A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision

Transcription

1 (Read at the Autumn Meeting of The Society of Naval Architects of Japan, November, 1984) A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision by Hisashi Ito*, Member Kiyoshi Kondo*, Member Nobutoshi Yoshimura*, Member Minoru Kawashima**, Member Satoshi Yamamoto***, Member Summary The strength of ship structures in collision is an important matter in terms of saving life, preventing pollution and from an economic point of view, especially in the case of hazardous cargo carriers, oil tankers and so on. So far, several analysis methods or formulae have been presented to estimate the collision strength of such ships. However, there are few papers in which the accuracy of the methods have been verified. In this paper, the collision strength of a typical double hulled structure was examined. The types of collisions were classified into five groups from a geometric view point between a colliding bow and a hull. Two kinds of experiment (which were considered to be more critical than others among those five groups), were carried out using large scale models. The first was an experiment in which a stem collided against the ship's side and in the other a bulbous bow collided against it. In both cases, the bow models were assumed to be rigid. A simplified method to analyse the damage of double hulled structures in collision was developed on the basis of the results from the experiments. As far as this method. is concerned, a double hulled structure is considered to consist of three main structural members, the side shell, trans web frames and side stringers. The side shell is modelled into plastic membrane plates, and trans webs and side stringers are assumed to support the side shell rigidly and buckle when critical load is imposed. The method was formulated in matrix form, triangular membrane elements and buckling elements are used to model a double hulled structure. The accuracy of the analysis method was then examined by comparing the calculated values with the experimental ones. From these, a strong correlation emerged. I. Introduction The strength of ship structures in collisions or stranding used to be a subject of study mainly when examining the safety of nuclear ships. Recently, however, it has become a very important matter especially in terms of preventing pollution and other such disasters, especially as the number of hazardous cargo carriers has increased and numerous accidents involving oil tankers have been reported. In the collision of such types of ships, investigation into minor collisions is most important to guarantee the * Tsu Research Laboratories, Nippon Kokan K.K. ** Basic Ship Design Department, Nippon Kokan K.K. *** Ship & Offshore Unit Design Department, Nippon Kokan K.K. prevention of cargo leakage ; very little research has been done on the effects of minor collisions in contrast to the case of nuclear ships major collisions have been more thoroughly investigated.1) `4) This paper is confined to minor collisions involving ships with double hulled structures. It examines the safety of hazardous cargo carriers and oil tankers in collision. So far, several papers have been written on ship collisions. References 5)- 13) deal with the minor collisions which have a connection with the subject of this paper. These papers are divided into two groups according to the kind of analysis method. The first group5) `8) adopts the empirical method proposed by Minorsky or variations of it. The other group9) `13) of papers have their own methods of analysis. However, there are few papers9),10) in which the accuracy of their methods was verified in comparison to experimental or full scale data,

2 Journal of The Society of Naval Architects of Japan, Vol. 156 as far as the authors know. In this paper, the damage to double hulled structure was examined experimentally using large scale models. Next, an analysis method was proposed which was based on the experiment mentioned above. Lastly, the accuracy of the analysis was examined by comparing the calculated and experimental values, and these showed a strong correlation. 2. Double hulled structure model tests 2.1 Summary The nature of ship collisions are so complicated that it is necessary to examine them in broad terms. In general there are numerous categories of collisions. Therefore, we calssified the types of collisions into five groups as indicated in Fig. 1, from a geometric view point between the two ships. Exact collision type actually depends on the size, loading conditions, and motion of the two ships involved. Two types may happen simultaneously. The purpose of this study was to estimate how double hulled structures are damaged in each type of collision. Some restrictions were imposed Type (a) Type (b) Type (c) Type (d) Type (e) Fig. 1 Classification of collision by type in order to simplify the experiment, analysis and collision strength estimation. The following con ditions were assumed :- (1) The bow of the colliding ship was rigid. (2) One ship collided against the other ship perpendicular to the side shell. (3) The double hulled structure was damaged in the vicinity of the point of collision. It did not collapse in its entirety. (4) The damage was not large in scale. Only that type of damage in which the bow reached the inner hull (but which was not damaged) was considered. Generally, Type (a), (b), (c) are considered to be more critical than others in Fig. 1. In this paper, Type (b) and (c) were selected to be studied. The experiments corresponding to these two types were carried out. 2.2 Test models and test conditions Two types of experiments were carried out, in which a typical double hulled structure was ex amined. They are shown in Fig. 2. The first was a test in which a stem collided against the ship's side and in the other a bulbous bow collided against it. Henceforth, we will refer to them as the "stem test" and the "bulb test", respectively The double hulled structure models used in the tests were partial structure models as shown in Fig. 2. The details of one model used in the stem test is given in Fig. 3, and the other is simi lar to it. The models consisted of the side shell the inner hull, the upper deck, the bilge shell the transverse webs, the side stringers and the stiffeners. Whereas the longitudinals were not considered to be independent elements from the shells to which they were attached, the thick ness of the plates was increased to compensate for the effect of the longitudinals. The scantlings of the members were approximately proportional to those used in an ordinary double hulled structure. The material used in their construction was mainly JIS SS41 mild steel. The thickness of plates used in the models were 1.2, 1.6, 2.3 and 3.2 mm. Table 1 shows their tensile test resulti Fig. 2 Two types of experiments

