07-04-2012, 11:35 AM
Analysis of functionally graded plates
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INTRODUCTION
Functionally graded structures are those in which the volume fractions of two or more materials
are varied continuously as a function of position along certain dimension(s) of the structure to
achieve a required function. For example, thermal barrier plate structures for high-temperature
applications may form from a mixture of ceramic and a metal. The composition is varied from a
ceramic-rich surface to a metal-rich surface, with a desired variation of the volume fractions of
the two materials in between the two surfaces. The ceramic constituent of the material provides
the high-temperature resistance due to its low thermal conductivity [1].
THEORETICAL FORMULATION
The First-order Shear Deformation Theory (FSDT) is the simplest plate theory that accounts
for transverse shear strains (see Reddy [24; 25]), which are represented as constant through the
plate thickness, and the theory requires shear correction coecients to compute transverse shear
forces. In the Third-order Shear Deformation Theory (TSDT) of Reddy [24; 25], the transverse
shear stresses are represented as quadratic through the thickness and consequently it requires no
shear correction factors. The theory also contains the rst-order shear deformation theory as a
special case. Here we develop the equations of motion of functionally graded plates using TSDT.
CONCLUSION
Theoretical formulation and nite element models based on the third-order shear deformation
theory advanced by the author are presented. The formulation accounts for the thermomechanical
coupling, time dependency, and von Karman-type geometric non-linearity. The Navier solutions for
simply supported plates based on the linear third-order theory and non-linear static and dynamic
nite element results based on the rst-order theory are presented to show the eects of volume
fractions and modulus ratio of the constituents on de
ections and transverse shear stresses. It is
seen that the basic response of the plates that correspond to properties intermediate to that of
the metal and the ceramic, does not necessarily lie in between that of the ceramic and metal.
The non-dimensional de
ection was found to reach a minimum at a volume fraction index that
depends on the properties and the ratio of the properties of the constituents. In the absence of
thermal loading, the dynamic response of the graded plates is intermediate to that of the metal
and ceramic plates.