Stochastic Finite element analysis of the free vibration of functionally graded material plates |
| |
Authors: | Afeefa Shaker Wael Abdelrahman Mohammad Tawfik Edward Sadek |
| |
Affiliation: | (1) Department of Aerospace Engineering, Cairo University, Cairo, Egypt;(2) Department of Aerospace Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia;(3) Mechanical Engineering Department, British University in Egypt, El-Shorouk City, Cairo, 11837, Egypt |
| |
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. |
| |
Keywords: | FGM Stochastic finite element analysis Shear deformable plate FORM SORM |
本文献已被 SpringerLink 等数据库收录! |
|