Hydro-Elastic Criterion for Practical Design

Transcription

1 Hydro-Elastic Criterion for Practical Design Hannes Bogaert ), Mirek Kainski ) ) MARIN, Hydro-Structural Services, Wageningen, Netherlands & Delft University of Technology, Ship Structures Laboratory, Delft, Netherlands ) MARIN, Hydro-Structural Services, Wageningen, Netherlands Abstract A new hydro-elastic criterion which can be used in practical design of arine structures is proposed in this paper. By application of this criterion a designer will be able to decide whether a hydro-elastic proble can still be addressed by the standard two-step practice whereby in the first step the hydrodynaic load is deterined on a rigid odel of the structure and in the second step the accopanying structural response is calculated. The criterion has been developed based on nondiensional nuerical calculations using a siple luped-ass odel of a flexible cone ipacting the free water surface. The penetration velocity is hereby in contrast to the assuptions so far in previous investigations not prescribed, but results fro the nuerical odel. In addition the paper will deonstrate that the standard two step practice does not essentially lead to conservative results toward the response of the structure. Based on the findings of this paper the research is continued at MARIN and experiental validation is under way. Keywords Hydro-elastic analysis; quasi-static analysis; fluidstructure interaction; design philosophy; slaing; sloshing; response of arine structure Introduction The prediction of the response of s and other arine structures caused by wave loads is an iportant issue in odern design practice. The prediction ethodologies and capabilities are hereby continuously challenged by the growing arine transport arket. After all these arkets evolve to larger scales and to sever environents whereby the structural integrity and the passengers cofort need to be guaranteed. The coon or standard design practice for the prediction of this response is denoted as the quasi-static analysis. In the quasi-static analysis the hydrodynaic force is coupled with the rigid body otions and the resulting hydrodynaic force and the resulting inertia force are statically iposed on the structure. This iplies however that the quasi-static analysis first of all neglects the coupling between the structural vibrations and the hydrodynaic force. In addition this analysis neglects the influence of the dynaic properties (natural frequencies, odal shapes and odal daping) in the deterination of the structural response and according to the first oission also in the coupling with the hydrodynaic force. The hydro-elastic design practice on the other hand intends to incorporate this coplex chain of cause and effect of the hydrodynaic force, the otions of the structure (rigid body otions as well as structural vibrations) and the dynaic properties of the structure in the prediction of the response. Considering the coplexity but at the sae tie the correctness of this hydro-elastic analysis the question is however in the viewpoint of the design process, in the viewpoint of a business characteried by a short engineering tie when it is required to carry out a hydroelastic analysis and what the consequences are of still applying the quasi-static analysis. This question is addressed at MARIN fro a systeatic, step by step research philosophy. This approach deands for siplifications and abstractions in the first steps of the research but allows for the identification of the involved processes, their influences and their utual relations. The focus is hereby on only ipulsive wave loads such as slaing and sloshing loads. In this paper a new hydro-elastic criterion which can be used in practical design of arine structures, is proposed. By application of this criterion a designer will be able to decide whether a hydro-structural proble can still be addressed by the standard quasi-static analysis. The forulation of this criterion is a progress in answering the above entioned question and does not iply that the question can generally be answered as a theore. After all the criterion contains soe siplifications which are justified and essential for practical design applications. First of all the basic principle of the hydro-elastic criterion is introduced. The basic principle translates a practical design application in several ipact situations. The necessity and the effect of hydro-elasticity for these

