Experimental and numerical analysis of container stack dynamics using a scaled model test Vinicius Aguiar de Souza n , Levent Kirkayak, Katsuyuki Suzuki, Hideyuki Ando, Hidetoshi Sueoka Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa no Ha 5-1-5, Chiba 277-8568, Japan article info Article history: Received 17 January 2011 Accepted 8 October 2011 Editor-in-Chief: A.I. Incecik Available online 3 December 2011 Keywords: Container scaled model Shaking table testing Finite element analysis Froude scaling Container stack dynamics abstract This paper describes an approach to simulate a seven-tier stack consisting of scaled model of a 20 ft ISO freight container and its linking connectors, denominated twist locks, subjected to dynamical load induced by its base. The physical (dimensions, mass, and moments of inertia) and structural (longitudinal, transversal and torsional stiffness) characteristics of the scaled models were decided based on two dimensionless numbers: ratios between gravity force and inertia force, and elastic force divided by inertia force, through experimental and numerical analysis. A series of experiments with controlled parameters were performed using a shaking table test to understand the effects of each variable in the container stack dynamics and present enough data to validate the numerical model. The results of this study indicate that the numerical model built is a promising tool for further study. Moreover, the model is able to predict conditions close to real situations faced by container stacks while storage on a ship’s deck. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Objectives and significance During the centuries that followed the Age of Discovery, when Europeans, notably Portugal and Spain, started to cruise the Seven Seas, the first navigators faced a dilemma that threatened their well being and the success of their enterprise: how to transport goods safely and efficiently across the oceans? Moreover, how to do it avoiding deterioration and consequent losses? The final answer for these questions was the creation of containers: a geometrically simple structure that facilitated maritime trans- portation. Nowadays, sea surface transportation accounts for 99% of all international transportation. Of this amount, the biggest part of the fleet corresponds to container ships. The use of containers to transport numerous manufactured goods is rela- tively new. Since this piece of equipment was invented in 1937 by Malcolm MacLean, a revolution was seen in maritime transporta- tion, with consequent improvements in efficacy and reliability. Despite its young age, containers became broadly popular and their use quickly spread around the globe. Levinson (2006) stated that nowadays, about 90% of all non-bulk cargo maritime trans- portation worldwide is performed employing containers stacked in container ships. However, such popularization brought some concerns: tight schedules allied a recent increase in the height of stacks carried on deck, coinciding with a substantial increase in the number of containers lost at sea. Podsada (2001) estimated that this number is something around 10 thousand each year, and although the total number involved is a matter of controversy among experts, this still represents a significant economic loss to the liner industry. Often, extreme sea conditions that eventually induce parametric rolling in the vessel are considered the most probable culprit behind those losses. However, one factor that is sometimes neglected is that with the new container ships becoming bigger, consequently their elastic behavior (whipping, heaving, etc.) induces higher values of acceleration on deck. Since this increase in container ships size, numerous cases of container losses have been reported. France et al. (2003) reported the loss of about 400 containers aboard of APL China in 1998, which is credited as the biggest cargo loss since the dawn of contain- erization. More recently, container ships: OOCL America (2000), Sea-Land Hawaii (2000), Sea-Land Pacific (2000), Xin Qing Dao (2004), Mondriann (2006), Saga Spray (2006), Jeppesen Maersk (2006), Ital Florida (2007), CMA CGM Dahlia (2008) just to mention a few, also lost containers at sea. Another factor that must be considered is the fact that the present regulation and norms for securing equipment are calcu- lated based on static loads with the relevant dynamic effects implicitly accounted through conservative, experience-calibrated, engineering approach, and despite its efficacy, it does not explicitly approach the dynamic nature of the conditions faced by containers during maritime transportation, which includes a range of distinct Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2011.10.004 n Corresponding author. Tel.: þ81 90 6509 0695. E-mail address: aguiar@nasl.t.u-tokyo.ac.jp (V. Aguiar de Souza). Ocean Engineering 39 (2012) 24–42