functionally graded beam,Piezoelectric layer
http://jsm.iau-arak.ac.ir/article_514269.html
http://jsm.iau-arak.ac.ir/article_514269_58961ebf70c30302479eddc7e6aa3c24.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Free Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods
29
36
EN
M.T
Ahmadian
Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology
ahmadian@mech.sharif.ir
M
Mojahedi
School of Mechanical Engineering, Sharif University of Technology
H
Moeenfard
School of Mechanical Engineering, Sharif University of Technology
In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions are valid for a wide range of vibration amplitudes. Comparing the semi-analytic solutions with numerical results, presented in the literature, indicates good agreement. The results signify the fact that HPM is a powerful tool for analyzing dynamic and vibrational behavior of structures analytically.
Free vibration,Nonlinear beam,Homotopy Perturbation method,Lindstedt-Poincare method,Axial load
http://jsm.iau-arak.ac.ir/article_514270.html
http://jsm.iau-arak.ac.ir/article_514270_6114dc2fcf889c99b56ee414af167aa9.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Transverse Vibration of Clamped and Simply Supported Circular Plates with an Eccentric Circular Perforation and Attached Concentrated Mass
37
44
EN
S.M
Mirkhalaf Valashani
Department of Mechanical Engineering, Islamic Azad University, Arak Branch
mohsen_61m@yahoo.com
In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part of this study ABAQUS software is used to compute vibration natural frequency for some special combinations of geometrical and mechanical parameters. Then results of Rayleigh-Ritz method have been obtained for the mentioned special cases. It can be seen that the agreement between them is acceptable.
Vibration,Circular plate,Eccentric circular perforation,Concentrated mass
http://jsm.iau-arak.ac.ir/article_514272.html
http://jsm.iau-arak.ac.ir/article_514272_747c16bb9b7314fbab00c473a947ae41.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Mechanical Behavior of an Electrostatically-Actuated Microbeam under Mechanical Shock
45
57
EN
M
Fathalilou
Sama Organization (Affiliated with Islamic Azad University), Khoy Branch
A
Motallebi
Department of Mechanical Engineering, Islamic Azad University, Khoy Branch
H
Yagubizade
Department of Mechanical Engineering, Urmia University
Gh
Rezazadeh
Department of Mechanical Engineering, Urmia University
g.rezazadeh@urmia.ac.ir
K
Shirazi
Sama Organization (Affiliated with Islamic Azad University), Khoy Branch
Y
Alizadeh
Sama Organization (Affiliated with Islamic Azad University), Khoy Branch
In this paper static and dynamic responses of a fixed-fixed microbeam to electrostatic force and mechanical shock for different cases have been studied. The governing equations whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear elasto-electrostatic equations. Due to the nonlinearity and complexity of the derived equations analytical solution are not generally available; therefore, the obtained differential equations have been solved by using of a step by step linearization method (SSLM) and a Galerkin based reduced order model. The pull-in voltage of the structure and the effect of shock forces on the mechanical behavior of undeflected and electrostatically deflected microbeam have been investigated. The proposed models capture the other design parameters such as intrinsic residual stress from fabrication processes and the nonlinear stiffening or stretching stress due to beam deflection.
MEMS,Microbeam,Electrostatic actuation,Pull-in voltage,Mechanical shock
http://jsm.iau-arak.ac.ir/article_514273.html
http://jsm.iau-arak.ac.ir/article_514273_135440dfdad1ff96cbeb7b1a72734e7d.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Buckling Analyses of Rectangular Plates Composed of Functionally Graded Materials by the New Version of DQ Method Subjected to Non-Uniform Distributed In-Plane Loading
58
72
EN
R
Kazemi Mehrabadi
Department of Mechanical Engineering, Islamic Azad University, Arak Branch
V.R
Mirzaeian
Iran University of Science and Technology
mirzaeian224@yahoo.com
In this paper, the new version of differential quadrature method (DQM), for calculation of the buckling coefficient of rectangular plates is considered. At first the differential equations governing plates have been calculated. Later based on the new version of differential quadrature method, the existing derivatives in equation are converted to the amounts of function in the grid points inside the region. Having done that, the equation will be converted to an eigen value problem and the buckling coefficient is obtained. Solving this problem requires two kinds of loading: (1) unaxial half-cosine distributed compressive load and (2) uni-axial linearly varied compressive load. Having considered the answering in this case and the analysis of the effect of number of grid points on the solution of the problem, the accuracy of answering is considered, and also the effect of power law index over the buckling coefficient is investigated. Finally, if the case is an isotropic type, the results will be compared with the existing literature.
Buckling,Functionally Graded Materials,Rectangular plates,Differential quadrature method,Non-uniform distributed in-plane loading
http://jsm.iau-arak.ac.ir/article_514274.html
http://jsm.iau-arak.ac.ir/article_514274_4c2e0a858a00ac581cef8ed45bf3c053.pdf
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
1
1
2009
04
30
Comparison of Various Shell Theories for Vibrating Functionally Graded Cylindrical Shells
73
83
EN
M
Javadinejad
Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch
mehdy.javady@yahoo.com
The classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of functionally graded cylindrical shells are derived by Hamilton’s principle. Resulting equations are solved using the Navier-type solution method for a functionally graded cylindrical shell with simply supported edges. The effects of transverse shear deformation, geometric size, and configurations of the constituent materials on the natural frequencies of the shell are investigated. Validity of present formulation was checked by comparing the numerical results with the Love’s shell theory.
Functionally graded material,Cylindrical shell,Natural frequency,Various shell theories
http://jsm.iau-arak.ac.ir/article_514275.html
http://jsm.iau-arak.ac.ir/article_514275_54c8f1977fe61de99df9a37d0af7278f.pdf