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: 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.
Abstract: This paper deals with the thermo-mechanical deformation behavior of shear deformable functionally graded ceramicmetal (FGM) plates. Theoretical formulations are based on higher order shear deformation theory with a considerable amendment in the transverse displacement using finite element method (FEM). The mechanical properties of the plate are assumed to be temperaturedependent and graded in the thickness direction according to a powerlaw distribution in terms of the volume fractions of the constituents. The temperature field is supposed to be a uniform distribution over the plate surface (XY plane) and varied in the thickness direction only. The fundamental equations for the FGM plates are obtained using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite element with thirteen degrees of freedom per node have been employed to accomplish the results. Convergence and comparison studies have been performed to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index and temperature rise with different loading and boundary conditions. Numerical results for the FGM plates are provided in dimensionless tabular and graphical forms. The results proclaim that the temperature field and the gradient in the material properties have significant role on the thermo-mechanical deformation behavior of the FGM plates.
Abstract: The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.
Abstract: Stress analysis of functionally graded composite plates
composed of ceramic, functionally graded material and metal layers is
investigated using 3-D finite element method. In FGM layer, material
properties are assumed to be varied continuously in the thickness
direction according to a simple power law distribution in terms of the
volume fraction of a ceramic and metal. The 3-D finite element model
is adopted by using an 18-node solid element to analyze more
accurately the variation of material properties in the thickness
direction. Numerical results are compared for three types of materials.
In the analysis, the tensile and the compressive stresses are
summarized for various FGM thickness ratios, volume fraction
distributions, geometric parameters and mechanical loads.
Abstract: Equilibrium and stability equations of a thin rectangular plate with length a, width b, and thickness h(x)=C1x+C2, made of functionally graded materials under thermal loads are derived based on the first order shear deformation theory. It is assumed that the material properties vary as a power form of thickness coordinate variable z. The derived equilibrium and buckling equations are then solved analytically for a plate with simply supported boundary conditions. One type of thermal loading, uniform temperature rise and gradient through the thickness are considered, and the buckling temperatures are derived. The influences of the plate aspect ratio, the relative thickness, the gradient index and the transverse shear on buckling temperature difference are all discussed.
Abstract: This paper presents an exact analytical model for
optimizing stability of thin-walled, composite, functionally graded
pipes conveying fluid. The critical flow velocity at which divergence
occurs is maximized for a specified total structural mass in order to
ensure the economic feasibility of the attained optimum designs. The
composition of the material of construction is optimized by defining
the spatial distribution of volume fractions of the material
constituents using piecewise variations along the pipe length. The
major aim is to tailor the material distribution in the axial direction so
as to avoid the occurrence of divergence instability without the
penalty of increasing structural mass. Three types of boundary
conditions have been examined; namely, Hinged-Hinged, Clamped-
Hinged and Clamped-Clamped pipelines. The resulting optimization
problem has been formulated as a nonlinear mathematical
programming problem solved by invoking the MatLab optimization
toolbox routines, which implement constrained function
minimization routine named “fmincon" interacting with the
associated eigenvalue problem routines. In fact, the proposed
mathematical models have succeeded in maximizing the critical flow
velocity without mass penalty and producing efficient and economic
designs having enhanced stability characteristics as compared with
the baseline designs.
Abstract: The aim of the work was to attenuate the vibration amplitude in CESNA 172 airplane wing by using Functionally Graded Material instead of uniform or composite material. Wing strength was achieved by means of stress analysis study, while wing vibration amplitudes and shapes were achieved by means of Modal and Harmonic analysis. Results were verified by applying the methodology in a simple cantilever plate to the simple model and the results were promising and the same methodology can be applied to the airplane wing model. Aluminum models, Titanium models, and functionally graded materials of Aluminum and titanium results were compared to show a great vibration attenuation after using the FGM. Optimization in FGM gradation satisfied our objective of reducing and attenuating the vibration amplitudes to show the effect of using FGM in vibration behavior. Testing the Aluminum rich models, and comparing it with the titanium rich model was an optimization in this paper. Results have shown a significant attenuation in vibration magnitudes when using FGM instead of Titanium Plate, and Aluminium wing with FGM Spurs instead of Aluminium wings. It was also recommended that in future, changing the graphical scale to 1:10 or even 1:1 when the computers- capabilities allow.
