scholarly journals A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 92
Author(s):  
Shaima M. Dsouza ◽  
Tittu Mathew Varghese ◽  
P. R. Budarapu ◽  
S. Natarajan
Keyword(s):  
Zirconium Oxide ◽  
Isogeometric Analysis ◽  
Deformation Theory ◽  
Polynomial Chaos ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
B Splines ◽  
First Order ◽  
Graded Material

A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples.

A simple size-dependent isogeometric approach for bending analysis of functionally graded microplates using the modified strain gradient elasticity theory

2020 ◽  
Vol 42 (3) ◽  
pp. 255-267
Author(s):  
Chien H. Thai ◽  
H. Nguyen-Xuan
Keyword(s):  
Strain Gradient ◽  
Isogeometric Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Length Scale ◽  
First Order ◽  
Size Dependent ◽  
Material Length Scale ◽  
Material Length

In this study, a simple size-dependent isogeometric approach for bending analysis of functionally graded (FG) microplates using the modified strain gradient theory (MSGT), simple first-order shear deformation theory (sFSDT) and isogeometric analysis is presented for the first time. The present approach reduces one variable when comparing with the original first-order shear deformation theory (FSDT) within five variables and only considers three material length scale parameters (MLSPs) to capture size effects. Effective material properties as Young’s modulus, Poisson’s ratio and density mass are computed by a rule of mixture. Thanks to the principle of virtual work, the essential equations which are solved by the isogeometric analysis method, are derived. Rectangular and circular FG microplates with different boundary conditions, volume fraction and material length scale parameter are exampled to evaluate the deflections of FG microplates.

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