2 ipact situations is at this stage of the research evaluated by the necessity and the effect of hydro-elasticity for the luped-ass odel of a flexible cone. The derivation of the necessity and the effect of hydroelasticity for the luped-ass odel of this flexible cone is addressed in this paper and is associated with previous investigations of e.g. Faltinsen (999) and Berenitski (003). In order to express the necessity and the effect of hydroelasticity for the ipact situations specified by the basic principle in function of the necessity and the effect of hydro-elasticity for the luped-ass odel of the flexible cone, a relation between these ipact situations and the flexible cone is established and discussed in the paper. This relation could only be accoplished by siplification of these ipact situations. Due to these siplifications the applicability of the hydro-elastic criterion will accordingly be liited at this stage of the research. Nevertheless the basis of the criterion is founded and further research needs to reveal the required accuracy in relation to the usability of the hydroelastic criterion. Basic Principle of Hydro-Elastic Criterion The practical design applications under consideration are the prediction of the response of s and other arine structures caused by external ipulsive loads (slaing and green-water on deck) as well as by internal ipulsive loads (sloshing). Several types of slaing are herby considered, naely forward botto slaing, aft body slaing, flare slaing, wave slap and wet-deck slaing. In the proposed hydroelastic criterion the arine structure is divided into successive structural levels, naely fro a local structural level to a global structural level. This division depends on the type of ipulsive load and the location of ipact. An overview for the response of a caused by the above entioned types of slaing, by green water on deck or by sloshing is given in Table. The basic principle of the hydro-elastic criterion can now be forulated as followed: The evaluation of the response of one of the above entioned structural levels takes the influence of the reaining part of the accopanying successive level into account. In contrast to the considered structural level the reaining part of the accopanying successive level is hereby considered to be rigid (non-deforable). If for exaple the response of a caused by forward botto slaing is investigated than the influence of the reaining of the double botto which includes this, is taken into account. The is hereby considered to be flexible (deforable) while the reaining part of the double botto is considered to be rigid. Since for exaple a is supported by stiffeners foring together a and this is supported by a double botto, the is in principle not only supported by the reaing of the which includes this but as well by the adjoining s and other parts of the double botto. Following this line of reasoning this iplies in principle that the is supported by all other parts of the. However in order to siplify the proble and the utiliation of the hydro-elastic criterion, the boundary of influence is set by the basic principle to the adjacent successive construction level which includes the previous. In Fig. the division into structural levels in case of forward botto slaing is illustrated. The basic principle of the hydro-elastic criterion is illustrated for the evaluation of the response of a, a, a double botto and a section in case of forward botto slaing in Fig.. This results in four different ipact situations wherefore the necessity and Table : Division of a in successive structural levels local global local global local global forward botto slaing double botto section wave slap e.g. at the bow bow section aft body slaing double botto aft peak wet-deck slaing double deck section sloshing containent syste: - one CS box - one NO96 box - one MARIK III box covered with containent syste double side shell covered with containent syste flare slaing bow section green water section

3 Fig. : Forward botto slaing - division into structural levels the effect will be evaluated by eans of the lupedass odel of the flexible cone. Luped-Mass Model of Flexible Cone In the last decade the effect of hydro-elasticity on the local response due to ipulsive loads were studied theoretically and experientally by Haugen and Faltinsen (999), Faltinsen (999) and Berenitski (003). All conclude that hydro-elasticity is iportant for sall values of the ratio between the duration of the loading and the longest natural period of vibration. This ratio is directly related to the ipact velocity, the deadrise angle, the structural stiffness and air entrapent. However the precise values of this ratio for which a hydro-elastic analysis for the bea odel (Haugen and Faltinsen (999) and Berenitski (003)) or the orthotropic odel (Faltinsen (999)) is iportant and the error ade by the quasi-static analysis could only be established for iposed global velocities which are constant during ipact. The physical iplication of a constant global velocity during ipact is a fluid ipact of a bea or an orthotropic which is supported by an infinite large ass. This physical incorrectness and the close link between the retardation of the velocity of the object of ipact, the ass and the deadrise angle of the object of ipact and the hydrodynaic force on the object of ipact underline the iportance of a hydro-elastic odel whereby the velocity of the structure during ipact is not iposed to the odel but results fro the nuerical odel. In other words in order to correctly specify the necessity and the effect of hydro-elasticity a odel is required with full coupling between the otions (rigid body otions and structural vibrations) and the hydrodynaic force. The creation of this odel inherently calls for siplification of the fluid ipact proble. Siplification is possible at three levels: the object of ipact, the dynaic structural properties of the object and the conditions of ipact. Fig. : Forward botto slaing - evaluation of the response of,, double botto and section according to the basic principle of the hydro-elastic criterion The above entioned previous investigations considered a bea or an orthotropic as object of ipact. Although these objects of ipact see to be siple in nature copared to a arine structure, the investigations could not lead to conclusive answers with respect to the ain question of this paper. As a consequence in this investigation the object of ipact is further siplified toward a three-diensional cone which has the atheatical benefit of being axisyetric. The dynaic structural properties of the cone are in addition siplified toward a luped-ass odel with two degrees of freedo, whereby the flexibility of the cone is represented by a linear spring. The degrees of freedo are in the direction perpendicular to the free surface. The lower part of this syste is an undeforable cone which directly ipacts the free surface. The upper part which is suspended over the lower ass by way of the spring, is as well unde-

4 forable. A scheatic presentation of the lupedass odel of the flexible cone is given in Fig. 3. The conditions of ipact for the final level of siplification. The hydro-elastic odel considers an ipact with no air entrapent, no copressibility of the fluid and an axisyetric ipact. Furtherore only water entry stage and not the possible water exit stage is investigated. Fig. 3: Scheatic presentation of the luped-ass odel of the flexible cone The dynaic equations of this hydro-elastic odel are forulated as followed: ( ) ( ) ( 0) ( 0) ( ) F (,, ipact ) ( ) = g k = g+ k With application of following initial conditions 0 = 0 = 0 = = V ipact Whereby : : displaceent of lower part of cone : displaceent of upper part of cone : ass of lower part of cone : ass of upper part of cone k : spring stiffness g : acceleration of gravity F ipact (,, ) : ipact force on lower part of cone In order to specify the necessity and the effect of hydro-elasticity not only a hydro-elastic analysis is required but as well a quasi-static analysis of the cone ipacting the free surface. In a quasi-static analysis the ipact force is evaluated on a rigid odel of the cone and is accordingly only coupled with the rigid body otions. The rigid counterpart of the lupedass odel of the flexible cone is the ipact of an undeforable cone with ass ( + ) and only one degree of freedo in the direction perpendicular to the free surface. The equation of otion of the rigid odel is written as followed: () ( ) ( ) + = + g F ipact (,, ) With application of following initial conditions ( 0) = 0 ( 0) = V ipact Once the ipact force and the acceleration of the rigid body are specified, they are statically iposed on the luped-ass odel of the flexible cone. Consequently it is assued that at each tie instant the ipact force and the inertial force are in equilibriu with the elastic force. The structural deforation ( - ) is accordingly specified as followed in the quasistatic analysis: ( g = ) k or ( g) + Fipact = k both resulting in the sae deforation Ki et al. (996) as well as Lafrati et al. (000) studied also the ipact of a luped-ass odel with two degrees of freedo onto the free surface. However the lower part of the odel is a two-diensional, undeforable wedge in these studies. Moreover both investigations where not aied at answering the ain question of this paper. The axisyetric hydrodynaic proble of Eq. and Eq. is evaluated in the fraework of the Wagner theory and is based on the work presented in Scolan and Korobkin (003) which is on its turn founded on Wagner (93), Arand and Cointe (986) and Zhao and Faltinsen (993). In this frae work the hydrodynaic force is defined as followed: ct ( ) F ipact (,, ) = π pouter, root ( r, t) rdr (4) 0 + π p jet ( r, t) rdr ct ( ) + Whereby: r () c t : radial position on cone at which pressure is evaluated : radial position of contact line of fluid 4 doain on cone defined as π tan β pouter, root : pressure at contact region 0 p jet : pressurein jet region r r c t ( ()) ( > c() t ) The pressure at the contact region and the pressure in the jet region are hereby atheatically expressed as: () (3)

