• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.33-41
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• 2018

In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.

• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.449-463
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• 2011

A free vibration analysis is made of a moderately-thick toroidal shell based on a shear deformation (Timoshenko-Mindlin) shell theory. This work represents an extension of earlier work by the authors which was based on a thin (Kirchoff-Love) shell theory. The analysis uses a modal approach in the circumferential direction, and numerical results are found using the differential quadrature method (DQM). The analysis is first developed for a shell of revolution of arbitrary meridian, and then specialized to a complete circular toroidal shell. A second analysis, based on the three-dimensional theory of elasticity, is presented to cover thick shells. The shear deformation theory is validated by comparing calculated results with previously published results for fifteen cases, found using thin shell theory, moderately-thick shell theory, and the theory of elasticity. Consistent agreement is observed in the comparison of different results. New frequency results are then given for moderately-thick and thick toroidal shells, considered to be completely free. The results indicate the usefulness of the shear deformation theory in determining natural frequencies for toroidal shells.

• Steel and Composite Structures
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• v.31 no.4
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• pp.397-408
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• 2019

In this paper, a geometrically nonlinear meshfree analysis of 3D various forms of shell structures using the double director shell theory with finite rotations is proposed. This theory is introduced in the present method to remove the shear correction factor and to improve the accuracy of transverse shear stresses with the consideration of rotational degrees of freedom.The present meshfree method is based on the radial point interpolation method (RPIM) which is employed for the construction of shape functions for a set of nodes distributed in a problem domain. Discrete system of geometrically nonlinear equilibrium equations solved with the Newton-Raphson method is obtained by incorporating these interpolations into the weak form. The accuracy of the proposed method is examined by comparing the present results with the accurate ones available in the literature and good agreements are found.

• Steel and Composite Structures
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• v.27 no.4
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• pp.479-493
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• 2018

In this paper nonlocal free vibration analysis of a doubly curved piezoelectric nano shell is studied. First order shear deformation theory and nonlocal elasticity theory is employed to derive governing equations of motion based on Hamilton's principle. The doubly curved piezoelectric nano shell is resting on Pasternak's foundation. A parametric study is presented to investigate the influence of significant parameters such as nonlocal parameter, two radii of curvature, and ratio of radius to thickness on the fundamental frequency of doubly curved piezoelectric nano shell.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.575-587
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• 2015

This paper focuses on vibration analysis of functionally graded cylindrical shell submerged in an incompressible fluid. The equation is established considering axial and lateral hydrostatic pressure based on first order shear deformation theory of shell motion using the wave propagation approach and classic Fl$\ddot{u}$gge shell equations. To study accuracy of the present analysis, a comparison carried out with a known data and the finite element package ABAQUS. With this method the effects of shell parameters, m, n, h/R, L/R, different boundary conditions and different power-law exponent of material of functionally graded cylindrical shells, on the frequencies are investigated. The results obtained from the present approach show good agreement with published results.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.125-131
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• 2019

A nine node isoparametric plate bending element is used for bending analysis of laminated composite skew cylindrical shell panels. Both thick and thin shell panels are solved. Rotary inertia and shear deformation are incorporated by considering first order shear deformation theory. The analysis is performed considering shallow shell theory. Both shallow and moderately deep skew cylindrical shells are investigated. Skew cylindrical shell panels having different thickness ratios (h/a), radius to length ratios (R/a), ply angle orientations, number of layers, aspect ratio (b/a), boundary conditions and various loading (concentrated, uniformly distributed, linear varying and doubly sinusoidal varying) conditions are analysed. Various new results are presented.

• Advances in aircraft and spacecraft science
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• v.7 no.1
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• pp.19-40
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• 2020

In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.41-58
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• 2004

The postbuckling behaviour of thin shells has fascinated researchers because the theoretical prediction and their experimental verification are often different. In reality, shell panels possess small imperfections and these can cause large reduction in static buckling strength. This is more relevant in thin laminated composite shells. To study the postbuckling behaviour of thin, imperfect laminated composite shells using finite elements, explicit incremental or secant matrices have been presented in this paper. These incremental matrices which are derived using Marguerre's shallow shell theory can be used in combination with any thin plate/shell finite element (Classical Laminated Plate Theory - CLPT) and can be easily extended to the First Order Shear deformation Theory (FOST). The advantage of the present formulation is that it involves no numerical approximation in forming total potential energy of the shell during large deformations as opposed to earlier approximate formulations published in the literature. The initial imperfection in shells could be modeled by simply adjusting the ordinate of the shell forms. The present formulation is very easy to implement in any existing finite element codes. The secant matrices presented in this paper are shown to be very accurate in tracing the postbuckling behaviour of thin isotropic and laminated composite shells with general initial imperfections.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.217-224
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• 2005

A higher order zig-zag shell theory is developed to refine the predictions of the mechanical and thermal behaviors partially coupled. The in-plane displacement fields are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. Thus the proposed theory has only seven primary unknowns and they do not depend upon the number of layers. In the description of geometry and deformation of shell surface, all rigorous exact expressions are used. Through the numerical examples of partially coupled analysis, the accuracy and efficiency of the present theory are demonstrated. The present theory is suitable in the predictions of deformation and stresses of thick composite shell under mechanical and thermal loads combined.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.177.2-177.2
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• 2005