3 A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision Table 1 Tensile test results of material used in the ship side models (a) Stern indenter (b) Bulb indenter Fig. 4 Shape of rigid bow indenters Notes 1. Test pieces are JIS No.5. The gauge length is 50mm. 2. All data listed are the mean value of every 4 test pieces. 3. Eu means the strain at maximum nominal stress. 4. Lb means the breaking strain kg/mm2 = 9.80 MPa ( a) Stem test ( b) Bulb test Fig. 5 Loading conditions Fig. 3 Ship side model for the stem test (the unit is mm) The construction method used was continuous staggered intermittent, fillet welding. The leg lengths of the welding were kept as small as pos- are illustrated in Fig. 5. The double hulled structure models were considered to be clamped at all edges. The points of collision were set along the center line of the two transverse bulkheads, and were set along the center line of the two side stringers. The bow models were pushed out to the hull models gradually by a hydraulic jack. Then measurements were taken on the load, penetration, deformation and strain. 2.3 The test results The stem test Fig. 6 shows the load and penetration relationship obtained from the test. The numbers in the figure indicate the measuring sequence. The state of the damage after the test is shown in Photo 1. The details of the destruction are out- sible. All edges of both models were stiffened by a very rigid frame. The two bow indenters, the stein indenter and the bulb indenter, were cast to the shapes shown in Fig. 4. Their geometry was determined by NKK's experience here:- In the stem indenter the stem angle: ƒæ and the radius of the upper deck circle : R were kept constant. The radius of the stem wedge tip : r was equal to 2-3 mm. In the bulb indenter, the profile of the center line section was parabolic. The radius of the circle in the water line section: R and the water line incident angle: ƒ were constant. The stern test and the bulb test were carried out once, in each case. The loading conditions Fig. 6 Load-penetration curve of the stem test

4 286 Photo Journal 1 of The Society of Naval Architects The state of damage to the ship side model after the experiment Fig. of Japan, 8 Vol. 156 Load-penetration test curve of the bulb (Stem test) Fig. 7 Damage characteristics side model (stem test) of the ship lined as follows (see Fig. 7) :The stem touched the web (a) at P2, and the web (b) at P3. These webs deformed, buckled and further deformed as a direct action of the stem. The actual loading point was a little left of the planned point. The deformed area of the side shell consisted of one panel surrounded by webs and stringers at the start and it grew to three panels by the end of P3. The deformation of the whole structure surrounding the panels was very small. During P4 to P5 cusps appeared on the side shell at each location of the stiffener on the web (a) and (b). Just before P6 a loud noise was heard and the load was instantly decreased. The side shell ruptured ((c)) along the upper deck of the stem over an area of more than one web frame space. The web plates also ruptured. From P8 to P14, the stem continued to penetrate while the structures outside of the penetration area hardly deformed at all. At P15 the crack on the side shell changed its direction downwards ((d)). At P16 the lower part of the stem touched the side stringer (e), which was destroyed as a direct action of the stem. At about this time, the stem was considered to have Photo 2 The state of damage to the ship side model after the experiment (Bulb test) reached the inner hull and the load was in creased substantially. The side shell stopped deforming at this point in time. The inner hull had hardly deformed until P15. However, after P15 or P16 when the step reached the inner hull, the deformation clearly showeda wedgeshapeassumingtheshapeoftit stem tip The bulb test Fig. 8 shows the load and penetration relation ship obtained from the test. The state of the damage after the test is shown in Photo. 2. The characteristics of the destruction were as follows (see Fig. 9) :Only the side shell of the area of 1 web frame space by 1 stringer space carrying the load direct ly, was dented until P4. The webs (a) and (b) the loading point collapsed at P4 and P5 respectively. The deformed area of the side shell spread to the area of the 3 web spaces by 1 stringer space. The side stringer (c) just above the loading point was depressed. At P7 the wave pattern deformation occured in the bilge sgell