5 pouter, root ( r, t) = ρ c() t r π dc τ + ρ( ) dt ( + τ ) ρ dc + ( ) π dt r r c t () c() t dc τ p jet ( r, t) = ρ( ) dt ( + τ ) Whereby: τ : specified by the following equations δ r c() t = ( logτ 4 τ τ + 5) π c() t δ = π dc ( ) dt (5) (6) (7) Eq. 4~7 are valid for the ipact force on the rigid odel (Eq. ) as well as for the ipact force on the luped-ass odel (Eq. ). They differ only by the independent variables, naely the penetration depth, the velocity and the acceleration of the rigid cone as a whole respectively of the lower rigid part of the flexible cone. By introducing the following four non-diensional paraeters:. The ratio of the gravity force relative to the buoyancy force C = (8) 3 ρr. The ratio of the deforation energy relative to the kinetic energy of the fluid C k k = (9) V ρ ipact R 3. The ratio of the gravity force relative to the inertial force. This paraeter is the reciprocal of the square of the Froude nuber. gr G = (0) V ipact 4. The ratio of the upper ass of the cone relative to the ass of the lower part of the cone. α = () the dynaic equations of the hydro-elastic odel can be rewritten in non-diensional for as: ( ) ( ) ' ' ' ' C = C G C k F ipact ' ' ' αc = αc G+ C k Likewise the quasi-static odel given by Eq. and Eq. 3 can be expressed as function of these four nondiensional paraeters. Since oreover the ipact force (F ipact ) is a function of the deadrise angle of the cone (β), it can be concluded that the hydro-elastic and the quasi-static odel are characteried by the following paraeters: C, C k, G, α and β. In the derivation of the hydrodynaic force (Eq. 4~7) the influence of gravity is however neglected in the dynaic boundary condition at the free surface and consequently as well in the linearised Navier-Stokes equations. This iplies that Eq. 4~7 can only be cobined correctly with either Eq. or Eq. ~3 if the influence of gravity is as well neglected in Eq. and Eq. ~3. In other words the derived hydro-elastic and quasi-static odels are applicable for ipact situations whereby the non-diensional paraeter G is set to ero. Necessity and Effect of Hydro-Elasticity for Luped-Mass Model The investigation of the ain question deands for the coparison of a hydro-elastic analysis with a quasi-static analysis in order to evaluate the necessity and the effect of the application of a hydro-elastic analysis. The indicator also denoted as the operational definition - used in this research to observe the necessity and the effect of hydro-elasticity is the reduction in the axiu of the absolute value of the deforation of the cone. The deforation of the cone is indicated by the deforation of the spring, naely -. Moreover the reduction is indicated by considering the difference between the deforation obtained by applying a quasi-static analysis and by a hydroelastic analysis relative to the quasi-static analysis. The operational definition is accordingly forulated as: ax reduction = () ( ) ax ( q s h e) ax ( q s) (3) Whereby: q s: basedon quasi-static analysis h e: based on hydro-elastic analysis This operational definition is close to the one applied in Berenitski (003). However in Berenitski (003) the deforation was indicated by the deforation at the center of the bea. The operational definitions in Haugen and Faltinsen (999) and Faltinsen (999) were indicated by a non-diensional axiu stress

6 and did not directly include the difference in ethod of analysis, naely a hydro-elastic or quasi-static analysis. Since the Wagner fraework considers the initial stage of the ipact of a blunt, convex body onto an inviscid, irrotational and incopressible flow with no air entrapent, the defined operational definition can only correctly be evaluated by the developed odels (Eq. ~7) if the following conditions are fulfilled:. 5 β 0. = 0 take place before one of the t following events occur: a. the flow becoes copressible b. the velocity of the cone changes direction which would result in a water exit instead of a water entry event c. the jet reaches the chines of the cone. As a consequence the influence of flow separation at the chine of the cone on the response can not been evaluated These conditions define the nuerical doain of the developed hydro-elastic and quasi-static odel and accordingly liit the possible cobinations of the non-diensional paraeters (C,C k,α,β) that can be investigated. The values of the operational definition evaluated for cobinations of these non-diensional paraeters which are included in the nuerical doain are first of all expressed as function of the following nondiensional hydro-elastic ratio (HER): rise tie of ipact force on rigid cone HER = (4) longest natural period of dry cone The rise tie of the ipact force (T rise tie ) is defined as