A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells

Wu, Chih Ping; Liu, Yan Cheng

doi:10.1016/j.compstruct.2016.03.031

Cited by 122 publications

(30 citation statements)

References 181 publications

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“…Compared with traditional isotropic materials, the vibration characteristics of orthotropic materials may be more complicated because of the material anisotropy. Traditional analytical and semianalytical numerical methods were used to solve the sandwich plate, laminated composite, and multilayered plates or functionally graded material plates with simply supported or clamped boundary conditions [1][2][3]. erefore, it is very urgent and necessary to develop a method to handle the orthotropic plates under the conditions of arbitrary boundary.…”

Section: Introductionmentioning

confidence: 99%

A Semianalytical Three‐Dimensional Elasticity Solution for Vibrations of Orthotropic Plates with Arbitrary Boundary Conditions

Cui

et al. 2019

Shock and Vibration

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A semianalytical three-dimensional (3D) elasticity solution for the vibration of the orthotropic plate is presented under arbitrary boundary conditions. Three-dimensional (3D) elasticity theory provides the theoretical support for the energy function of orthotropic plates. The orthotropic plates which have the arbitrary boundary condition are realized by the way of arranging three sets of linear springs at the edges. With the aim of eliminating the nonsmooth phenomenon at the edges, the admissible displacement function of an orthotropic plate is expressed with a modified Fourier series solution. Under this framework, a change that occurs on the boundary conditions only needs to modify the boundary parameters of the orthotropic plate, without the need for new derivation, thus greatly saving the modeling time. The convergence and accuracy of the proposed method are better than those of the published literature. Lastly, the new vibration results and parametric research of thick orthotropic plates as well as the geometric parameter are also presented.

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Section: Introductionmentioning

confidence: 99%

A Semianalytical Three‐Dimensional Elasticity Solution for Vibrations of Orthotropic Plates with Arbitrary Boundary Conditions

Cui

et al. 2019

Shock and Vibration

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“…This semi-analytical DQ method was also extended to the quasi-3D nonlinear thermoelastic analysis of thick-walled FG piezoelectric cylinders by Arefi [42], and the thermoelastic analysis of multi-directional FG rectangular plates resting on an elastic foundation by Adineh and Kadkhodayan [43]. A comprehensive survey with regard to the exact and approximate 3D methods for assorted structural analyses of laminated composite structures and multi-layered FG ones in the literature was carried out by Wu et al [44] and Wu and Liu [45].…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic Stress and Deformation Analyses of Functionally Graded Doubly Curved Shells

Wu¹,

He²

2019

J. Compos. Sci.

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In this paper, the authors develop Reissner’s mixed variational theorem (RMVT)-based finite layer methods for the three-dimensional (3D) coupled thermoelastic analysis of simply supported, functionally graded, doubly curved (DC) shells with temperature-independent material properties. A two-phase composite material is considered to form the shell, and its material properties are assumed to obey a power–law distribution of the volume fractions of the constituents through the thickness direction of the shell. The effective material properties are estimated using the Mori–Tanaka scheme. The accuracy and convergence rate of these RMVT-based finite layer methods are validated by comparing their solutions with the quasi 3D and accurate two-dimensional solutions available in the literature.

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“…A comprehensive review of research, specifically on functionally graded plates, is presented by Birman and Byrd [23], Jha et al [24], Thai at al. [25], Swaminathan et al [26], and Wu and Liu [27]. However, most of the studies reported in literature are related to the category in which material property varies along the thickness direction by following the various law (power law, exponential law, etc.).…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Bending Analysis of Axially Functionally Graded Angle-Ply Flat Panels

Singh

Kumari

Hazarika

2018

Mathematical Problems in Engineering

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In this paper, the analytical solution is presented for axially functionally graded (AFG) angle-ply flat panels subjected to arbitrary boundary condition. Material properties of AFG panels are assumed to vary linearly along x-direction. Reissner-type variation principle is used to derive the governing equations in mixed form. By employing extended Kantorovich method (EKM), a set of nonhomogeneous ordinary differential equations (ODEs) are obtained along the in-plane (x) and thickness (z) direction. The system of ODEs along the z-direction has constant coefficients, solved analytically. However, the system of ODEs along x-direction has variable coefficients, solved using modified power series method. The influence of property variation on the deflection and stresses is studied and discussed comprehensively for different sets of boundary conditions. Numerical results are validated through comparison with 3D FE. The presented analytical solution can serve as a benchmark for assessing the accuracy of the two-dimensional solution or 3D numerical solutions.

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A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells

Cited by 122 publications

References 181 publications

A Semianalytical Three‐Dimensional Elasticity Solution for Vibrations of Orthotropic Plates with Arbitrary Boundary Conditions

A Semianalytical Three‐Dimensional Elasticity Solution for Vibrations of Orthotropic Plates with Arbitrary Boundary Conditions

Thermoelastic Stress and Deformation Analyses of Functionally Graded Doubly Curved Shells

Analytical Solution for Bending Analysis of Axially Functionally Graded Angle-Ply Flat Panels

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