Advanced Materials Research Online: 2011-09-02 ISSN: 1662-8985, Vol. 339, pp 553-556 doi:10.4028/www.scientific.net/amr.339.553 2011 Trans Tech Publications, Switzerland The Simulation of Dropped Objects on the Offshore Structure Liping SUN 1,a, Gang MA 1,b, Chunyong NIE 2,c, Zihan WANG 1,d 1 Deepwater Engineering Research Center, Harbin Engineering Univ., Harbin, 150001, China 2 Texas A&M University, College Station, TX 77843, U.S.A. a Lsun@deepwatercenter.com, b gma@deepwatercenter.com, c mukdenson@163.com, d wangzihan@hrbeu.edu.cn Keywords: offshore structures, dropped objects, impact load, stiffened plate, falling process Abstract. Dropped objects accidents frequently happen during offshore structures operating. In this paper models of dropped objects on the platform were built to simulate the whole falling process by nonlinear FEM software. The shape of dropped objects, the horizontal velocity of dropped objects, dropped into water, different boundary conditions etc. were considered. The safety and feasibility of an approximate method that simplified a stiffened plate into an equivalent panel were also discussed. According to the simulation, it is found that the effective contact area, the velocity of the dropping objects and dropping position are the main factors to the safety of the structure. The simulation with the Fluid-Solid approach was also be verified to be more conservative. Based on the calculation results, it s proved that the simplified equivalent panel can not be substituted for the stiffened plate, because the girders and stiffeners on the plate promote the crashworthiness of the plate. Introduction Objects falling from lift equipment and superstructure of the platform frequently happens. The damage of dropped objects may have a bad influence on the platform s safety and serviceable life, even results in personal injury or death. According to statistics of British mobile platform accidents, the quantity of dropped objects accidents ranks the first among all kinds of offshore structure accidents, that is to say, dropped objects pose a great threaten to the safety of offshore structure. Based on previous data of dropped objects accidents (Wimpey Laboratories, I. C. Brown, S. H. Perry 1989), the response process of the platform was analyzed by using nonlinear finite element software. Establishment of Finite Element Model Referring to the real offshore platform structure, a typical Finite Element Model with stiffeners (DNV 2005) was built (Fig.1). Its dimension is 2412cm 804cm, thickness is 1.5cm, spacing between transverse girders is 201cm, spacing between longitudinal stiffener is 67cm, transverse girders are applied as T-bar and dimension 91.44 1.27/30.28 1.58mm, longitudinal stiffeners are applied as angle bar and dimension L25 9 1.5mm. The whole element model was consisted of shell unit (Zhou Guobao, Wang Lin 2007). Plastic kinematical Model was chosen as constitutive equation, boundary conditions of plates and girders were set to free support. Block and tubular were applied to be the dropped objects. Block body is a hollow cube of 200 200 200, whose thickness is 5cm, volume is 1.2 m 3 and density is 7700kg/m 3. Cubic object is 3m long, OD is 0.9m, thickness is 0.1m, volume is 0.7536m 3, quality is 5ton, and density is 6712.7kg/m 3. The falling height is 20m. Gravitational acceleration is 9.81m/s 2. Elastic modulus of dropped object is 2.0E11, poisson ratio is 0.27. The material parameters are listed in Table.1. Table.1 The parameters of the model material Cowper-Symonds Failure Yield modulus parameters strain Fig.1 The finite model of the platform deck 40 5 0.5 763[MPa] All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 130.203.136.75, Pennsylvania State University, University Park, USA-06/03/16,00:59:07)
554 Advanced Manufacturing Systems, ICMPMT 2011 Numerical Analysis of Dropped Objects Influences of Dropped Objects Shape and Falling Position. The shapes of the dropped objects are taken as cubic block and tubular respectively. Assuming the contact point was over the girders, cubic block dropping model and tubular dropping model were built respectively. Simulating the whole dropping process, and the response of the deck was analyzed. It can be known from the calculation results that the distribution of stress caused by tubular objects dropping is more concentrated than that caused by block objects, whereas the influence area caused by block objects dropping is much larger, maximum equivalent stress caused by tubular objects dropping focused on girders while block objects dropping had greater impact onstiffeners. Choose two nodes (A, C) on girder and two nodes (B, D) on stiffener respectively to analyze their displacement responses. Fig.2 The main nodes' displacement in Y Fig.3 The main nodes' displacement in Y direction & time curve (tube dropped) direction & time curve (block dropped) Fig.2 and Fig.3 show platform s dynamic response during dropping and after dropping. Only the first cycle was considered here, because the following cycles are determined by mode of vibration of offshore structure. One conclusion can be drawn from the simulation results: the displacement of contact points caused by tubular objects dropping was obviously bigger than that of block, and the displacement gradient was much bigger. Then the contact position was discussed. The tube model was applied to analyze, discussed three situations respectively: 1). contact happened on the girder'mid-span. 2). contact happened on the stiffener's mid-span. 3). contact happened on the middle of the plate. The simulation results show that the maximum stress is on the mid-span of the stiffener. The danger was bigger when dropping points is on the stiffener's mid span, because at this time all the striking force concentrated on stiffener whose strength was weaker than that of plate or girder. It can be seen from those three different dropping positions above, the plastic strain range was the biggest when objects dropped on the node of girder, but the maximum value of plastic strain was relatively smaller. Analyzing Objects Dropping In The Water. According to the dropping velocity theory, the difference between objects dropping in the air and those dropping in the water was accelerated velocity. The final accelerated velocity of objects was 0 when they dropped into water. The damage of the underwater structure caused by dropping was simulated here. There were a great many of stiffened plates in offshore structures, so we could still choose a typical stiffened plate to analyze. The tubular object was applied here, which weighed 5 tons, drop from the 20 meters high (end velocity is 19.8m/s). It showed from the simulation results that there was no difference for the stress distribution of objects between dropping in the water and dropping in the air, the maximum equivalent stress also appeared at the first time of collision, lying in the girder. It can be seen that the difference of the maximum equivalent stress was caused by gravitational acceleration. Except the stress magnitude, the deformation and the energy conversion were all similar with the analysis above, therefore, a conclusion can be drawn that the crash was weaker when objects dropped in the water and had an unserious impact on the platform. Initial Horizontal Velocity Influences On Dropping Response. Many dropping accidents happen because of lifting equipment holding objects unsteady. Generally in this case, the object has certain original horizontal velocity, so objects drop with initial velocity was discussed here. The block-shape objects was adopted on simulating the equipment dropped from the lifting equipment whose original horizontal velocity was 2m/s. The simulation results demonstrated that, stress development process of objects with original horizontal velocity was much longer than that of
Advanced Materials Research Vol. 339 555 having no horizontal velocity. The maximum von Mises stress is 5.516E8 Pa, which was smaller than that of with no horizontal velocity. Comprehensively judging from the several time steps of dropping process, the high stress lasted longer but fluctuation of stress was relatively small. After the contact happened, the value of the plastic deformation of the plate kept growing rapidly until the objects bounded. By comparing Fig.4 and Fig.5, it appears that the last time of the plastic deformation was longer when the object dropped with the horizontal velocity, which could make worse damage on the structure. Fig.4 Plastic deformation of the girder in Fig.5 Plastic deformation of the girder in bulkhead - time curve (with horizontal velocity) bulkhead - time curve without horizontal velocity Simplified Equivalent Panel Model. Appropriate equivalent equation of stiffened panel is as follows: n m h = h ' + FL i + FjB / LB i= 1 j= 1 (1) Where L is the length of the plate, B is the width of the plate, h' is the thickness of the plate, n, m are the number of the longitudinal and transverse stiffeners, F i, F j are Area of cross-section of the longitudinal and transverse stiffener. According to Eq.1, the equivalent thickness of the stiffened panel is 2.915cm. The tube model is adopted here as a dropped object, whose quality is 5 tons, and dropping height is 20 meters. The energy conversion, the value of the stress and strain, and the displacement of the nodes were all considered to verify the feasibility of the equivalent panel. Judging from the simulated results, the equivalent panel absorbed less energy than the actual stiffened plate. Fig.6 and Fig.7 show the process of kinetic energy conversion, when objects reached the minimum velocity, the equivalent plate had much more kinetic energy than that of stiffened plate, which means that equivalent panel has a great elastic deformation during the collision whereas plastic deformation is smaller. Fig.6 The system kinetic energy variable curve Fig.7 The system kinetic energy variable curve (the equivalent panel) (the plate with girder) Through the analysis, we can learn that the girders and stiffeners on the structure are important to the strength structure, after simplified into equivalent panel, it lost the features of original stress distribution. From the analysis, the strength of equivalent panel was bigger, but its plastic strain range was smaller, therefore, the energy absorbed by the plastic deformation was smaller, which means that it is easier to damage. So In the design and practical calculation, adopt the simplified equivalent panel model is not precise. Fig.8 is the typical nodes' displacement in Y direction (equivalent panel). Compared figure 8 with Fig.2, the nodes' displacement of equivalent panel in Y direction is twice bigger than that of actual stiffened plate. The equivalent panel's free vibration cycle is longer, and amplitude is bigger, which is consistent with previous results. The Influence of Boundary Condition. Changed plate's boundary condition into rigid fixed. The tubular objects dropping model was applied to analyze. Make a comparison with the previous results. Several key elements were selected respectively and drew the stress curve (see Fig.9 and Fig.10). Element 320 was on the flange of the girder, element 943 was on the stiffener, element 325 was on the web plate of the girder.
