| 1. |
- Fadaee, M., et al.
(author)
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Free vibration analysis of Lévy-type functionally graded spherical shell panel using a new exact closed-form solution
- 2013
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In: International Journal of Mechanical Sciences. - : Elsevier BV. - 0020-7403. ; 77, s. 227-238
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Journal article (peer-reviewed)abstract
- An exact closed-form analysis for describing the natural vibrations of a FG moderately thick spherical shell panel is developed. The strain-displacement relations of Donnell and Sanders theories are used to obtain the exact solutions. The shell has two opposite edges simply supported (i.e., Lévy-type). The material properties change continuously through the thickness of the shell, which can vary according to a power-law distribution of the volume fraction of the constituents. The new auxiliary and potential functions are employed to exactly decouple the governing equations of the vibrated spherical shell panel, leading to the exact closed-form frequency equation in the form of determinant. The accuracy and validity of the solutions are established with the aid of a 3D finite element analysis as well as by comparing the results with the data reported in the literature. The effects of various stretching-bending couplings on the frequency parameters are discussed.
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| 2. |
- Hashemi, S.H., et al.
(author)
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An exact analytical approach for in-plane and out-of-plane free vibration analysis of thick laminated transversely isotropic plates
- 2012
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In: Archive of Applied Mechanics. - : Springer Science and Business Media LLC. - 0939-1533 .- 1432-0681. ; 82:5, s. 677-698
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Journal article (peer-reviewed)abstract
- In this article, the governing equations of motion of thick laminated transversely isotropic plates are derived based on Reddy's third-order shear deformation theory. These equations are exactly converted to four uncoupled equations to study the in-plane and out-of-plane free vibrations of thick laminated plates without any usage of approximate methods. Based on the present analytical approach, exact Levy-type solutions are obtained for thick laminated transversely isotropic plates and, for some boundary conditions, the exact characteristic equations hitherto not reported in the literature are given. Also, the in-plane and out-of-plane deformed mode shapes are plotted for different boundary conditions. The present solutions can accurately predict both the in-plane and out-of-plane natural frequencies and mode shapes of thick laminated transversely isotropic plates.
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| 3. |
- Hosseini-Hashemi, S., et al.
(author)
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A new exact analytical approach for free vibration of ReissnerMindlin functionally graded rectangular plates
- 2011
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In: International Journal of Mechanical Sciences. - : Elsevier BV. - 0020-7403 .- 1879-2162. ; 53:1, s. 11-22
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Journal article (peer-reviewed)abstract
- An exact closed-form procedure is presented for free vibration analysis of moderately thick rectangular plates having two opposite edges simply supported (i.e. Lvy-type rectangular plates) based on the ReissnerMindlin plate theory. The material properties change continuously through the thickness of the plate, which can vary according to a power law distribution of the volume fraction of the constituents. By introducing some new potential and auxiliary functions, the displacement fields are analytically obtained for this plate configuration. Several comparison studies with analytical and numerical techniques reported in literature are carried out to establish the high accuracy and reliability of the solutions. Comprehensive benchmark results for natural frequencies of the functionally graded (FG) rectangular plates with six different combinations of boundary conditions (i.e. SSSSSSSCSCSCSCSFSSSFSFSF) are tabulated in dimensionless form for various values of aspect ratios, thickness to length ratios and the power law index. Due to the inherent features of the present exact closed-form solution, the present results will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.
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| 4. |
- Hosseini-Hashemi, S., et al.
(author)
-
An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory
- 2012
-
In: Archive of Applied Mechanics. - : Springer Science and Business Media LLC. - 0939-1533 .- 1432-0681. ; 82:7, s. 985-1002
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Journal article (peer-reviewed)abstract
- This paper deals with closed-form solutions for in-plane and out-of-plane free vibration of moderately thick laminated transversely isotropic spherical shell panels on the basis of Sanders theory without any usage of approximate methods. The governing equations of motion and the boundary conditions are derived using Hamilton's principle. The highly coupled governing equations are recast to some uncoupled equations by introducing four potential functions. Also, some relations were presented for the unknowns of the original set of equations in terms of the unknowns of the uncoupled equations. According to the proposed analytical approach, both Navier and Lévy-type explicit solutions are developed for moderately thick laminated spherical shell panels. The efficiency and high accuracy of the present approach are investigated by comparing some of the present study with the available results in the literature and the results of 3D finite element method. The effects of various shell parameters like shear modulus ratio of transversely isotropic materials and curvature ratio on the natural frequencies are studied. Clearly, the proposed solutions can accurately predict the in-plane and out-of-plane natural frequencies of moderately thick transversely isotropic spherical shell panels.
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| 5. |
- Hosseini-Hashemi, S., et al.
(author)
-
On the buckling analysis of isotropic, transversely isotropic, and laminated rectangular plates via Reddy plate theory: An exact closed-form procedure
- 2012
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In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. - : SAGE Publications. - 2041-2983 .- 0954-4062. ; 226:5, s. 1210-1224
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Journal article (peer-reviewed)abstract
- Based on Reddy's third-order shear deformation theory, an exact closed-form solution is proposed to describe linear buckling of transversely isotropic laminated rectangular plates under either mono- or bi-axial compressive in-plane loads. To this end, the coupled governing equations are exactly converted to two sets of uncoupled equations for in-plane and transverse deformations of symmetric laminated plates. The new uncoupled equations are analytically solved by applying both Navier and Lévy-type solution methods. The validity and high accuracy of the current exact solution are evaluated by comparing the present results with their counterparts reported in literature.
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| 6. |
- Hosseini-Hashemi, S., et al.
(author)
-
Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure
- 2011
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In: Composite Structures. - : Elsevier BV. - 0263-8223 .- 1879-1085. ; 93:2, s. 722-735
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Journal article (peer-reviewed)abstract
- In this article, a new exact closed-form procedure is presented to solve free vibration analysis of functionally graded rectangular thick plates based on the Reddy's third-order shear deformation plate theory while the plate has two opposite edges simply supported (i.e., Lévy-type rectangular plates). The elasticity modulus and mass density of the plate are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents whereas Poisson's ratio is constant. Based on the present solution, five governing complicated partial differential equations of motion were exactly solved by introducing the auxiliary and potential functions and using the method of separation of variables. The validity and high accuracy of the present solutions are investigated by comparing some of the present results with their counterparts reported in literature and the 3-D finite element analysis. It is obvious that the present exact solution can accurately predict not only the out of plane, but also the in-plane modes of FG plate. Furthermore, a new eigenfrequency parameter is defined having its special own characteristics. Finally, the effects of boundary conditions, thickness to length ratio, aspect ratio and the power law index on the frequency parameter of the plate are presented.
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| 7. |
- Nasr, A., et al.
(author)
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An elasticity solution for static analysis of functionally graded curved beam subjected to a shear force
- 2010
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In: International Journal of Engineering. Transactions B: Applications. - 1728-144X. ; 23, s. 169-178
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Journal article (peer-reviewed)abstract
- In this paper, using 2-D theory of elasticity, a closed-form solution is presented for stress distributions and displacements of a FG curved beam under shear force at its free end. The material properties are assumed to vary continuously through the radial direction based on a simple power law model and Poisson’s ratio is supposed to be constant. In order to verify the solution, it is shown that allstress and displacement relations are converted to those of a homogenous curved beam when the inhomogeneity constant approaches zero. The effects of inhomogeneity on stress distributions are investigated. It is shown that specified stress distribution profiles can be obtained by changing the variation of volume fraction of constituents. It is observed that for a specific value of inhomogeneity constant, a proper stress distribution along the radial direction is obtained for designing purposes.
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