Abstract: This paper describes a study of geometrically
nonlinear free vibration of thin circular functionally graded (CFGP)
plates resting on Winkler elastic foundations. The material properties
of the functionally graded composites examined here are assumed to
be graded smoothly and continuously through the direction of the
plate thickness according to a power law and are estimated using the
rule of mixture. The theoretical model is based on the classical Plate
theory and the Von-Kármán geometrical nonlinearity assumptions.
An homogenization procedure (HP) is developed to reduce the
problem considered here to that of isotropic homogeneous circular
plates resting on Winkler foundation. 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. On the other hand, the
influence of the foundation parameters on the nonlinear fundamental
frequency has also been analysed.
Abstract: New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.
Abstract: Structural behavior of ring stiffened thick walled
cylinders made of functionally graded materials (FGMs) is
investigated in this paper. Functionally graded materials are inhomogeneous composites which are usually made from a mixture
of metal and ceramic. The gradient compositional variation of the
constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses that are
induced when two dissimilar materials with large differences in material properties are bonded. FGM formation of the cylinder is
modeled by power-law exponent and the variation of characteristics is supposed to be in radial direction.
A finite element formulation is derived for the analysis. According to the property variation of the constituent materials in the radial
direction of the wall, it is not convenient to use conventional elements to model and analyze the structure of the stiffened FGM
cylinders. In this paper a new cylindrical super-element is used to model the finite element formulation and analyze the static and
modal behavior of stiffened FGM thick walled cylinders. By using
this super-element the number of elements, which are needed for
modeling, will reduce significantly and the process time is less in comparison with conventional finite element formulations. Results for static and modal analysis are evaluated and verified by
comparison to finite element formulation with conventional
elements. Comparison indicates a good conformity between results.
Abstract: This paper presents the buckling analysis of short and
long functionally graded cylindrical shells under thermal and
mechanical loads. The shell properties are assumed to vary
continuously from the inner surface to the outer surface of the shell.
The equilibrium and stability equations are derived using the total
potential energy equations, Euler equations and first order shear
deformation theory assumptions. The resulting equations are solved
for simply supported boundary conditions. The critical temperature
and pressure loads are calculated for both short and long cylindrical
shells. Comparison studies show the effects of functionally graded
index, loading type and shell geometry on critical buckling loads of
short and long functionally graded cylindrical shells.
Abstract: This paper presents a generalized formulation for the
problem of buckling optimization of anisotropic, radially graded,
thin-walled, long cylinders subject to external hydrostatic pressure.
The main structure to be analyzed is built of multi-angle fibrous
laminated composite lay-ups having different volume fractions of the
constituent materials within the individual plies. This yield to a
piecewise grading of the material in the radial direction; that is the
physical and mechanical properties of the composite material are
allowed to vary radially. The objective function is measured by
maximizing the critical buckling pressure while preserving the total
structural mass at a constant value equals to that of a baseline
reference design. In the selection of the significant optimization
variables, the fiber volume fractions adjoin the standard design
variables including fiber orientation angles and ply thicknesses. The
mathematical formulation employs the classical lamination theory,
where an analytical solution that accounts for the effective axial and
flexural stiffness separately as well as the inclusion of the coupling
stiffness terms is presented. The proposed model deals with
dimensionless quantities in order to be valid for thin shells having
arbitrary thickness-to-radius ratios. The critical buckling pressure
level curves augmented with the mass equality constraint are given
for several types of cylinders showing the functional dependence of
the constrained objective function on the selected design variables. It
was shown that material grading can have significant contribution to
the whole optimization process in achieving the required structural
designs with enhanced stability limits.