5 A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision 287 Fig. 10 Membrane force Fig. 9 Damage characteristics of the ship side model (Bulb test) as the stringer a still did not deform. At P10 the four corners of the panel carrying the load directly, began to collapse. Just after P12 a loud. noise was heard and the load was instantly decreased. After that we retracted the indenter, and we found the side shell rupture at the loading point running in a vertical direction (T). At P14 the indenter appeared to have touched the side stringer Z. During P15 to P16 the load and deformation did not change, while the penetration of the indenter actually increased. The load was then increased again at P16. The indenter was thought to have touched the inner hull. The inner hull had hardly deformed until P9. During P10 to P15 the inner hull deformation increased to a maximum of 38 mm in the area beneath the loading point. At P17 the inner hull deformation clearly showed a bulb shape assuming the shape of the indenter. By the end of test, the inner hull had still not ruptured. 3. The method of analysis A method of analysis was developed based on the results of the experiments mentioned before. This method was aimed at obtaining the overall behaviour of double hulled structure in collision efficiently rather than carrying out detailed analysis by a comprehensive approach, for example by a finite element method. Therefore, many kinds of simplification and approximation were employed in the analysis as is outlined in the following sections. 3.1 Idealization of the structure A double hulled structure is considered to consist of three main structural members, that is a side shell, trans web frames and side stringers. The side shell is modelled into membrane plates which do not have bending rigidity. Trans webs and side stringers are assumed to support the side shell rigidly and buckle when critical load is imposed. The inner hull plating is assumed not to deform in any direction. The spacing of webs and stringers is assumed to be constant. The membrane model of the side shell is assumed to be orthotropic with constant tensile forces as illustrated in Fig. 10. The membrane forces are given as follows : q= the membrane force per unit breadth ay= the yield stress of the side shell t= the equivalent thickness of the membrane X, Y indicate longitudinal and vertical directions, respectively The equivalent thickness tx,, is calculated to compensate for the effect of the longitudinals and stiffeners on the side shell. According to Mc- Dermott et al.9), the behaviour of longitudinals are divided into two phases; in the first phase, they behave as bending elements until lateral buckling happens, then the second phase begins they behave as tensile elements. Usually the lateral buckling occurs at such an early stage that the contribution of phase-1 to the total amount of absorbed energy can be considered to be negligible. That is the reason why longitudinals and stiffeners are ignored, but the thickness of the side shell has to be increased to compensate for the effect of phase-2 in each direction of the longitudinals and the stiffeners. Next, the behaviour of trans webs and side stringers are idealized as follows :- Generally, their buckling behaviour is illustrated as in Fig. 11 (a). When large scale damage occurs as in a collision, the amount of plastic deformation is so much greater than that of elas- Fig. 11 Post-buckling behaviour

