Noon Digital Resources
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Abstract
The superior properties of Functionally Graded Materials (FGM) are
usually accompanied by randomness in their properties due to difficulties in
tailoring the gradients during manufacturing processes. Using the Stochastic
Finite Element Method (SFEM) proved to be a powerful tool in studying the
sensitivity of the static response of FGM plates to uncertainties in their
material properties. This tool is yet to be used in studying free vibration
of FGM plates. The aim of this work is to use both a First Order Reliability
Method (FORM) and the Second Order Reliability Method (SORM), combined with
a nine-noded isoparametric Lagrangian element based on the third order shear
deformation theory to investigate sensitivity of the fundamental frequency
of FGM plates to material uncertainties. These include the effect of
uncertainties on both the metal and ceramic constituents. The basic random
variables include ceramic and metal Young’s modulus and Poisson’s ratio,
their densities and ceramic volume fraction. The developed code utilizes
MATLAB capabilities to derive the derivatives of the stiffness and mass
matrices symbolically with a considerable reduction in calculation time.
Calculating the eigenvectors at the mean values of the variables proves to
be a reasonable simplification which significantly increases solution speed.
The stochastic finite element code is validated using available data in the
literature, in addition to comparisons with results of the well-established
Monte Carlo simulation technique with importance sampling. Results show that
SORM is an excellent rapid tool in the stochastic analysis of free vibration
of FGM plates, when compared to the slower Monte Carlo simulation
techniques.
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