Abstract: In the present investigation, free vibration of functionally graded material (FGM) skew plates under thermal environment is studied. Kinematics equations are based on the Reddy’s higher order shear deformation theory and a nine noded isoparametric Lagrangian element is adopted to mesh the plate geometry. The issue of C1 continuity requirement related to the assumed displacement field has been circumvented effectively to develop C0 finite element formulation. Effective mechanical properties of the constituents of the plate are considered to be as position and temperature dependent and assumed to vary in the thickness direction according to a simple power law distribution. The displacement components of a rectangular plate are mapped into skew plate geometry by means of suitable transformation rule. One dimensional Fourier heat conduction equation is used to ascertain the temperature profile of the plate along thickness direction. Influence of different parameters such as volume fraction index, boundary condition, aspect ratio, thickness ratio and temperature field on frequency parameter of the FGM skew plate is demonstrated by performing various examples and the related findings are discussed briefly. New results are generated for vibration of the FGM skew plate under thermal environment, for the first time, which may be implemented in the future research involving similar kind of problems.
Abstract: In this study, thermal elastic stress distribution occurred on long hollow cylinders made of functionally graded material (FGM) was analytically defined under thermal, mechanical and thermo mechanical loads. In closed form solutions for elastic stresses and displacements are obtained analytically by using the infinitesimal deformation theory of elasticity. It was assumed that elasticity modulus, thermal expansion coefficient and density of cylinder materials could change in terms of an exponential function as for that Poisson’s ratio was constant. A gradient parameter n is chosen between - 1 and 1. When n equals to zero, the disc becomes isotropic. Circumferential, radial and longitudinal stresses in the FGMs cylinders are depicted in the figures. As a result, the gradient parameters have great effects on the stress systems of FGMs cylinders.
Abstract: Creep behavior of thick-walled functionally graded cylinder consisting of AlSiC and subjected to internal pressure and high temperature has been analyzed. The functional relationship between strain rate with stress can be described by the well known threshold stress based creep law with a stress exponent of five. The effect of imposing non-linear particle gradient on the distribution of creep stresses in the thick-walled functionally graded composite cylinder has been investigated. The study revealed that for the assumed non-linear particle distribution, the radial stress decreases throughout the cylinder, whereas the tangential, axial and effective stresses have averaging effect. The strain rates in the functionally graded composite cylinder could be reduced to significant extent by employing non-linear gradient in the distribution of reinforcement.
Abstract: In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.
Abstract: In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.
Abstract: This paper interested in the mechanical deformation behavior of shear deformable functionally graded ceramic-metal (FGM) plates. Theoretical formulations are based on power law theory when build up functional graded material. The mechanical properties of the plate are graded in the thickness direction according to a power-law Displacement and stress is obtained using finite element method (FEM). The load is supposed to be a uniform distribution over the plate surface (XY plane) and varied in the thickness direction only. An FGM’s gradation in material properties allows the designer to tailor material response to meet design criteria. An FGM made of ceramic and metal can provide the thermal protection and load carrying capability in one material thus eliminating the problem of thermo-mechanical deformation behavior. This thesis will explore analysis of FGM flat plates and shell panels, and their applications to r structural problems. FGMs are first characterized as flat plates under pressure in order to understand the effect variation of material properties has on structural response. In addition, results are compared to published results in order to show the accuracy of modeling FGMs using ABAQUS software.
Abstract: The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.
Abstract: This paper studies free vibration of functionally
graded beams Subjected to Axial Load that is simply supported at
both ends lies on a continuous elastic foundation. The displacement
field of beam is assumed based on Engesser-Timoshenko beam
theory. The Young's modulus of beam is assumed to be graded
continuously across the beam thickness. Applying the Hamilton's
principle, the governing equation is established. Resulting equation is
solved using the Euler's Equation. The effects of the constituent
volume fractions and foundation coefficient on the vibration
frequency are presented. To investigate the accuracy of the present
analysis, a compression study is carried out with a known data.
Abstract: In the present study, the problem of geometrically nonlinear free vibrations of functionally graded circular plates (FGCP) resting on Pasternak elastic foundation with immovable ends was studied. The material properties of the functionally graded composites examined were assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the classical Plate theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results dealing with the problem of functionally graded plates. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the FGCP has been studied. The effect of the linear and shearing foundations is to decrease the frequency ratio, where it increases with the effect of the nonlinear foundation stiffness.
Abstract: The use of a conventional air plasma-sprayed thermal barrier coating (TBC) and a porous, functionally graded TBC as a thermal insulator for Al7075 alloy was explored. A quench test at 1200°C employing fast heating and cooling rates was setup to represent a dynamic thermal condition of an aerospace component. During the test, coated samples were subjected the ambient temperature of 1200°C for a very short time. This was followed by a rapid drop in temperature resulting in cracking of the coatings. For the conventional TBC, it was found that the temperature of the Al7075 substrate decreases with the increase in the ZrO2 topcoat thickness. However, at the topcoat thickness of 1100 µm, large horizontal cracks can be observed in the topcoat and at the topcoat thickness of 1600 µm, the topcoat delaminate during cooling after the quench test. The porous, functionally graded TBC with 600 µm thick topcoat, on the other hand, was found to be as effective at reducing the substrate temperature as the conventional TBC with 1100 µm thick topcoat. The maximum substrate temperature is about 213°C for the former and 208°C for the latter when a heating rate of 38°C/s was used. When the quench tests were conducted with a faster heating rate of 128°C/s, the Al7075 substrate heat up faster with a reduction in the maximum substrate temperatures. The substrate temperatures dropped from 297 to 212°C for the conventional TBC and from 213 to 155°C for the porous TBC, both with 600 µm thick topcoat. Segmentation cracks were observed in both coating after the quench test.
