A unified solution for vibration analysis of laminated functionally graded shallow shells reinforced by graphene with general boundary conditions

A semi-analytical method for vibration analysis of functionally graded (FG) sandwich doubly-curved panels and shells of revolution

Functionally graded materials (FGMs) are novel materials whose properties change gradually with respect to their dimensions. It is the advanced development of formerly used composite materials and consists of two or more materials in order to achieve the desired properties according to the application where an FGM is used. FGMs have obtained a great attention of researchers in the past decade due to their graded properties at every single point in various dimensions. The properties of an FGM are not identical to the materials that constitute it. This paper aims to present an overview of the existing literature on stability, buckling, and free vibration analysis of FGM carried out by numerous authors in the past decade. Moreover, the analyses of mathematical models adopted for the aforementioned analyses are not the core purpose of this paper. At the end, future work is also suggested in this review paper.

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Functionally Graded Materials: An Overview of Stability, Buckling, and Free Vibration Analysis

This study demonstrates the effectiveness of functionally graded coatings in the vibration of sandwich truncated conical shells. First order shear deformation shell theory (FOSDT) and Donnell kinematics assumptions are used to establish the governing equations. The problem is solved for piecewise and continuous through-the-thickness coatings stiffness variations. The closed-form solution is obtained for frequency parameters of homogeneous truncated conical shells coated by functionally graded (FG) layers within the FOSDT. The analysis is extended to account for the influences of transverse shear deformations and functionally graded material (FGM) layers on the frequency parameters of sandwich truncated conical shells. Parametric studies are conducted for two configurations, different volume fraction index and different geometrical parameters of FGM sandwich truncated cones.

The free vibration of sandwich truncated conical shells containing functionally graded layers within the shear deformation theory

A new porosities distribution is proposed for bending analysis of new model of functionally graded material (FGM) sandwich plates. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. New higher-order deformation theory is proposed to derive the field equations of the FG sandwich plates with simply-supported edge conditions. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The accuracy of this theory is ascertained by comparing it with other published results.

https://iopscience.iop.org/article/10.1088/2053-1591/ab0971/pdf

Effect of porosity on the bending analysis of various functionally graded sandwich plates

Buckling, free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation

Computational semi-analytical method for the 3D elasticity bending solution of laminated composite and sandwich doubly-curved shells

An axiomatic/asymptotic evaluation of the best theories for free vibration of laminated and sandwich shells using non-polynomial functions

This paper presents a static analysis of laminated composite doubly-curved shells using refined kinematic models with polynomial and non-polynomial functions recently introduced in the literature. To be specific, Maclaurin, trigonometric, exponential and zig-zag functions are employed. The employed refined models are based on the equivalent single layer theories. A simply supported shell is subjected to different mechanical loads, specifically: bi-sinusoidal, uniform, patch, hydrostatic pressure and point load. The governing equations are derived from the Principle of Virtual displacement and solved via Navier-Type closed form solutions. The results are compared with results from Layer-wise solutions and different higher order shear deformation theories available. It is shown that refined models with non-polynomial terms are able to accurately predict the through-thethickness displacement and stress distributions maintaining less computational effort compared to a Layer-wise models.

https://robots.iopscience.iop.org/article/10.1088/1757-899X/473/1/012006/pdf

J.C. Monge

Papers

Buckling, free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation

Computational semi-analytical method for the 3D elasticity bending solution of laminated composite and sandwich doubly-curved shells

An axiomatic/asymptotic evaluation of the best theories for free vibration of laminated and sandwich shells using non-polynomial functions

Bending Response of Doubly Curved Laminated Composite Shells using Hybrid Refined Models

Three dimensional numerical solution for the bending study of magneto-piezo-elastic spherical and cylindrical shells