Ocean Engineering 187 (2019) 106188 0029-8018/© 2019 Elsevier Ltd. All rights reserved. Dimensional and similitude analysis of stiffened panels under longitudinal compression considering buckling behaviours Zhao Jun Song a , Ming Cai Xu a, b, * , Torgeir Moan c , Jin Pan d, e a School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, China b Collaborative Innovation Centre for Advanced Ship and Deep-Sea Exploration (CISSE), Wuhan, China c Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway d School of Transportation, Wuhan University of Technology, Wuhan, Hubei Province, China e Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Ministry of Education, Wuhan, China A R T I C L E INFO Keywords: Stiffened panel Ultimate strength Finite element method Ship Similitude analysis ABSTRACT The collapse behaviours of ship structures are usually validated by testing their small scale models. For thin-wall structures, the scale models obtained by complete geometrical similarity might not be economical or practical in test. The present study aims to figure out an approach to determine the dimensions of small scale models, which have similar collapse behaviours and load carrying capacity with full scale prototypes. For this purpose, the partial similarity methods are used to design the dimensions of scale stiffened panels considering the influence of collapse modes, which could be employed for the experiment in laboratory condition. The proposed approaches assume that three principle parameters dominate the buckling behaviours of stiffened panels, including plate, column and torsional slenderness, which are considered as determinate variables in the analyses of partial similarity methods. The stiffened panels under uniaxial longitudinal compression are simulated by finite element method. The dimensional and similitude analyses of stiffened panels with flanged profiles and flat bars are also performed. The ultimate strength and collapse mode are compared between the small and full scale models. From the comparison, the small scale stiffened panels designed by the partial similarity methods could reasonably represent the collapse behaviours of full scale models. 1. Introduction It’s vital to accurately calculate the ultimate compression capacity of stiffened panels to guarantee the safety of ships and human lives. Five types of methods are generally used to evaluate the ultimate strength of ship structures, including the simple closed-form formulations initiated by Caldwell (1965), simplified element methods such as idealized structural unit method (ISUM) (Ueda and Rashed, 1984), incremental-iterative method firstly proposed by Smith (1977) and employed in IACS CSR-H requirement (2014. Common struct, 2014), finite element (FE) method consisting of both implicit static analysis and explicit dynamic analysis (Xu et al., 2017a), and experimental methods (Xu and Guedes Soares, 2013). Since researchers normally can’t afford the time and financial costs to test actual ship structures, the small scale box girder, e.g. Gordo&Guedes Soares (Gordo and Guedes Soares, 2009) and Dow’s 1/3 scale frigate model (Dow, 1991), or stiffened panel models (Xu and Guedes Soares, 2012) have been frequently adopted to test the pre- and post-collapse behaviours as the simulation of actual ship structures. With respect to the geometrical range of selected stiffened panels to conduct compression tests or FE analyses, Paik et al. (Paik and Thayamballi, 2007) introduced four kinds of structural modelling, including: (a) one stiffener/span plate-stiffener combination model; (b) one stiffener/two spans plate-stiffener combination model; (c) multiple stiffeners/one span stiffened panel model between transverse frames; (d) multiple stiffeners/spans stiffened panel model. Generally if the rotational restraints along the transverse frames have ignorable in- fluences on the ultimate strength, the one-span models could be effective and available; otherwise two-span models are considered more realistic, since they can take account for the rotational restraints of two adjacent inter-frame stiffened panels along the transverse frames. For the purpose of simplifying analytical conditions and reducing computational re- sources, one stiffener stiffened plates were adopted to assess the ultimate compression capacity, such as Wang and Moan (1997). Xu et al. (2013a) adopted two bays/spans stiffened panels with the periodical and * Corresponding author. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan, China. E-mail address: xumc@163.com (M.C. Xu). Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng https://doi.org/10.1016/j.oceaneng.2019.106188 Received 12 November 2018; Received in revised form 10 May 2019; Accepted 4 July 2019