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Steel and Composite Structures Volume 44, Number 5, September10 2022 , pages 651-676 DOI: https://doi.org/10.12989/scs.2022.44.5.651 |
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Stochastic buckling quantification of porous functionally graded cylindrical shells |
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Minh-Chien Trinh and Seung-Eock Kim
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| Abstract | ||
| Most of the experimental, theoretical, and numerical studies on the stability of functionally graded composites are deterministic, while there are full of complex interactions of variables with an inherently probabilistic nature, this paper presents a non-intrusive framework to investigate the stochastic nonlinear buckling behaviors of porous functionally graded cylindrical shells exposed to inevitable source-uncertainties. Euler-Lagrange equations are theoretically derived based on the three variable refined shear deformation theory. Closed-form solutions for the shell buckling loads are achieved by solving the deterministic eigenvalue problems. The analytical results are verified with numerical results obtained from finite element analyses that are conducted in the commercial software ABAQUS. The non-intrusive framework is completed by integrating the Monte Carlo simulation with the verified closed-form solutions. The convergence studies are performed to determine the effective pseudorandom draws of the simulation. The accuracy and efficiency of the framework are verified with statistical results that are obtained from the first and second-order perturbation techniques. Eleven cases of individual and compound uncertainties are investigated. Sensitivity analyses are conducted to figure out the five cases that have profound perturbative effects on the shell buckling loads. Complete probability distributions of the first three critical buckling loads are completely presented for each profound uncertainty case. The effects of the shell thickness, volume fraction index, and stochasticity degree on the shell buckling load under compound uncertainties are studied. There is a high probability that the shell has non-unique buckling modes in stochastic environments, which should be known for reliable analysis and design of engineering structures. | ||
| Key Words | ||
| finite element analysis; Monte Carlo simulation; nonlinear buckling analysis; perturbation technique; porous functionally graded shell; uncertainty quantification | ||
| Address | ||
| Minh-Chien Trinh:1)Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea 2)Division of Mechanical System Engineering, Jeonbuk National University, 567, Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 54896, Republic of Korea Seung-Eock Kim:epartment of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea | ||