Abstract
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.
Highlights
Composite materials are widely used in a large variety of structures due to their high strength to weight ratio and excellent thermo-mechanical and corrosion resistance properties [1,2,3]
It is observed that the results obtained from polynomial chaos expansion (PCE) order one are comparable with Monte Carlo simulation (MCS)
This clearly shows the benefits of the non-intrusive PCE analysis over MCS, with only a few evaluations required in case of the latter
Summary
Composite materials are widely used in a large variety of structures due to their high strength to weight ratio and excellent thermo-mechanical and corrosion resistance properties [1,2,3]. The spectral stochastic isogeometric analysis (SSIGA) using the first order deformation theory was implemented by Keyen Li et al to obtain the static response of the FGM plates [13]. Shaker [12] studied the stochastic free vibrations of FGM plates using the third order shear deformation theory, with uncertainties in the constituent material properties and the volume fraction index. Employed a cell-based smoothed discrete shear gap method to study the stochastic free vibration characteristics of functionally graded material plates. The influence of the randomness in the material properties, Young’s modulus and density on the uncertainty in the static bending and free vibration characteristics of FGM plates were studied using a non-intrusive approach.
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