Abstract: In this paper a study on the vibration of thin
cylindrical shells with ring supports and made of functionally
graded materials (FGMs) composed of stainless steel and
nickel is presented. Material properties vary along the
thickness direction of the shell according to volume fraction
power law. The cylindrical shells have ring supports which are
arbitrarily placed along the shell and impose zero lateral
deflections. The study is carried out based on third order shear
deformation shell theory (T.S.D.T). The analysis is carried out
using Hamilton-s principle. The governing equations of motion of
FGM cylindrical shells are derived based on shear deformation
theory. Results are presented on the frequency characteristics,
influence of ring support position and the influence of boundary
conditions. The present analysis is validated by comparing results
with those available in the literature.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free boundary conditions.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free and clamped-clamped boundary conditions.
Abstract: This paper studies mechanical buckling of
functionally graded beams subjected to axial compressive load that is
simply supported at both ends lies on a continuous elastic foundation.
The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the
equilibrium equation is established. The influences of dimensionless geometrical parameter, functionally graded index and foundation
coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study
is carried out with a known data.
Abstract: In this study, it is investigated the stability boundary of
Functionally Graded (FG) panel under the heats and supersonic
airflows. Material properties are assumed to be temperature
dependent, and a simple power law distribution is taken. First-order
shear deformation theory (FSDT) of plate is applied to model the
panel, and the von-Karman strain- displacement relations are
adopted to consider the geometric nonlinearity due to large
deformation. Further, the first-order piston theory is used to model the
supersonic aerodynamic load acting on a panel and Rayleigh damping
coefficient is used to present the structural damping. In order to find a
critical value of the speed, linear flutter analysis of FG panels is
performed. Numerical results are compared with the previous works,
and present results for the temperature dependent material are
discussed in detail for stability boundary of the panel with various
volume fractions, and aerodynamic pressures.
Abstract: The static stability analysis of stiffened functionally
graded cylindrical shells by isotropic rings and stringers subjected to
axial compression is presented in this paper. The Young's modulus of
the shell is taken to be function of the thickness coordinate. The
fundamental relations, the equilibrium and stability equations are
derived using the Sander's assumption. Resulting equations are
employed to obtain the closed-form solution for the critical axial
loads. The effects of material properties, geometric size and different
material coefficient on the critical axial loads are examined. The
analytical results are compared and validated using the finite element
model.
Abstract: Study of the vibration cylindrical shells made of
a functionally gradient material (FGM) composed of stainless
steel and nickel is important. Material properties are graded in
the thickness direction of the shell according to volume
fraction power law distribution. The objective is to study the
natural frequencies, the influence of constituent volume
fractions and the effects of boundary conditions on the natural
frequencies of the FG cylindrical shell. The study is carried
out using third order shear deformation shell theory. The
governing equations of motion of FG cylindrical shells are
derived based on shear deformation theory. Results are
presented on the frequency characteristics, influence of
constituent volume fractions and the effects of clampedclamped
boundary conditions.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions
Abstract: In the recent years, functionally gradient materials (FGMs) have gained considerable attention in the high temperature environment applications. In this paper, free vibration of thin functionally graded cylindrical shell with hole composed of stainless steel and zirconia is studied. The mechanical properties vary smoothly and continuously from one surface to the other according to a volume fraction power-law distribution. The Influence of shell geometrical parameters, variations of volume fractions and boundary conditions on natural frequency is considered. The equations of motion are based on strains-displacement relations from Love-s shell theory and Rayleigh method. The results have been obtained for natural frequencies of cylindrical shell with holes for different shape, number and location in this paper.
Abstract: This study aims to investigate mechanical behavior of
deep-drawn cups consisting of aluminum (A1050)/ duralumin
(A2017) multi-layered clad structures with micro- and macro-scale
functional gradients. Such multi-layered clad structures are possibly
used for a new type of crash-boxes in automobiles to effectively
absorb the impact forces generated when automobiles having
collisions. The effect of heat treatments on microstructure,
compositional gradient, micro hardness in 2 and 6-layered aluminum/
duralumin clad structures, which were fabricated by hot rolling, have
been investigated. Impact compressive behavior of deep-drawn cups
consisting of such aluminum/ duralumin clad structures has been also
investigated in terms of energy absorption and maximum force.
Deep-drawn cups consisting of 6-layerd clad structures with microand
macro-scale functional gradients exhibit superior properties in
impact compressive tests.