eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
1
13
514232
Bending Analysis of Laminated Composite Plates with Arbitrary Boundary Conditions
A.M Naserian Nik
1
M Tahani
mtahani@ferdowsi.um.ac.ir
2
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad
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.
http://jsm.iau-arak.ac.ir/article_514232_ca9273a6a843db9bd8473959baf90199.pdf
Laminated plates
Analytical solution
Arbitrary boundary conditions
First-order shear deformation theory
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
14
21
514233
The Buckling of Non-Homogeneous Truncated Conical Shells under a Lateral Pressure and Resting on a Winkler Foundation
A.H Sofiyev
asofiyev@mmf.sdu.edu.tr
1
A Valiyev
2
P Ozyigit
3
Department of Civil Engineering, Suleyman Demirel University, Isparta 32260, Turkey
Chair of Mathematics and General Technical Subjects of Odlar Yurdu University, Baku, Azerbaijan
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.
http://jsm.iau-arak.ac.ir/article_514233_b25ce19600f4c1585380e26c17dcc3e4.pdf
Buckling
Non-homogeneous material
Truncated conical shell
Winkler foundation
Critical uniform lateral pressure
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
22
28
514269
Free Vibration of Functionally Graded Beams with Piezoelectric Layers Subjected to Axial Load
M Karami Khorramabadi
mehdi_karami2001@yahoo.com
1
Faculty of Engineering, Islamic Azad University, Khorramabad Branch
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.
http://jsm.iau-arak.ac.ir/article_514269_58961ebf70c30302479eddc7e6aa3c24.pdf
Free vibration
Functionally graded beam
Piezoelectric layer
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
29
36
514270
Free Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods
M.T Ahmadian
ahmadian@mech.sharif.ir
1
M Mojahedi
2
H Moeenfard
3
Center of Excellence in Design, Robotics and Automation, School of Mechanical Engineering, Sharif University of Technology
School of Mechanical Engineering, Sharif University of Technology
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.
http://jsm.iau-arak.ac.ir/article_514270_6114dc2fcf889c99b56ee414af167aa9.pdf
Free vibration
Nonlinear beam
Homotopy Perturbation method
Lindstedt-Poincare method
Axial load
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
37
44
514272
Transverse Vibration of Clamped and Simply Supported Circular Plates with an Eccentric Circular Perforation and Attached Concentrated Mass
S.M Mirkhalaf Valashani
mohsen_61m@yahoo.com
1
Department of Mechanical Engineering, Islamic Azad University, Arak Branch
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.
http://jsm.iau-arak.ac.ir/article_514272_747c16bb9b7314fbab00c473a947ae41.pdf
Vibration
Circular plate
Eccentric circular perforation
Concentrated mass
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
45
57
514273
Mechanical Behavior of an Electrostatically-Actuated Microbeam under Mechanical Shock
M Fathalilou
1
A Motallebi
2
H Yagubizade
3
Gh Rezazadeh
g.rezazadeh@urmia.ac.ir
4
K Shirazi
5
Y Alizadeh
6
Sama Organization (Affiliated with Islamic Azad University), Khoy Branch
Department of Mechanical Engineering, Islamic Azad University, Khoy Branch
Department of Mechanical Engineering, Urmia University
Department of Mechanical Engineering, Urmia University
Sama Organization (Affiliated with Islamic Azad University), Khoy Branch
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.
http://jsm.iau-arak.ac.ir/article_514273_135440dfdad1ff96cbeb7b1a72734e7d.pdf
MEMS
Microbeam
Electrostatic actuation
Pull-in voltage
Mechanical shock
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
58
72
514274
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
R Kazemi Mehrabadi
1
V.R Mirzaeian
mirzaeian224@yahoo.com
2
Department of Mechanical Engineering, Islamic Azad University, Arak Branch
Iran University of Science and Technology
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.
http://jsm.iau-arak.ac.ir/article_514274_4c2e0a858a00ac581cef8ed45bf3c053.pdf
Buckling
Functionally Graded Materials
Rectangular plates
Differential quadrature method
Non-uniform distributed in-plane loading
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2009-04-30
1
1
73
83
514275
Comparison of Various Shell Theories for Vibrating Functionally Graded Cylindrical Shells
M Javadinejad
mehdy.javady@yahoo.com
1
Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr Branch
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.
http://jsm.iau-arak.ac.ir/article_514275_54c8f1977fe61de99df9a37d0af7278f.pdf
Functionally graded material
Cylindrical shell
Natural frequency
Various shell theories