Three-dimensional elastic deformation of functionally graded isotropic plates under point loading

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

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Three-Dimensional Parametric Finite-Volume Homogenization of Periodic Materials with Multi-Scale Structural Applications

International Journal of Applied Mechanics ◽

10.1142/s175882511850045x ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850045 ◽

Cited By ~ 7

Author(s):

Qiang Chen ◽

Guannan Wang ◽

Xuefeng Chen

Keyword(s):

Finite Volume ◽

Three Dimensional ◽

Functionally Graded ◽

Attractive Alternative ◽

Matrix Assembly ◽

Functionally Graded Composite ◽

Multi Scale ◽

Hexahedral Elements ◽

Stiffness Matrices ◽

Structural Applications

In order to satisfy the increasing computational demands of micromechanics, the Finite-Volume Direct Averaging Micromechanics (FVDAM) theory is developed in three-dimensional (3D) domain to simulate the multiphase heterogeneous materials whose microstructures are distributed periodically in the space. Parametric mapping, which endorses arbitrarily shaped and oriented hexahedral elements in the microstructure discretization, is employed in the unit cell solution. Unlike the finite-element (FE) technique, the expressions for local stiffness matrices are derived explicitly, enabling efficient global stiffness matrix assembly using an easily implementable algorithm. To demonstrate the accuracy and efficiency of the proposed theory, the homogenized moduli and localized stress distributions produced by the FE analyses are given for comparisons, where excellent agreement is always obtained for the 3D microstructures with different geometrical and material properties. Finally, a multi-scale stress analysis of functionally graded composite cylinders is conducted. This extension further increases the FVDAM’s range of applicability and opens new opportunities for pursuing other areas, providing an attractive alternative to the FE-based approaches that may be compared.

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Analytical and numerical methods of solution of three-dimensional problem of elasticity for functionally graded coated half-space

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2011.10.001 ◽

2012 ◽

Vol 54 (1) ◽

pp. 105-112 ◽

Cited By ~ 9

Author(s):

Roman Kulchytsky-Zhyhailo ◽

Adam Bajkowski

Keyword(s):

Numerical Methods ◽

Half Space ◽

Three Dimensional ◽

Functionally Graded ◽

Dimensional Problem

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Three-dimensional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method

Thin-Walled Structures ◽

10.1016/j.tws.2018.10.005 ◽

2019 ◽

Vol 134 ◽

pp. 189-202 ◽

Cited By ~ 5

Author(s):

C.S. Huang ◽

H.T. Lee ◽

P.Y. Li ◽

K.C. Hu ◽

C.W. Lan ◽

...

Keyword(s):

Functionally Graded Material ◽

Ritz Method ◽

Three Dimensional ◽

Functionally Graded ◽

Graded Material

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