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Probabilistic eigenvalue buckling analysis solved through the ratio of polynomial response surface
Authors:U. Alibrandi  N. Impollonia  G. Ricciardi
Affiliation:1. Dipartimento di Ingegneria Civile, University of Messina, Contrada di Dio, 98166, Villaggio S. Agata, Messina, Italy;2. Dipartimento ASTRA, University of Catania, Via delle Maestranze, 99, 96100 Siracusa, Italy;1. Dept. of Aeronautical Engg., Institute of Aeronautical Engineering, Hyderabad, India;2. Institute of Structural Mechanics, Bauhaus Univesity of Weimar, 99423 Weimar, Germany;3. Structural Test Facility, DRDL, Hyderabad, India;1. Graduate School of Engineering, Osaka University, 2-1 Yamadaoka Suita, Osaka 565-0871, Japan;2. School of Material Science and Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, Shaanxi 710049, PR China;3. Joining and Welding Research Institute, Osaka University, 11-1 Mihogaoka Ibaraki, Osaka 567-0047, Japan;1. Department of Mechanical Engineering, Northeastern University, Boston, MA 02115, USA;2. Department of Engineering Science, University of Oxford, Parks Road, Oxford OX13PJ, UK;1. National University of Singapore, Department of Civil and Environmental Engineering, 1 Engineering Drive 2, Singapore 117576, Singapore;2. University of Messina, Department of Civil and Environmental Engineering, DICIEAMA, Villaggio S. Agata, 98166 Messina, Italy
Abstract:An efficient procedure for the reliability analysis of frame structures with respect to the buckling limit state is proposed under the assumption that no imperfections are present and that the elastic parameters are uncertain and modeled as random variables. The approach allows a deeper investigation of structures which are not sensitive to imperfections. The procedure relies on a Response Surface Method adopting simple ratio of polynomials without cross-terms as performance function. Such a relationship approximates analytically the dependence between the buckling load and the basic variables furnishing a limit state equation which is very close to the exact one when a proper experimental design is adopted. In this way a Monte Carlo Simulation applied to the response surface leads to a good approximation with low computational effort. Several numerical examples show the accuracy and effectiveness of the method varying structural complexity, correlation between basic variables and their distribution.
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