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.
Highlights
Because of the demand of conflicting property requirement in engineering applications, pure metals are of little use
Before functionally graded material (FGM) were found, over the past three decades in Japan thin layers or laminates were used in plane structures, but temperature variation occurred through the thickness
The design variable for this problem is the volume fraction Ψ(y) of the power (P-FGM) and the sigmoid (S-FGM), which is described by the material gradient index “w.” the objective function for this problem is to minimize the maximum von Mises stress in a rectangular plate model which is put under uniaxial tension with the two unloaded edges held fixed
Summary
Because of the demand of conflicting property requirement in engineering applications, pure metals are of little use. The primary objective of this study is to discuss the difference between these distribution functions for the constituents’ volume fraction and using the optimization techniques that are available in the ANSYS package [17] to determine the optimum material gradient of a rectangular plate made of FGM. Very few investigators have studied the difference between the power law, exponential, or sigmoid functions for the constituents’ volume fraction. Elastic modulus of a 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, or sigmoid functions. The value of Poisson coefficient is constant and was set to 0.3 in this study
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