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first-order-shear-deformation-theory
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Interlaminar stress analysis of general composite laminates
, Article International Journal of Mechanical Sciences ; Volume 53, Issue 11 , 2011 , Pages 958-967 ; 00207403 (ISSN) ; Yazdani Sarvestani, M ; Sharif University of Technology
Abstract
In this study, based on the reduced from of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates under the extension and bending. The constant parameters, which describe the global deformation of a laminate, are properly computed by means of the improved first-order shear deformation theory. Reddys layerwise theory is subsequently utilized for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. A variety of numerical results are obtained for the interlaminar normal and shear stresses along the...
Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory
, Article Mechanics of Advanced Materials and Structures ; Volume 23, Issue 5 , 2016 , Pages 565-577 ; 15376494 (ISSN) ; Kargarnovin, M. H ; Satouri, S ; Satouri, A ; Sharif University of Technology
Taylor and Francis Inc
2016
Abstract
Based on the first-order shear deformation theory, the free vibration of the functionally graded (FG) truncated conical shells is analyzed. The truncated conical shell materials are assumed to be isotropic and inhomogeneous in the longitudinal direction. The two-constituent FG shell consists of ceramic and metal. These constituents are graded through the length, from one end of the shell to the other end. Using Hamilton's principle the derived governing equations are solved using differential quadrature method. Fast rate of convergence of this method is tested and its advantages over other existing solver methods are observed. The primary results of this study were obtained for four...
Free vibration of a functionally graded annular sector plate integrated with piezoelectric layers
, Article Applied Mathematical Modelling ; Volume 79 , 2020 , Pages 341-361 ; Rahnama, H ; Sharif University of Technology
Elsevier Inc
2020
Abstract
Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then...
Stress Analysis in Symmetric Composite Laminates Subjected to Shearing Load
, M.Sc. Thesis Sharif University of Technology ; Nosier, Asghar (Supervisor)
Abstract
In the present study, an analytical solution is developed to calculate the interlaminar stresses in long symmetric laminated composite plates subjected to shearing load. At first, upon the successive integrations of the strain-displacement relations and using the existing patterns in deformation of a long symmetric laminate, the general displacement field is extracted and simplified to the final form. Presented solution is based on a combined method containing the equivalent single-layer (ESL) theories beside the Reddy’s layerwise theory. In this method, the equivalent single-layer theories are utilized because of their simplicity and low computational efforts rather than the layerwise...
Panel Flutter Analysis of Cylindrical Constrained Layer Damping (CLD) Panels
, M.Sc. Thesis Sharif University of Technology ; Haddadpour, Hassan (Supervisor)
Abstract
The purpose of this study is to analytically study the aeroelastic characteristics of the cylindrical shells fully treated with passive constrained layer damping (PCLD) to indicate the effects of various parameters on the behavior of such structures. Constraining the viscoelastic layers increases the amount of dissipated energy and the bending stiffness of the structure without considerable change of the weight.
A thin shell theory in conjunction with the Donell assumptions is employed for the shell and the constraining layer (CL) and the first order shear deformation theory (FSDT) is used for the viscoelastic layer to construct the model. The effects of rotary inertia and shear...
A thin shell theory in conjunction with the Donell assumptions is employed for the shell and the constraining layer (CL) and the first order shear deformation theory (FSDT) is used for the viscoelastic layer to construct the model. The effects of rotary inertia and shear...
Free Vibration Analysis of Moderately Thick Rectangular Plate Made of Functionally Graded Material on Arbitrary Supports Using Extended Kantorovich Method
, M.Sc. Thesis Sharif University of Technology ; Kargarnovin, Mohammad Hossein (Supervisor) ; Mohammadi Aghdam, Mohamamd (Supervisor)
Abstract
In this study, free vibration analysis of moderately thick rectangular FG plates with general boundary conditions is investigated. Governing equations of motion are obtained based on the Mindlin plate theory. A semi analytical solution is presented for the governing equations using extended Kantorovich method (EKM). Results are compared and validated with available results in the literature. Effects of different parameters such as boundary conditions, material and geometrical parameters on natural frequencies of the FG plates are investigated
Free Vibration Analysis of FG Annular Sector Plates Using Extended Kantrovich Method
, M.Sc. Thesis Sharif University of Technology ; Fallah Rajabzadeh, Famida (Supervisor)
Abstract
In this study the free vibration of annular sector plates made of functional materials with using the extended Katrovich method is investigated for a variety of boundary conditions. For this purpose, based on the first order shear deformation theory and Hamilton's principle, equations of motion that they are five differential equations and coupled, are derived. Due to the difficulty of the equations obtained by applying extended kantrovich method on these equations, two ordinary differential equations obtained, the two categories combined fixed and simple boundary conditions will be solved by using generalized differential quadrature and in an iterative process system natural frequency is...
