Journal ArticleDOI
A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions
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In this article, a general formulation for free, steady-state and transient vibration analyses of functionally graded shells of revolution subjected to arbitrary boundary conditions was derived by means of a modified variational principle in conjunction with a multi-segment partitioning procedure on the basis of first-order shear deformation shell theory.Abstract:
This paper describes a general formulation for free, steady-state and transient vibration analyses of functionally graded shells of revolution subjected to arbitrary boundary conditions. The formulation is derived by means of a modified variational principle in conjunction with a multi-segment partitioning procedure on the basis of the first-order shear deformation shell theory. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. Fourier series and polynomials are applied to expand the displacements and rotations of each shell segment. The versatility of the formulation is demonstrated through the application of the following polynomials: Chebyshev orthogonal polynomials, Legendre orthogonal polynomials, Hermite orthogonal polynomials and power polynomials. Numerical examples are given for the free vibrations of functionally graded cylindrical, conical and spherical shells with different combinations of free, shear-diaphragm, simply-supported, clamped and elastic-supported boundary conditions. Validity and accuracy of the present formulation are confirmed by comparing the present solutions with the existing results and those obtained from finite element analyses. As to the steady-state and transient vibration analyses, functionally graded conical shells subjected to axisymmetric line force and distributed surface pressure are investigated. The effects of the material power-law distribution, boundary condition and duration of blast loading on the transient responses of the conical shells are also examined.read more
Citations
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Journal ArticleDOI
Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs)
TL;DR: In this paper, the nonlinear bending behavior of a novel class of multi-layer polymer nanocomposite beams reinforced with graphene platelets (GPLs) that are non-uniformly distributed along the thickness direction was investigated.
Journal ArticleDOI
Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory
TL;DR: In this article, through-the-thickness transverse normal and shear strains and stresses in statically deformed functionally graded (FG) doubly-curved sandwich shell structures and shells of revolution using the generalized zigzag displacement field and the Carrera Unified Formulation (CUF).
Journal ArticleDOI
Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories
TL;DR: In this article, the authors used the generalized displacement field of the Carrera Unified Formulation (CUF), including the Zig-Zag (ZZ) effect given by the Murakami's function.
Journal ArticleDOI
Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method
TL;DR: In this paper, free vibration analysis of conical and cylindrical shells and annular plates made of composite laminated and functionally graded materials (FGMs) is investigated for FGM cases.
Journal ArticleDOI
Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions
TL;DR: In this paper, a 3D exact solution for the free vibrations of arbitrarily thick functionally graded rectangular plates with general boundary conditions is presented, where the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on Rayleigh-Ritz procedure by the energy functions of the plate.
References
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Book
Mechanics of Laminated Composite Plates and Shells : Theory and Analysis, Second Edition
TL;DR: The use of composite materials in engineering structures continues to increase dramatically, and there have been significant advances in modeling for general and composite materials and structures in particular as discussed by the authors. But the use of composites is not limited to the aerospace domain.
Book
Variational Methods in Elasticity and Plasticity
TL;DR: In this article, the Statique Reference Record was created on 2004-09-07, modified on 2016-08-08, and was used for Elasticite and Plasticite.
Journal ArticleDOI
A higher-order shear deformation theory of laminated elastic shells
J. N. Reddy,C.F. Liu +1 more
TL;DR: In this article, a higher-order shear deformation theory for elastic shells was developed for shells laminated of orthotropic layers, which is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces.
Journal ArticleDOI
Historical review of Zig-Zag theories for multilayered plates and shells
TL;DR: A review of the Zig-Zag theories for multilayered structures can be found in this article, where the authors refer to these three theories by using the following three names: Lekhnitskii Multi-layered Theory, ~LMT!, Ambartsumian Multi-Layered Theory ~AMT!, and Reissner Multilayed Theory ~RMT.
Journal ArticleDOI
Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shells
TL;DR: In this article, an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures is presented. But, although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations.