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

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.

Metamodel-based approach for stochastic free vibration analysis of functionally graded carbon nanotube reinforced plates

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Determination of the Optimum Material Gradient for a Functionally Graded Endodontic Prefabricated Post Using a Sub-Problem Approximation Method

“…Helal and Shi [8] discussed the difference between the distribution functions for the constituents'volume fraction, and the results outcomes from their investigation have indicated that, the optimum material gradient for FGMs can be described by using a modified sigmoid function. Thus, in the current study, the elastic modulus (E) of FGEPP will be assumed to vary continuously throughout the height of the EPP, according the volume fraction of the constituent materials based on the sigmoid function.…”

Optimum Gradation Direction for a Functionally Graded Endodontic Prefabricated Parallel Post: A Finite Element Method

“…Wasim and Dong [9] discussed the difference between the distribution functions for the constituents'volume fraction, and the results have indicated that, the optimum material gradient for FGMs can be described by using a modified sigmoid function. Thus, in this paper, E of FGEPPP will be assumed to vary continuously throughout the height of the EPPP, according the volume fraction of the constituent materials based on the sigmoid function.…”