Dynamic Stability of Cylindrical Shells Made of Functionally-Graded Materials under Axial Follower Forces
, M.Sc. Thesis Sharif University of Technology ; Kazemi, Mohammad Taghi (Supervisor)
Abstract
Due to major problems induced by delamination in laminated composites, functionally-graded materials (FGM) have been put to growing use in recent years. In the present research, dynamic stability of FGM cylindrical shells under axial follower loads is addressed. Loading was considered in three forms: concentrated (Beck’s problem), uniformly-distributed (Leipholz’s problem), and linearly-distributed (Hauger’s problem). In order to derive the governing equations, Love’s hypotheses and First-order Shear Theory (FST) were used. To solve the equations, polynomial mode shapes were used to approximate the displacements, and the extended Galerkin method was applied. The problem was solved for mild...
Bending Analysis of Rectangular FG Micro Plates using Modified Couple Stress Theory and first Order Shear Deformation Theory
, M.Sc. Thesis Sharif University of Technology ; Fallah Rajabzadeh, Famida (Supervisor) ; Farrahi, Gholamhossein (Supervisor)
Abstract
Based on the modified couple stress and Mindlin plate theories, a Levy type solution is presented for bending and vibration analysis of rectangular isotropic micro plates with simple supports at opposite edges and different boundary conditions at the other two ones. Modified couple stress theory is taken into account to capture the size effect and the governing equations are derived using Hamilton's principle, and solved by Levy solution and space-state method. The results are verified with the existing ones in the literature. As a benchmark, additional tables for vertical deflections and free vibrations of plate with various boundary conditions are presented
Buckling Analysis of Reinforced Composite Conical Shells under Axial Compressive Load using GDQ Method
, M.Sc. Thesis Sharif University of Technology ; Kouchakzadeh, Mohammad Ali (Supervisor) ; Shakouri, Meysam ($item.subfieldsMap.e) ; Noghabi, Mohammad ($item.subfieldsMap.e)
Abstract
The object of this study is to determine the buckling load of reinforced composite conical shells under axial compression. . Shells are reinforced by stringers and rings and the boundary conditions are assumed to be simply supported. At first the equilibrium equations are obtained using the first order shear deformation theory (FSDT), smeared stiffener technique and principle of minimum potential energy. In the following, the resulting equations which are the system of five variable coefficient partial differential equations in terms of displacement components are investigated by generalized differential quadrature method (GDQM). Finally the standard eigenvalue equation is formed and the...
Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces
, Article Journal of Sound and Vibration ; Vol. 333, Issue. 3 , 3 February , 2014 , pp. 801-817 ; ISSN: 0022460X ; Kazemi, M. T ; Reddy, J. N ; Haddadpoud, H ; Mahmoudkhani, S ; Sharif University of Technology
Abstract
In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the...
Dynamic stability of cantilevered functionally graded cylindrical shells under axial follower forces
, Article Thin-Walled Structures ; Vol. 79, issue , June , 2014 , p. 138-146 ; Kazemi, M. T ; Haddadpour, H ; Mahmoudkhani, S ; Sharif University of Technology
Abstract
Flutter of cantilevered, functionally graded cylindrical shells under an end axial follower force is addressed. The material properties are assumed to be graded along the thickness direction according to a simple power law. Using the Hamilton principle, the governing equations of motion are derived based on the first-order shear deformation theory. The stability analysis is carried out using the extended Galerkin method and minimum flutter loads and corresponding circumferential mode numbers are obtained for different volume fractions, length-to-radius, and thicknesses-to-radius ratios. Two different configurations are considered for the FGM: one in which the metal phase is the outer layer...
