scholarly journals Nonlinear analysis of buckling and postbuckling for axially compressed functionally graded cylindrical panels with the Poisson's ratio varying smoothly along the thickness

2012 ◽  
Vol 34 (1) ◽  
pp. 27-44 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Compressive Load ◽  
Cylindrical Panel ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Postbuckling Behavior ◽  
Nonlinear Buckling ◽  
Dimensional Parameter ◽  
Classical Shell Theory

In this paper an approximate analytical solution to analyze the nonlinear buckling and postbuckling behavior of imperfect functionally graded panels with the Poisson's ratio also varying smoothly along the thickness is investigated. Based on the classical shell theory and von Karman's assumption of kinematic nonlinearity and applying Galerkin procedure, the equations for finding critical loads and load-deflection curves of cylindrical panel subjected to axial compressive load with two types boundary conditions, are given. Especially, the stiffness coefficients are analyzed in explicit form. Numerical results show various effects of the inhomogeneous parameter, dimensional parameter, boundary conditions on nonlinear stability of panel. An accuracy of present theoretical results is verified by the previous well-known results.

An analytical approach to the nonlinear buckling behavior of axially compressed auxetic-core cylindrical shells with carbon nanotube-reinforced coatings

2021 ◽  
pp. 146442072110333
Author(s):  
Le Ngoc Ly ◽  
Vu Minh Duc ◽  
Nguyen-Thoi Trung ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Volume Fraction ◽  
Load Capacity ◽  
Cylindrical Shells ◽  
Compressive Load ◽  
Functionally Graded ◽  
Honeycomb Lattice ◽  
Geometrical Parameters ◽  
Postbuckling Behavior ◽  
Nonlinear Buckling

Auxetic materials are usually designed as cores for structures subject to high impulse loads. Furthermore, the lightweight and high load capacity of the auxetic core construction is also an important advantage even for structures subjected to static loads. The combination of auxetic core and face sheets made by the advanced composite materials is a solution to dramatically increase the load-carrying capacity of the structure. In this paper, a new design of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings is presented. Additionally, the nonlinear buckling behaviors of auxetic-core cylindrical shells with carbon nanotube-reinforced coatings under axially compressive loads are investigated. Three distributed types of functionally graded carbon nanotube-reinforced coatings and the honeycomb lattice form of the auxetic core are investigated. The homogenization model for auxetic lattice structures is considered to constitute the formulations of stiffnesses of the core layer. The nonlinear basic formulations are formulated by using the geometrically nonlinear Donnell shell theory considering Pasternak’s foundation. The Galerkin procedure can be applied three times for three states of buckling behaviors, and the expressions of the compressive load-maximal deflection and compressive load-average end shortening postbuckling curves are achieved. The numerically obtained investigations present the significant effects of auxetic core, volume fraction, direction arrangement and distributed law of carbon nanotube, foundation stiffnesses, geometrical parameters of auxetic core and shell on the critical buckling load and postbuckling behavior of structures.

Free vibration and sound insulation of functionally graded honeycomb sandwich plates

2021 ◽  
pp. 109963622110204
Author(s):  
Fenglian Li ◽  
Wenhao Yuan ◽  
Chuanzeng Zhang
Keyword(s):  
Free Vibration ◽  
Poisson’S Ratio ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Dynamic Equations ◽  
Sound Insulation ◽  
Sandwich Plates ◽  
Negative Poisson’S Ratio ◽  
Honeycomb Sandwich ◽  
Negative Poisson's Ratio

Based on the hyperbolic tangent shear deformation theory, free vibration and sound insulation of two different types of functionally graded (FG) honeycomb sandwich plates with negative Poisson’s ratio are studied in this paper. Using Hamilton’s principle, the vibration and vibro-acoustic coupling dynamic equations for FG honeycomb sandwich plates with simply supported edges are established. By applying the Navier’s method and fluid–solid interface conditions, the derived governing dynamic equations are solved. The natural frequencies and the sound insulation of FG honeycomb sandwich plates obtained in this work are compared with the numerical results by the finite element simulation. It is proven that the theoretical models for the free vibration and the sound insulation are accurate and efficient. Moreover, FG sandwich plates with different honeycomb cores are investigated and compared. The corresponding results show that the FG honeycomb core with negative Poisson’s ratio can yield much lower frequencies. Then, the influences of various geometrical and material parameters on the vibration and sound insulation performance are systematically analyzed.

Vibrations of Functionally Graded Shells

2007 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Composite Material ◽  
Modulus Of Elasticity ◽  
Poisson’S Ratio ◽  
Functionally Graded ◽  
New Method ◽  
Poisson's Ratio ◽  
Tabular Form ◽  
Graded Structures ◽  
Functionally Graded Structures

The behavior of functionally graded structures has received a great deal of attention in recent years. Usually, these structures are made out of a composite material with a modulus of elasticity, a Poisson’s ratio, and a density that vary through the thickness. The non-uniformity through the thickness introduces coupling between the transverse deformations and the deformations of the mid-surface. Previous publications have shown how to account for these added complexities and have presented extensive results in tabular form. In this article, available results are used to show that the behavior of functionally graded shells is similar to that of homogeneous isotropic shells. It is well known that for isotropic shells, results can be presented in non-dimensional form so that, once results are obtained for one material, they can be simply scaled to obtain the corresponding results for shells made out of another material. The same can then be done for functionally graded shells. In addition, if functionally graded shells behave like homogeneous shells, no new method of analysis is required. The second part of the paper examines why this is true.

Thermo-Elasto-Plastic Analysis of Thick-Walled Spherical Pressure Vessels Made of Functionally Graded Materials

2016 ◽  
Vol 08 (04) ◽  
pp. 1650054 ◽  
Author(s):  
Zeinab Mazarei ◽  
Mohammad Zamani Nejad ◽  
Amin Hadi
Keyword(s):  
Heat Flux ◽  
Functionally Graded Materials ◽  
Poisson’S Ratio ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Material Behavior ◽  
Poisson's Ratio ◽  
Uniform Heat Flux ◽  
Plastic Behavior ◽  
Graded Materials

An exact closed-form analytical solution is presented to solve the thermo-elasto-plastic problem of thick-walled spherical vessels made of functionally graded materials (FGMs). Assuming that the inner surface is exposed to a uniform heat flux, and that the outer surface is exposed to an airstream. The heat conduction equation for the one-dimensional problem in spherical coordinates is used to obtain temperature distribution in the sphere. Material properties are graded in the thickness direction according to a power law distribution, whereas the Poisson’s ratio is kept constant. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. The plastic model is based on von Mises yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. For various values of inhomogeneity constant, the so-obtained solution is then used to study the distribution of limit heat flux, displacement and stresses versus the radial direction. Moreover, the effect of increasing the heat flux and pressure on the propagation of the plastic zone are investigated. Furthermore, the effect of change in Poisson’s ratio on the value of the critical material parameter is demonstrated. The present study is also validated by comparing the numerical results for thick elasto-plastic spherical shells available in the literature. To the best of the authors’ knowledge, in previous studies, exact thermo-elasto-plastic behavior of FGM thick-walled sphrical pressure vessels has not investigated.

Finite element analysis of flexible functionally graded beams with variable Poisson’s ratio

2016 ◽  
Vol 33 (8) ◽  
pp. 2421-2447 ◽  
Author(s):  
João Paulo Pascon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Poisson’S Ratio ◽  
Scientific Literature ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Transverse Strain ◽  
Thickness Direction ◽  
Element Analysis ◽  
Content Type

Purpose The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio. Design/methodology/approach The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated. Findings In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution. Originality/value In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

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