6 Journal of The Society of Naval Architects of Japan, Vol. 156 tic deformation that the elasticity can well be ignored. Therefore, the elements can be idealized as rigid-plastic bodies. Their P-6 curves are illustrated as in Fig. 11 (b). The precise value of Pmax in the curve cannot be obtained easily, so approximate methods are used according to Refs 15)-18). In short, the failure patterns of trans webs and side stringers are assumed and the minimum value of ultimate loads calculated in each pattern is selected as the Pmax value. The failure patterns are divided into groups of :- total failure in a stiffened plate, failure of panels between stiffeners caused by compression, shear failure, etc. An evaluation of the bifurcation load Po. is not necessary. 3.2 The analysis of the damage development The damage develops as a rigid indenter penetrates into the side shell plating which is idealized as plastic membranes supported by webs and girders as described in the preceding section. The principle of stationary potential energy is adopted to analyse the development of damage every structural member is assumed to be a rigidplastic body and the strain reversal ignored. It is shown as follows :- effect is The total potential energy of a deformed structure : II is written as in Eq. (2) :- Um= the strain energy of the side shell membranes UB = the energy required to destroy the webs and girders W= the work done by external forces displacements is specified, the remaining variables including the external force and displacements can be evaluated. Next, the strain energy Um and the destruction energy UB are evaluated as follows :- According to Eq. (1) and the assumption that the surrounding boundary of a membrane does not displace in the in-plane direction, the strain energy Um resulting from the extension of membranes is expressed as follows :- A= the area of all membranes w(x, Y) = the deflection function of membranes qx, = the membrane forces per unit breadth in the direction of X and Y The deflection function ƒö(x, Y) has to be determined before the strain energy UM is calculated. In the present analysis, ƒö(x, Y) is approximated to consist of triangular planes as shown in Fig. 14 (a) for example a con- centrated force is acting on the middle of the center panel. The destruction energy, UB, of webs and girders can be obtained as follows :- There are various types of destruction as shown in Fig. 12. In this analysis, the types of destruction as shown in the diagram are examined. UB is equivalent to the work done by the post-buckl- ing reaction with respect to the displacement in the destruction, as shown in Fig. 13. Then UB is given in Eq. (6) :- It is assumed that UM and UB are expressed in terms of the displacements (uo, U1, c, u _v) of certain selected points and W is expressed by such displacements and external forces (Po, P1, c, FN) applied to those points acting in the same direction as the displacements (uo, ul, c, u,y). Then Eq. (3) is derived from the stationary condition of the total potential energy: Eq. (3) gives the relationship between the external forces (Po, P1, c PI) and the corresponding Fig. 12 Types of destruction in webs and girders displacements (uo, ui, c ux). When a single force P acts on the point zto is defined, Eq. (3) leads to Eq. (4) : Eq. (4) are N+ 1 simultaneous equations involving an external force P and displacements zto u as variables and the total number of variables is N+2. Therefore, if the value of any one of the Fig. 13 Destruction energy (UB) of webs and girders

7 A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision development process mentioned above. When a rigid bow indenter meets a web or a girder during the course of loading, the area of contact deforms according to the shape of the indenter. This is responsible for the constraints of the displacement coordinates. In general, the number of independent node displacements is reduced by the number of constraints among Fig. 14 The development of damage in the side shell them. 3.3 Membrane rupture of the side shell plating and damage development after the rupture Cracks appear in the side shell during the course of the damage development. In general, cracks are initiated at the place of maximum strain and stretch gradually until static equilibrium conditions are not satisfied, that is, a sudden rupture happens and the load decreases substantially. This process is verified in many kinds of experiments. The analysis of crack propagation, how-- ever, is so complex that a simplification is em- Fig. 15 The load-deformation relationship during the damage development stage ployed : the rupture happens as soon as an assummed condition is satisfied, and the process of crack propagation is ignored. The membrane rupture of the side shell plating has a considerable effect on the amount of the energy which may be absorbed by a double hulled Q= the maximum load of webs or girders B= the coefficient to determine the reduction rate of the post-buckling reaction u= the displacement in the destruction Thus, the total potential energy can be obtained by Eq. (2),(5) and (6). And the damage development calculation is obtained as follows :- A part of a side shell which is supported by webs and girders is chosen to demonstrate the procedure as shown in Fig. 14. When a concentrated load acts on a panel of the side shell, only the panel which carries the load deforms so long as the surrounding webs and girders are not damaged (Fig. 14 (a)). As the load is increased, the deformation grows and some of the webs and girders begin to buckle. If the girder just below the panel buckles for example, the damage develops from Fig. 14 (a) to Fig. 14 (b). Assuming all the possibilities of the damage development process, the load which is responsible for each sequence in the damage development is calculated. From these calculations, we know that the actual path of the damage development is the one in which the smallest value of the load increment is necessary to cause it. Thus, a load and displacement curve can be obtained as shown in Fig. 15 from the damage development stage. The damage development calculation concerning the side shell plating can be performed by repeating the single damage structure in collision. The quantitative condition for a membrane rupture is so difficult to determine theoretically that most conditions proposed. in the papers of the past were obtained experi- mentally. In this analysis, we depend on the results of past studies and assume the conditions for a membrane rupture as follows :- (i) the membrane ruptures at the contact point with the stem top (This condition is available for R/t 5/2ƒÃu). the maximum principal strain at the contact point the radius of curvature of the stem top in the direction of ei the thickness of side shell plating the strain when the maximum load is reached in a tensile test (ii) the membrane rupture in the side shell is caused by uniform extension (a) When the deformation is limited to within an area of one web frame space by one girder space, the condition is expressed as follows (Fig. 16 (a)) :- the maximum of ect) and ƒã2, ƒãw and are the maximum principal strains in the areas shown in Fig. 16 (a)

