Interval static analysis of multi-cracked beams with uncertain size and position of cracks |
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| Institution: | 1. Department of Engineering, University of Messina, Villaggio S. Agata, 98166 Messina, Italy;2. Department of Civil, Energy, Environmental and Materials Engineering (DICEAM), University of Reggio Calabria, Via Graziella, 89124 Reggio Calabria, Italy;1. School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, P.R. China;2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an Jiaotong University, Xi''an 710049, Shaanxi, P.R. China;3. School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, P.R. China;1. Department of Mathematics, Sarala Birla University, Ranchi-835103, India;2. Department of Mathematics, Birla Institute of Technology, Mesra-835215, India;1. Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China;1. Wuyi University, Department of Mathematics and Computer, Fujian 354300, China;2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China;3. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, China;4. Changzhou Institute of Technology, Changzhou 213032, China;1. School of Computer and Information, Anhui Normal University, Wuhu 241002, China;2. School of Management, Guangzhou University, Guanghzou 510006, China;3. School of Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;1. Department of Mechanical Engineering, Urmia University, Urmia, Iran;2. Urmia University of Technology, Urmia, Iran;3. College of Engineering, Swansea University, Bay Campus, Fabian Way, Swansea, SA1 8EN United Kingdom;4. South Ural State University, Chelyabinsk, Russian Federation |
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| Abstract: | This paper deals with beams under static loads, in presence of multiple cracks with uncertain parameters. The crack is modelled as a linearly-elastic rotational spring and, following a non-probabilistic approach, both stiffness and position of the spring are taken as uncertain-but-bounded parameters.A novel approach is proposed to compute the bounds of the response. The key idea is a preliminary monotonicity test, which evaluates sensitivity functions of the beam response with respect to the separate variation of every uncertain parameter within the pertinent interval. Next, two alternative procedures calculate lower and upper bounds of the response. If the response is monotonic with respect to all the uncertain parameters, the bounds are calculated by a straightforward sensitivity-based method making use of the sensitivity functions built in the monotonicity test. In contrast, if the response is not monotonic with respect to even one parameter only, the bounds are evaluated via a global optimization technique. The presented approach applies for every response function and the implementation takes advantage of closed analytical forms for all response variables and related sensitivity functions.Numerical results prove efficiency and robustness of the approach, which provides very accurate bounds even for large uncertainties, avoiding the computational effort required by the vertex method and Monte Carlo simulation. |
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