Table of Contents
Indian Journal of Materials Science
Volume 2014, Article ID 501935, 7 pages
http://dx.doi.org/10.1155/2014/501935
Research Article

Optimum Material Gradient for Functionally Graded Rectangular Plate with the Finite Element Method

College of Mechanical & Electrical Engineering, Harbin Engineering University, Harbin 150001, China

Received 7 October 2013; Accepted 16 December 2013; Published 17 February 2014

Academic Editors: V. Rajagopal Reddy and V. Srivastava

Copyright © 2014 Wasim M. K. Helal and Dongyan Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The optimum material gradient of a rectangular plate made of functionally graded material (FGM) is determined in this study. Elastic modulus of functionally graded (FG) rectangular plate is assumed to vary continuously throughout the height of the plate, according to the volume fraction of the constituent materials based on the power law, exponential model I, exponential model П, or sigmoid functions. The difference between these distribution functions for the constituents’ volume fraction is discussed in this study. To determine the optimum material gradient of a rectangular plate made of FGM, the finite element method and the optimization techniques are used. In this study, von Mises stress, shear stress, and deformation in FGM case with the power law, exponential model I, exponential model П, or sigmoid functions are investigated. Simulation results indicate that the optimum material gradient for FG rectangular plate can be described by using a modified sigmoid function. The maximum values of von Mises stress, shear stress, and deformation in FG rectangular plate with the optimum material gradient are reduced compared with the pure material case by around 22%, 11%, and 24%, respectively.