Bending analysis of moderately thick functionally graded conical panels with various boundary conditions using GDQ method
, Article Composite Structures ; Volume 103 , September , 2013 , Pages 68-74 ; 02638223 (ISSN) ; Shakouri, M ; Kouchakzadeh, M. A ; Sharif University of Technology
2013
Abstract
This study presents the bending analysis of functionally graded conical panels under transverse compression with various boundary conditions. Equations was derived using first order shear deformation theory (FSDT) and solved using generalized differential quadrature (GDQ) method. Using this method results in the capability of studying any combinations of boundary conditions on four edges of the panel. Results are compared and validated with the results available in the literature. Effect of boundary conditions, volume fractions, panel length, semi-vertex angle and subtended angle on deflection of the panel was investigated
Free-edge stresses in general composite laminates
, Article International Journal of Mechanical Sciences ; Volume 50, Issue 10-11 , 2008 , Pages 1435-1447 ; 00207403 (ISSN) ; Maleki, M ; Sharif University of Technology
2008
Abstract
In the present study, by starting from the reduced form of elasticity displacement field for a long flat laminate, an analytical method is developed in order to accurately calculate the interlaminar stresses near the free edges of generally laminated composite plates under extension. The constant parameter appearing in the reduced displacement field, which describes the global rotational deformation of a laminate, is appropriately obtained by employing an improved first-order shear deformation theory. The accuracy and effectiveness of the proposed first-order theory are verified by means of comparison with the results of Reddy's layerwise theory as a three-dimensional benchmark. Reddy's...
Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell
, Article Engineering with Computers ; Volume 37, Issue 4 , 2021 , Pages 3359-3374 ; 01770667 (ISSN) ; Ebrahimi, F ; Habibi, M ; Safarpour, H ; Foong, L. K ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2021
Abstract
In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers’ number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure...
Dynamic analysis of three-layer cylindrical shells with fractional viscoelastic core and functionally graded face layers
, Article JVC/Journal of Vibration and Control ; Volume 27, Issue 23-24 , 2021 , Pages 2738-2753 ; 10775463 (ISSN) ; Permoon, M. R ; Askarian, A ; Haddadpour, H ; Sharif University of Technology
SAGE Publications Inc
2021
Abstract
Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz...
Stress Analysis of in Cross-ply Laminates in Bending
, M.Sc. Thesis Sharif University of Technology ; Nosier, Asghar (Supervisor)
Abstract
In the present study, an analytical solution is developed to calculate the interlaminar stresses in long generally cross-ply laminated composite plates subjected to bending. At first, upon the integration of the strain-displacement relations and using the existing patterns in deformation of the long laminate, the general displacement field is extracted and simplified to the final form. Presented solution is based on a combined method containing the equivalent single-layer (ESL) theories beside the Reddy’s layerwise theory. In this method, the equivalent single-layer theories are utilized because of their simplicity and low computational efforts rather than the layerwise theory in evaluation...
Hygrothermal Stress Analysis in Composite Laminatesby Perturbation Method
, M.Sc. Thesis Sharif University of Technology ; Nosier, Asghar (Supervisor)
Abstract
For studying the hygrothermal deformation of generally laminated composite platesunder uniform temperature change and uniform moisture absorption change, by starting from the reduced form of elasticity displacement field for a long flat laminate, an analytical method is developed in order to accurately calculate the interlaminar stresses near the free edges of the laminate. The constant parameters appearing in the reduced displacement field, describe the global deformation of the laminate and appropriately obtained by employing an improved first-order shear deformation theory.For solving the coupled equilibrium equations of agenerally laminated composite plate, some of the stiffness...
Nonlinear Elastic Analysis of FG Arcs under Thermo-Mechanical Loading
, M.Sc. Thesis Sharif University of Technology ; Fallah, Famida (Supervisor)
Abstract
Arcs and rings are used extensively in structures such as submarines and bridges due to their particular geometry. On the other hand, in multi-part rocket, due to the high temperature gradients, they form the fastening rings of functional materials (FGM). Considering the importance of this structural element, in this thesis, linear and nonlinear behavior (including bending and post-buckling) of rings made of functionally graded materials under different types of thermo-mechanical loading has been investigated. First, the governing equations are derived from the principle of minimum potential energy, based on the two theorems of Donnell and Love. Donnell's theory equations are solved...
Free-edge stresses in general cross-ply laminates
, Article Scientia Iranica ; Vol. 21, issue. 2 , April , 2014 , p. 387-402 ; Sharif University of Technology
Abstract
Within elasticity theory, the reduced form of a displacement field is obtained for general cross-ply composite laminates subjected to a bending moment. The firstorder shear deformation theory of plates and Reddy's layerwise theory are then utilized to determine the global deformation parameters and the local deformation parameters appearing in the displacement fields, respectively. For a special set of boundary conditions an elasticity solution is developed to verify the validity and accuracy of the layerwise theory. Finally, various numerical results are presented within the layerwise theory for edge-effect problems of several cross-ply laminates under the bending moment. The results...