the tie between the oent of ipact and the tie at which the ipact force attains its axiu value. Furtherore the longest natural period of a dry cone (T natural period ) is specified as: T natural period = π k + (5) The resulting relation between the values of the operational definition and the hydro-elastic ratio (Eq. 4) is visualied in Fig. 4 for three different values of the paraeter α. Although a different relation between the operational definition and the hydro-elastic ratio is applicable for each value of the paraeter α, each relation can be subdivided into the following three regions:. Region of positive reduction: In this region the axiu of the absolute value of the deforation of the spring of the cone is larger when it is evaluated by a quasi-static analysis instead of a hydro-elastic analysis. In other words in this region the quasi-static analysis overestiates the deforation.. Region of negative reduction: In this region the axiu of the absolute value of the deforation of the spring of the cone is saller when it is evaluated by a quasi-static analysis instead of a hydro-elastic analysis. In other words the quasistatic analysis underestiates the deforation 3. Region of ero reduction: In this region the axiu of the absolute value of the deforation of the spring of the cone reains the sae when it is evaluated by a quasi-static analysis instead of a hydro-elastic analysis. In other words in this region the quasi-static analysis correctly defines the deforation. Fig. 4: The reduction of the axiu deforation as function of the ratio between the rise tie of the ipact force on a rigid cone relative to the longest natural period of a dry cone The values of the hydro-elastic ratio which separate the region of positive and negative reduction and the region of negative and ero reduction are as well given in Fig. 4 as respectively point and point. Collecting these values of the hydro-elastic ratio for all other investigated values of the paraeter α results in Fig. 5. This figure presents the three regions of reduction as function of the hydro-elastic ratio and the paraeter α whereby the corresponding values of the reduction are indicated by contour lines. Finally the hydro-elastic ratio is forulated as function of the non-diensional paraeters (C,C k,α,β). To this end this ratio is now expressed in ters of the non-diensional fors of T rise tie and T natural period. Given Eq. 5 the non-diensional longest natural period is hereby related to the paraeters C and C k in the following way: T ' natural period V ipact = T R natural period α C = π ( + α ) C k The non-diensional rise tie of the ipact force on a rigid cone is covered by Eq., Eq. 4~7 and can be (6)

7 defined within the nuerical doain of the developed quasi-static odel by the following relation: (( α ) ) ' b T rise tie = a + C tan β a with 0.95π b 3 (7) value of the deforation but as well to the oscillating behavior of the deforation. This investigation of the extent of these consequences and when they can be neglected, has not been undertaken in these first steps, but will be essential for further developent of the hydro-elastic criterion. As a consequence at this oent the stringent definition of the word required is applied for forulation of the hydro-elastic criterion. With Eq. 6. and Eq. 7 the hydro-elastic ratio can accordingly be approxiated as: 53 ( + α ) C HER k tan β (8) α 3 C Fig. 6: Necessity and effect of hydro-elasticity for luped-ass odel of flexible cone expressed as function of the non-diensional (C,C k,α,β) Relation between ipact situations of hydroelastic criterion and ipact situations of flexible cone Fig. 5: Three regions of reduction as function of the hydro-elastic ratio and the paraeter α The cobination of the description of the three regions of reduction as function of the hydro-elastic ratio and the paraeter α (Fig. 5) with the expression of the hydro-elastic ratio as function of the nondiensional paraeters (Eq. 8), results in Fig. 6. This figure directly denotes as function of the nondiensional paraeters (C,C k,α,β) to which extend the quasi-static analysis either overestiates, underestiates or correctly defines the ipact of the luped-ass odel with respect to the hydro-elastic analysis. Fig. 6 expresses accordingly the necessity and the effect of hydro-elasticity for the luped-ass odel of the flexible cone within the nuerical doain of the developed odels. This stateent is only true if the ost stringent definition or interpretation of the word required is applied, naely it is required to carry out a hydro-elastic analysis if the quasi-static analysis either over- or underestiates the deforation of the spring. However in the viewpoint of the hydro-elastic criterion the word required should as well taken the extent of the consequences into account. After all the effort of a hydro-elastic