Fuzzy finite element analysis for free vibration response of functionally graded semi-rigid frame structures |
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| Institution: | 1. National University of Civil Engineering, 55 Giai Phong Road, Hanoi, Vietnam;2. Thuyloi University, 175 Tay Son Street, Hanoi, Vietnam;1. Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China;2. Qiushi Honors College, Tianjin University, Tian jin 300350, China;3. McGill Metals Processing Centre, McGill University, Montreal, Quebec H3A 2B2 Canada;1. School of Reliability and Systems Engineering, Beihang University, Beijing 100083, China;2. Science and Technology on Reliability and Environmental Engineering Laboratory, Beijing 100083, China;1. Institute of Petroleum Geology and Geophysics SB RAS, 3 Koptug ave., Novosibirsk 630090, Russia;2. Sobolev Institute of Mathematics SB RAS, 4 Koptug ave., Novosibirsk 630090, Russia;3. Novosibirsk State University, 2 Pirogova st., Novosibirsk 630090, Russia;4. Mathematical Center in Akademgorodok, 2 Pirogova st. & 4 Koptug ave., Novosibirsk 630090, Russia;1. National Research University Higher School of Economics, Moscow, Russia;2. Hydrometeorological Centre of Russia, Moscow 123242, Russia |
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| Abstract: | This study contributes a practical approach for the fuzzy free vibration quantification of functionally graded semi-rigid frame structures. A new Timoshenko beam element is formulated to include the connection rigidity for the analysis purpose. The finite element formulation is general to present different semi-rigid conditions, whereas hinged and rigid connections are special cases. Furthermore, an efficient response-surface-based fuzzy analysis is established based on the α–cut strategy and first-order Taylor's approximation to predict the fuzzy natural frequencies of the structures. Highlighted point is that various input uncertainties, such as the material characteristics, the member dimensions, and the connection rigidities, can be incorporated in the analysis by the presented fuzzy methodology. Computational efficiency and correctness of the proposed method are shown, and the effect of the uncertainties, especially of the connection rigidities, on the natural frequency of semi-rigid FGM structures is explored via solving some numerical examples. |
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