Size-dependent thermoelastic analysis of a functionally graded nanoshell

2018 ◽  
Vol 32 (03) ◽  
pp. 1850033 ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M. Zenkour
Keyword(s):  
Virtual Work ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Thermoelastic Analysis ◽  
Radial And Axial Displacements ◽  
Eigenvalue And Eigenvector

In this paper, two-dimensional thermoelastic analysis of a functionally graded nanoshell is presented based on nonlocal elasticity theory. To formulate this problem, first-order shear deformation theory (FSDT) is used for axial and radial deformations simultaneously. Material properties are assumed to be mixture of ceramic and metal based on a power law distribution. Principle of virtual work is used for derivation of the governing equations. The analytical approach is presented based on eigenvalue and eigenvector method to derive four unknown functions including radial and axial displacements and rotations along the longitudinal direction. In addition, the influence of nonlocal and in-homogeneous index parameter is studied on the responses of the system. Two-dimensional results are presented along the radial and longitudinal directions.

Thermal Post-Buckling Analysis of Functionally Graded Panels in Hypersonic Airflows

2008 ◽  
Vol 47-50 ◽  
pp. 387-390
Author(s):  
Sun Bae Kim ◽  
Ji Hwan Kim
Keyword(s):  
Volume Fraction ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
The Finite Element Method ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Third Order ◽  
Linear Rule ◽  
Post Buckling

In this study, thermal post-buckling characteristics of functionally graded (FG) panels in hypersonic airflows are investigated. The volume fraction and the material properties of FGMs are continuously changed from ceramic to metal in the thickness direction agreeably to a simple power law distribution and a linear rule of mixture, respectively. Using the principle of virtual work, the governing equations are derived and the finite element method is applied to obtain the solutions. Based on the first-order shear deformation theory (FSDT), the FG panels are modeled by the von Karman strain-displacement relation for the structural non-linearity. Also, the third-order piston theory is employed to consider the aerodynamic non-linearity.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

scholarly journals Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

A NEW SIMPLE HYPERBOLIC SHEAR DEFORMATION THEORY FOR FUNCTIONALLY GRADED PLATES RESTING ON WINKLER–PASTERNAK ELASTIC FOUNDATIONS

2014 ◽  
Vol 11 (06) ◽  
pp. 1350098 ◽  
Author(s):  
ABDERRAHMANE SAID ◽  
MOHAMMED AMEUR ◽  
ABDELMOUMEN ANIS BOUSAHLA ◽  
ABDELOUAHED TOUNSI
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Governing Equations ◽  
Pasternak Elastic Foundation ◽  
Shear Deformation Theories

An improved simple hyperbolic shear deformation theory involving only four unknown functions, as against five functions in case of first or other higher-order shear deformation theories, is introduced for the analysis of functionally graded plates resting on a Winkler–Pasternak elastic foundation. The governing equations are derived by employing the principle of virtual work and the physical neutral surface concept. The accuracy of the present analysis is demonstrated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories.

Free Vibration Responses of Functionally Graded Spherical Shell Panels Using Finite Element Method

2013 ◽  
Author(s):  
Vishesh Ranjan Kar ◽  
Subrata Kumar Panda
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Spherical Shell ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Vibration Responses ◽  
Support Conditions

Free vibration responses of functionally graded spherical shell panels are investigated in the present article. A general mathematical model is developed based on higher order shear deformation theory mid-plane kinematics. The effective material properties are graded in the thickness direction according to a power-law distribution and it varies continuously from metal (bottom surface) to ceramic (top surface). The model is discretized using a nine noded quadrilateral Lagrangian element. A convergence test has been done with different mesh refinement and compared with the available published results. In addition to that the present study includes an ANSYS model check with the developed mathematical model to show the efficacy. New results are computed for different parameters such as volume fraction, thickness ratio, curvature ratio and support conditions which indicates the effect of parametric study on non-dimensional frequency parameters.

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