analysis is only required if the consequences of not applying a hydro-elastic analysis can not be neglected. The extent of a consequence is hereby not only related to the The necessity and the effect of hydro-elasticity for the ipact situations specified by the introduced basic principle of the hydro-elastic criterion can finally be evaluated as function of the derived necessity and the effect of hydro-elasticity for the luped-ass odel of the flexible cone, by specification of a relation between these ipact situations and the flexible cone. This relation can coe about by application of the three levels of siplification, naely the object of ipact, the dynaic structural properties of the object of ipact and the conditions of ipact, as used in the derivation of the luped-ass odel of the flexible cone.. Object of ipact Since the luped-ass odel considers a threediensional axisyetric cone the identified ipact situations by the basic principle of the hydro-elastic criterion which have not essentially an axisyetric cone shape, need to be considered as a geoetrically axisyetric cone in their relation to the flexible cone.. Dynaic structural properties of object of ipact The dynaic structural properties of the flexible cone were siplified toward a luped-ass odel with two degrees of freedo. The dynaic structural properties of the ipact situations of the hydro-elastic

8 criterion need accordingly as well be siplified toward a luped-ass odel with two degrees of freedo in their relation to the flexible cone. In contrast to the flexible cone these ipact situations however consist of a flexible (considered structural level) as well as of a rigid (reaining of successive structural level) part. As a consequence the translation toward a luped-ass odel will be different for these ipact situations than for the flexible cone. The following procedure is applied: - The flexible part of the ipact situations, naely the structural level for which the response is evaluated, is siplified to a luped-ass odel with a lower and a upper ass equal to half of the ass of the flexible part ( flexilbe part ). The flexibility of this part is hereby represented by a linear spring with a spring stiffness specified as: k = ω flexible part flexible part (9) - The influence of the rigid part, naely the reaining of the successive level, is translated to the luped-ass odel in the following way: - The first natural frequency of the flexible part (ω flexible part ) takes the boundaries into account, naely the flexible part is considered to be fully supported in the direction of the ipact whereby all other restrains are neglected. - The ass of the reaining part of the successive level is added to the ass of the upper part of the luped-ass odel and accordingly influence the non-diensional paraeter α, whereby α increases as the ass of the reaining part of the successive level increases relative to the ass of the considered structural level. In this respect the reaing part of the successive level does not only influence the dynaic properties of considered structural level but as well the otions and the coupling to the hydrodynaic force of the considered structural level. stage and chines dry stage are described by these odels. The ipact conditions of the identified ipact of the hydro-elastic criterion are accordingly as well restricted to the above entioned ipact conditions in their relation to the flexible cone. An axisyetric ipact of a luped-ass odel of the cone iplies that the dead-rise angle (β) of the cone is not only geoetrical axisyetric but as well axisyetric with respect to the free surface. In the relation to the flexible cone this deadrise angle represents the angle between the object of ipact and the fluid surface of the identified ipact situations. For these ipact situations this angle is not essentially axisyetric but is however in its relation to the flexible cone assued to be geoetrically axisyetric as well as axisyetric with respect to the fluid surface. The resulting relation is suaried in Fig. 7. Although the applied siplifications in this relation liit in principle the applicability of the hydro-elastic criterion, only further research can reveal the required accuracy in relation to the usability of the hydroelastic criterion and can accordingly reveal the extend to which these siplifications need to be reduced. At this stage the basis of the hydro-elastic criterion is elaborated and can be suaried in the following three steps:. Specification of the ipact situations for the evaluation of the response of as structure by division in structural levels and application of the basic principle of the hydro-elastic criterion. - The lower part of the luped-ass odel which directly ipacts the free surface, is undeforable and has according to the first level of siplification an axisyetric cone shape. The radius of the cone is hereby equal to the half of the sallest of the breadth or length of the considered structural level. Since only the considered structural level and not also the reaining part of the successive level is geoetrically transfored into the lower part of the luped-ass odel where the hydrodynaic force acts on, this translation can only describe the ipact situations where the considered structural level is located at the position of ipact. 