8 Journal of The Society of Naval Architects of Japan, Vol. 156 Fig. 16 Illustration of e (b) When the deformation stretches over more than two web frame or girder spaces, the condition is expressed as follows (Fig. 16 (b)) :- the maximum of ċ1 and ċ2, ċ1 and are the maximum principal strains averaged over the areas shown in Fig. 16 (b) The side shell is assumed to rupture as soon as one of the conditions in Eq. (7-1)-(7-3) is satisfied. The damage development analysis after the rupture of the side shell is as follows :- The tension in the side shell is assumed to vanish as soon as it ruptures. Therefore, only webs and girders act against the indentation of a bow after the rupture happens. And the deformation at the time of rupture remains in the webs and girders, because they are assummed to be rigid plastic bodies. When the bow meets one of the webs or girders, its deformation increases, corresponding to the indentation made by the bow. The webs and girders which are in contact with the bow at the time of rupture continue to deform further. Thus, a relationship between the load and the amount of bow indentation after the rupture of the side shell can be obtained easily using the geometrical relationship between the shape of bow and the deformation of structural members at the time of the rupture. For example, the deformation at the moment of rupture is shown in Fig. 17 (a). In this case, the value of the load reaches zero at the time of the rupture. When the bow penetrates further by the value of Asi, it meets the web WI, and it meets the web W2 if it penetrates further by the value of 482. The reaction forces by the webs are calculated by the afore-mentioned method (Fig. 13). The result of the analysis is illustrated in Fig. 17 (b). 4. The formulation of a numerical method The analysis method presented in chapter 3 adopts the principle of stationary potential energy as long as the side shell does not rupture. In this case, the potential energy is presented by a polynomial of nodal displacements whose power doesn't exceed the second order. Therefore, the method can be expressed in matrix form like the finite element method. 4.1 Equation of equilibrium The total potential energy, H, can be expressed as in Eq. (8). t U) =the node displacement vector [A]=the total membrane stiffness matrix [Q) =the destruction load vector of webs and girders [B] = the total post-buckling stiffness matrix tp) = the external load vector (a ) The deformation of the side shell at the time of rupture (b) The relationship between the load and the amount of indentation Fig. 17 The damage analysis after the rupture of the side shell

9 A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision Eq. (9) is derived from the stationary of the total potential energy H. conditions Eq. (9) is a general expression for the equation of equilibrium. In this equation, matrix [A] is calculated by summing up the membrane element stiffness matrix [K] (see 4.2) as shown in Eq. (10). triangle ABC after deformation. as in Eq. (11). tn) is expressed S=the area of triangle ABC before deformation (increase of the area due to deformation is ignored) 4.2 The stiffness matrix of a triangular membrane element A triangular membrane element represented by three nodes A, B and C on the X- Y plane is shown in Fig. 18. The Z axis is perpendicular to the X-Y plane. OXYZ is the rectangular cartesian coordinate system. The location of three nodes A, B and C before deformation are expressed as A (X, Y, 0), B (X, Y, 0) and C (X, Y, 0). Each node is assumed to displace only in the Z direction, that is, each node has a single degree of freedom. They are written as ua, ub and uc according to the points. So, the stiffness matrix of this triangular membrane element is given as follows :- (n} denotes the unit vector normal to the qx, qy denote the membrane tensile forces per unit breadth in X and Y directions respectively, and the membrane strain energy : Ue accumulated in the element is given as in Eq. (12). Therefore, the total potential energy of the system: [le is expressed as shown in Eq. (13). node force vector From the principle of stationary.potential energy, Eq. (14) is derived as follows :- Fig. 18 Triangular membrane element [K] is the stiffness matrix of a triangular membrane element. [K] matrix is shown in the components as in Eq. (15). 4.3 The treatment of linear constraint Certain constraints among the node displacements exist when a rigid bow indents a side structure. Taking them into account, Eq. (9) is modified as follows :- For practical reasons, the linear constraint quations can be expressed by one dependent variable and two independent variables as in Eq. (16).

