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Stochastic vibration and buckling analysis of functionally graded microplates with a unified higher-order shear deformation theory
https://orcid.org/0000-0002-1215-9348
Abstract Based on equations of the elasticity, this paper proposes a unified higher-order shear deformation theory for stochastic vibration and buckling analysis of the functionally graded (FG) microplates. The governing equations of motions are derived from Hamilton’s principle. The solutions are approximated by bi-directional series in which hybrid shape functions are proposed, then the stiffness and mass matrix are explicitly derived. In order to investigate the stochastic responses of the FG microplates, the polynomial chaos expansion (PCE) is used. The multiple uncertain material properties are randomly changed via the lognormal distributions. Numerical results are presented for different configurations of the FG microplates such as the power-law index, material length scale parameter, length-to-thickness ratio and boundary conditions on their critical buckling loads and natural frequencies. The results from PCE are evaluated by comparing with those from Monte Carlo simulation to show the efficiency and accuracy of the present approach. Some new results for stochastic analysis of the FG microplates are presented and can be used for future references.
Highlights Novel unified higher-order shear deformation microplate model is proposed. Monte Carlo simulation and polynomial chaos expansion approach are developed for stochastic analysis of FG microplates. Ritz method with hybrid shape functions yields fast convergence and accurate results. Reliability estimation and sensitivity analysis is performed. Effects of material distribution, side-to-thickness ratio, boundary conditions and thickness-to-material scale ratio are investigated.
Stochastic vibration and buckling analysis of functionally graded microplates with a unified higher-order shear deformation theory
https://orcid.org/0000-0002-1215-9348
Abstract Based on equations of the elasticity, this paper proposes a unified higher-order shear deformation theory for stochastic vibration and buckling analysis of the functionally graded (FG) microplates. The governing equations of motions are derived from Hamilton’s principle. The solutions are approximated by bi-directional series in which hybrid shape functions are proposed, then the stiffness and mass matrix are explicitly derived. In order to investigate the stochastic responses of the FG microplates, the polynomial chaos expansion (PCE) is used. The multiple uncertain material properties are randomly changed via the lognormal distributions. Numerical results are presented for different configurations of the FG microplates such as the power-law index, material length scale parameter, length-to-thickness ratio and boundary conditions on their critical buckling loads and natural frequencies. The results from PCE are evaluated by comparing with those from Monte Carlo simulation to show the efficiency and accuracy of the present approach. Some new results for stochastic analysis of the FG microplates are presented and can be used for future references.
Highlights Novel unified higher-order shear deformation microplate model is proposed. Monte Carlo simulation and polynomial chaos expansion approach are developed for stochastic analysis of FG microplates. Ritz method with hybrid shape functions yields fast convergence and accurate results. Reliability estimation and sensitivity analysis is performed. Effects of material distribution, side-to-thickness ratio, boundary conditions and thickness-to-material scale ratio are investigated.
Stochastic vibration and buckling analysis of functionally graded microplates with a unified higher-order shear deformation theory
https://orcid.org/0000-0002-1215-9348
Abstract Based on equations of the elasticity, this paper proposes a unified higher-order shear deformation theory for stochastic vibration and buckling analysis of the functionally graded (FG) microplates. The governing equations of motions are derived from Hamilton’s principle. The solutions are approximated by bi-directional series in which hybrid shape functions are proposed, then the stiffness and mass matrix are explicitly derived. In order to investigate the stochastic responses of the FG microplates, the polynomial chaos expansion (PCE) is used. The multiple uncertain material properties are randomly changed via the lognormal distributions. Numerical results are presented for different configurations of the FG microplates such as the power-law index, material length scale parameter, length-to-thickness ratio and boundary conditions on their critical buckling loads and natural frequencies. The results from PCE are evaluated by comparing with those from Monte Carlo simulation to show the efficiency and accuracy of the present approach. Some new results for stochastic analysis of the FG microplates are presented and can be used for future references.
Highlights Novel unified higher-order shear deformation microplate model is proposed. Monte Carlo simulation and polynomial chaos expansion approach are developed for stochastic analysis of FG microplates. Ritz method with hybrid shape functions yields fast convergence and accurate results. Reliability estimation and sensitivity analysis is performed. Effects of material distribution, side-to-thickness ratio, boundary conditions and thickness-to-material scale ratio are investigated.
Stochastic vibration and buckling analysis of functionally graded microplates with a unified higher-order shear deformation theory
Tran, Van-Thien (author) / Nguyen, Trung-Kien (author) / Nguyen, Phong T.T. (author) / Vo, Thuc P. (author)
Thin-Walled Structures ; 177
2022-05-19
Article (Journal)
Electronic Resource
English
| British Library Online Contents | 2015
| British Library Online Contents | 2015