3. The conditions of ipact: The derived odels (Eq. ~7) of the luped-ass odel of the cone consider an ipact with no air entrapent, no copressibility of the fluid and an axisyetric ipact. Furtherore only water entry Fig. 7: Relation between ipact situations of hydroelastic criterion and ipact situations of luped-ass odel of flexible cone

9 . Specification of the non-diensional paraeters of the luped-ass odel of the flexible cone by relating the identified ipact situations to flexible cone according the relation suaried in Fig Specification of the necessity and the effect of a hydro-elastic analysis by eans of Fig. 6 and the defined non-diensional paraeters. Conclusions The new hydro-elastic criterion proposed in this paper enables a designer to decide whether a hydro-elastic proble can still be addressed by the standard quasistatic analysis. The criterion subdivides the arine structure into successive structural levels based on the type of ipulsive load and the location of ipact. Within the proposed hydro-elastic criterion the evaluation of the response - caused by ipulsive wave loads - of such structural level takes the influence of the reaining of the accopanying successive level into account. In this criterion use is ade of the derived necessity and effect of hydro-elasticity for the ipact of a luped-ass odel of a flexible cone for the evaluation of the necessity and the effect of hydro-elasticity for the above entioned identified structural levels. This necessity and effect can be expressed as function of four non-diensional paraeters which characterie the ipact of the luped-ass odel of the flexible cone onto the free surface and can be suaried into three regions, naely a region where the quasistatic analysis overestiates the response, a region where the quasi-static analysis underestiates the response and finally a region where the quasi-static analysis correctly defines the response. In this forulation of the necessity of a hydro-elastic analysis the stringent definition of the word required is applied, naely it is required to carry out a hydroelastic analysis if the quasi-static analysis either overor underestiates the deforation. However the word required in the forulation of the necessity of hydroelasticity should as well taken the extent of the consequences into account. The investigation of the extent of these consequences and when they can be neglected is essential for further developent of the hydro-elastic odel. Together with further ipact odel developents and research toward the required accuracy in relation to the usability of the hydroelastic criterion, this investigation of consequences for the next steps in the systeatic, step by step research at MARIN toward the necessity and the effect of hydro-elasticity for practical design. At the oent of writing MARIN works at the experiental validation of the proposed hydro-elastic criterion. References Arand, J. and Cointe, R. (986). "Hydrodynaic ipact analysis of a cylinder", Proc. Fifth Int. Offshore Mech. and Arctic Engng. Syp., (OMAE), Tokyo, Japan, Vol, ASME, pp Berenitski, A. (003). "Local hydroelastic response of structures under ipact loads fro water (slaing)", PhD thesis, Delft University of Technology. Faltinsen, O. (999). "Water Entry of a Wedge by Hydroelastic Orthotropic Plate Theory", Journal of Ship Research, Vol. 43(3), pp Haugen, E. and Faltinsen, O. (999). Theoretical studies of wetdeck slaing and coparisions with full-scale easureents, Proceedings of the 5 th International Conference on Fast Sea Transportation (FAST 99), Seattle, Vol., SNAME, pp Ki, D., Vorus, W., Troesh, A. and Gollwiter, R. (996). Coupled Hydro-dynaic Inpact and Elastic Response, Proceedings of the st Syposiu on Naval Hydrodynaics, Trondhei, Norway, pp Lafrati, A., Carcaterra, A., Ciappi, E. and Capana, E. (000). Hydroelastic Analysis of a Siple Oscillator Ipacting the Free Surface, Journal of Ship Research, Vol. 44(4), pp Scolan, Y.-M. and Korobkin, A. (003). Energy distribution for vertical ipact of a threediensional solid body onto the flat free surface of an ideal fluid, Journal of Fluids and Structures, Vol 7, pp Wagner, H. (93), Über Stoss- und Gleitvorgänge an der Oberfläche von Flüssigkeiten, Z. Angew. Math. Mech., Vol., pp 93-5 Zhao, R. and Faltinsen, O.. (993). Water entry of two-diensional bodies, Journal of Fluid Mechanics, Vol. 46, pp