10 Journal of The Society of Naval Architects of Japan, Vol. 156 Eq. (16) is rewritten in matrix form as in Eq. (17) which is connected with some other nodes by means of constraint conditions. From Eq. (22), if a displacement of a certain node is given, an external force and other node displacements can be calculated as follows :- Furthermore, refering to Eq. (17), the node The force vector (F') is expressed as in Eq. (23). displacement vector {U} is rewritten as in Eq. (18). =a node displacement vector which is given by eliminating uk, UL, um from [I] =the unit matrix In the same manner that (UI) in Eq. (18) was obtained, by changing the order of components of matrix [D] and vector (F), the general equation of equilibrium can be rewritten as shown in Eq. (19). From [D'] {U'P} (ĉu) ĉil is Kronecker's delta, Eq. (26) is derived. Multiplying Eq. (19) by a variation vector from the left hand side, we get:- Furthermore letting um denote the coordinate whose value is given, a scalar equation (27) can be obtained from Eq. (24) and (25). According to Eq. (18), 8 ĉ{ U1}F= ĉ{u'}t[Ď]t Thus Eq. (20) leads on to Eq. (21). Consequently, an equation of equilibrium (in which components related to the variable UK are eliminated), is derived as shown in Eq. (22). Eq. (22) gives the relationship among the external loads and displacements when a linear constraint condition Eq. (16) is taken into account. If there are several such conditions, the same elimination process has to be repeated. 4.4 The solution of the equation of equilibrium. In this section, a single external force is assumed to act on only one node indicated as ui as shown in Eq. (28). = (F) and (Q) vectors in which components are rearranged in the same order as {U1} In the same manner, the displacement coordinate vector ( U') is divided into two components which are derived from (P1') and (Q*) denotes the displacement vector derived from the unit force, and {U'P} is expressed as in Eq. (25). Pi is the value of external force applied on the. point ui is defined. u'pm u'qm denotes the components corresponding to um in each. From Eq. (27), the external force P1 is calculated Where the value of u= is known, and u;,? and can be calculated by Eq. (26). Therefore, the right side of Eq. (28) can be obtained. Finally, other displacements are calculated as in Eq. (29). for independent for dependent displacements displacements

11 A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision 5. The comparison of the experimental results with the calculated results Numerical calculations corresponding to the stem test and the bulb test were done by means of the analysis method presented in chapters 3 and The stem test analysis It was observed in the experiment that the trans webs on both sides of the loaded panel did not collapse in their entirety but each stiffener on the webs and the effective breadth of web plates collapsed separately as a column (Fig. 19). In this analysis, therefore, two trans webs beside the loading point were modelled into a group of such independent columns. The effective breadth of the trans web plates was calculated by Faulkner's formula,17) and the collapse load of the columns was calculated by multiplying the total sectional area of a column by the yield stress. The action of these columns after buckling was assumed to be similar to that on the trans webs and the side stringers. The membrane force of the side shell was calculated by the method mentioned in 3.1. And the initial deflection which was equal to each thickness of plate was taken into account for calculating the destruction load of the trans webs, the side stringers and the columns, because there was a considerable initial deflection in the side model. Fig. 20 shows the mesh pattern of the side shell which was used in the damage development calculation. The calculation was done by means of a computer program as explained in chapter 4. In this figure, the loading point was 30 mm left of center because in the experiment, the load actually acted on such a point. The calculations were done assuming two different possibilities (see Fig. 21) ; i.e., Calculation (1)Assuming that the post-buckling reaction forces of the trans webs, columns, side stringers were constant, and Calculation (2)-.Assuming that the post-buckling reaction forces of them were reduced linearly to zero value at the time when they collapsed up to their depth. Fig. 22 shows the relationship between the calculated results and the experimental one. It shows that calculation (1) correlates to the experimental result, while calculation (2) underestimates the load after the rupture of the side shell. According to calculations (1)and (2), we can imagine the damage of the ship side model developed in the sequence as shown below :- ( 1 ) The tip of the stem makes contact with the side shell at node 46 (noted N46 henceforth). ( 2 ) At N 17, the stem makes contact with the trans web. After that, the column at N17 is crushed. Fig. 20 The mesh pattern of the side shell for the calculation of damage development (Stem test) Fig. 19 Columns in the trans webs Fig. 21 Calculation (1), (2)