556 Advanced Manufacturing Systems, ICMPMT 2011 Fig.8 The typical nodes displacement in Y direction time curve (equivalent plate) Fig.9 The main elements stress curve(the plate was rigid fixed) Fig.10 The main elements stress curve(the plates was free supported) Compared Fig.9 with Fig.10, every key elements' stress had the similar varying tendency under two boundary conditions. So the boundary condition of the plate has less influence on the collision of dropping, because the high-stress area converges in the local contact area. In fact, girders played an important role on resisting striking force. Summary Stiffened plate's responses to dropping objects were simulated by utilization of nonlinear finite element software in this paper. From the results, the following conclusions could be drawn. 1). Two different shapes of dropping objects were compared. The stress in the platform structure caused by tubular objects dropping was bigger than that of block dropping while the area of plastic deformation of former was smaller, which implies that the partial damage caused by object dropping was much more severe. 2). In comparison to the influence of contact positions, the plastic strain of platform structure was bigger when the objects dropped onto the stiffeners, and the range of high-strain however was relatively small. 3). The maximum equivalent stress in the platform caused by dropping objects with initial horizontal velocity was smaller than that without initial horizontal velocity, however, the high stress lasted longer. 4). The results effects caused by different boundary conditions were discussed and it could generate bigger plastic deformation if under the latter boundary condition. In this case, it's results show relatively conservative. 5) One simplified equivalent panel was analyzed. Compared with stiffened plate s model, the stress in equivalent panel model was smaller while the deformation is larger and mainly consists of elastic deformation. Besides, its amplitude of free vibration was bigger whereas the cycle is shorter. On the whole, it is unreliable to simulate platform response with simplified equivalent panel instead of stiffened plate. Acknowledgement Thanks for 111 projects foundation (Grant No.B07019) from State Administration of Foreign Experts Affairs of China and Ministry of Education of China. This paper is also supported by the Fundamental Research Funds for the Central Universities. References [1] W. Laboratories, I. C. Brown, S. H. Perry:The assessment of impact damage caused by dropped objects on concrete offshore structures, Concrete in the oceans technical report No.17 (1989). [2] DNV:Offshore standard DNV-OS-A101, Safety principles and arrangements, (10/2005). [3] Zhou Guobao, Wang Lin:Offshore platform's numerical simulation study under impact loading, Zhenjiang, Jiangsu Technology University. (In Chinese)(2007). [4] Longuet-Higgins, MS, and Fox, MJH:Theory of the Almost Highest Wave: the Inner Solution, J Fluid Mech, Vol 80, pp 721-41. (1977). [5] Smith, DE: Dynamics of Ice Cover Interacting with Ocean and Atmosphere, Int. J. Offshore and Polar Eng, ISOPE, Vol 3, No 1, pp 43-50. (1992).
Advanced Manufacturing Systems, ICMPMT 2011 10.4028/www.scientific.net/AMR.339 The Simulation of Dropped Objects on the Offshore Structure 10.4028/www.scientific.net/AMR.339.553 DOI References [4] Longuet-Higgins, MS, and Fox, MJH: Theory of the Almost Highest Wave: the Inner Solution, J Fluid Mech, Vol 80, pp.721-41. (1977). 10.1017/S0022112077002444