12 Journal of The Society of Naval Architects of Japan, Vol. 156 ( 3 ) The columns at N16 and N18 collapse. ( 4 ) At N28, the stem makes contact with the trans web. After that, N28 is crushed. ( 5 ) The columns at N27 and N29 collapse. ( 6 ) The columns at N15 and N19 collapse. ( 7 ) The columns at N14 and N20 collapse. ( 8 ) The columns at N26 and N30 collapse. ( 9 ) The columns at N25 and N31 collapse. (10) At N17, the side shell ruptures along the deck line of the stem, and the load decreases instantly. Since the membrane force of the side shell has a zero value, only the columns at N17 and N28 which have been crushed directly by the stem, react against it. (11) The stem crushes the columns directly at N16, N27, N15, and N26, and the side stringer at N45 in this order. (12) The stem reaches the inner hull plate. The details from the damage development sequence as described above were not recorded in the test but were assumed from the calculations. They are seen to correlate closely with Photo 1 which shows the state of the damage after the experiment. The absorbed energy-penetration curves are shown in Fig. 23. It shows a very strong correlation between the calculation and the experiment. 5.2 The bulb test analysis Fig. 24 shows the mesh pattern of the side shell. The loading point was 30 mm right of center in this case. The trans webs on both sides of the loaded panel were assumed to collapse in their entirety. The tension of the side shell and the destruction loads of the trans webs, the side stringers and the bilge webs were calculated by means of the method explained in 3.1, the initial deflections were taken into account as in 5.1. Fig. 25 shows the relationship between the The numbers indicate each nodal point number. Only the longitudinal component of membrane force ir the bilge part was taken into account. Fig. 22 The load-penetration relationship between the calculations and the experiment (Stem test) Fig. 24 The mesh pattern of the side shell for the calculation of damage de velopment (Bulb test) Fig. 23 The energy-penetration relationship between the calculation and the experiment (Stem test) Fig. 25 The load-penetration relationship between the calculations and the experiment (Bulb test)

13 A Simplified Method to Analyse the Strength of Double Hulled Structures in Collision Fig. 26 The energy-penetration relationship between the calculation and the experiment (Bulb test) calculated results and the experimental one. Calculations (1) and (2) adopt the same assumptions as those in 5.1. It shows that the calculated values and experimental ones correlate well except in the range of the small penetration. Calculations (1) and (2) gave almost the same results because the destruction of the trans webs and the side stringers was small. According to calculations (1) and (2), we can imagine the damage of the ship side model developed in the sequence as shown below :- (1) The top of the bulb makes contact with the side shell at N32. (2) The trans web at N16 collapses. (3) The side stringer at N21 collapses. (4) The trans web at N15 collpses. (5) The side stringer at N10 collapses. (6) The side shell ruptures, running in a vertical direction at the loading point N32. (7) The bulb crushes the side stringer at N10. In the case of calculation(2), (6) and (7) happen almost simultaneously. (8) The bulb crushes the side stringer at N21. (9) The bulb reaches the inner hull plate. The details on the damage development sequence as described above are seen to correlate closely with Photo 2. The absorbed energy-penetration curves are shown in Fig. 26. Again, it shows a very strong correlation between the calculation and the experiment. From the results of the above two analyses, it is considered that the analysis method presented in this paper is very useful both in calculating the load-penetration relationship and in examining other characteristics of the damage done to a double hulled structure in collision. As far as these calculations are concerned, calculation (1) is recommended. 6. Conclusion Static destruction tests were carried out using large scale detailed models of a side structure representative of those used in double hulled ships. And the destruction behaviour of a double hulled structure was investigated when it was struck by a bow stem or a bulb. Next, an analytical approach was developed using the experimental results. The main conclusions are as follows :- (1) When a bow collides against the side structure of a double hulled ship, the side shell can be regarded as a plastic membrane, and the trans webs as well as side stringers can be regarded as buckling members which support the plastic membrane, in the case of a minor collision. (2) The inner hull scarcely deforms during the damage process until that moment when it is actually struck by the bow. (3) A simplified methof of analysis was formulated from which the relationship between the amount of destruction and the destruction load in double hulled structures in collision can be calculated. Acknowledgement The authors wish to express their deep appreciation to Dr. H. Nagasawa, Director of the Ship Research Institute and Mr. K. Arita, Chief of Strength Section of the same institute for their valuable advice. References 1) Minorsky, VU.: REPORT ON SHIP COL- LISION STUDY PRESENT SITUATION SURVEY, George G. Sharp, Inc. Report No. MA-RD , (1975). 2) Jones, N.: ON THE COLLISION PRO- TECTION OF SHIPS, Nuclear Engineering and Design 38, (1976). 3) CRITICAL EVALUATION OF LOW- NERGY SHIP COLLISION-DAMAGE THEORIES AND DESIGN METHODO- LOGIES VOLUME I, VOLUME II, SSC- 284, SSC-285, (1979). 4) Woisin, G.: Konstruktion gegen Kollisionsauswirkungen, Schiff & Hafen, (1979). 5) Haywood, J. H.: A NOTE ON COLLI- SION ESTIMATES FOR LNG CAR- RIERS, NCRE Report (1971). 6) On the Prevention of Hazards of Ship Carrying Dangerous Cargoes, Assoc. of Prevention of Maritime Casualty of Japan, (1973). 7) Greuner, H. P., BOckenhauer, M.: STUD- IES OF THE RESISTANCE OF LNG CARRIERS TO COLLISIONS, LNG-6, (1980).

14 Journal of The Society of Naval Architects of Japan, Vol ) Glasfeld, R. D.: SOME ASPECTS OF LNG SHIP SAFETY AND RELIABILI- TY, GASTECH 79, (1979). 9) McDermott, J. F. et al.: Tanker Structural Analysis for Minor Collisions, Trans. SNAME paper No. 10, (1974). 10) Ando, N., Arita, K.: A study on the Strength of Double-Hull Structures in Collision (Part 1 Fracture Mechanism in Static Failure Test, J. Soc. Naval Arch. Japan, Vol. 139, (1976). 11) Kinkead, A. N.: A Method for Analysing cargo Protection Afforded by Ship Structures in Collision and its Application to an LNG Carrier, RINA Report W12, (1979). 12) van Mater Jr., P. R. et al. : A COMPARI- SON OF THE COLLISION RESISTANCE OF MEMBRANE TANK-TYPE AND SPHERICAL TANK-TYPE LNG TANK- ERS, GASTECH 81, (1981). 13) Shibue, T.: Energy Absorption Analysis for the LNG Carriers in Collision, TRANS. OF THE WEST-JAPAN SOCIETY OF NAVAL ARCHITECTS NO. 66, (1983). 14) Minorsky, V. U.: An Analysis of Ship Collision with Refference to Protection of Nuclear Power Plants, J. of Ship Research, (1959). 15) Fujita, U., Nomoto, T., Niho, O.: Ultimate strength of stiffened plates subjected to compression, J. Soc. Naval Arch. Japan, Vol. 141, (1977). 16) Nishihara, S., Fukuoka, T.: Analysis of Ultimate Strength of Stiffened Rectangular Plate (1st Report), J. Soc. Naval Arch. Japan, Vol. 148, (1980). 17) Faulkner, D.: A Review of Effective Plating for Use in the Analysis of Stiffened Plating in Bending and Compression, J. of Ship Research Vol. 19, No. 1, (1975). 18) Gerard, G.: The Crippling Strength of Compression Elements, J. of Aero. Science, (1958).