Following the first report the validation of accuracy is made of a new computation method, WISDAM-VI, which employs the density function technique on the free surface, and two applications to practical hulls are made. The first one is a flow around a tanker model in ballast condition and it is revealed that the wave breaking motion causes momentum defect and that it interacts with the viscous flow forming complicated wake. The second one is a flow around a high speed planing craft which involves highly nonlinear free-surface flow near the stern end. These demonstrate the versatile applicability of the WISDAM-VI method.

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Two one-equation turbulence models proposed recently were applied to Navier-Stokes computations of viscous flows around ship hulls. The turbulence models consist of a single advection/diffusion equation for eddy viscosity. Flows around two tanker models, the HSVA Tanker and the Dyne Tanker, as well as a a flat plate were computed with these turbulence models. Results were compared with measured data and the computations with the conventional algebraic turbulence model. Resistance values computed with the one-equation models were found to be reasonably accurate compared with other numerical results. The wake distributions predicted by the present models showed more rounded contours which were improved from the ones by the algebraic model.

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Characteristics of vortical flows around free surface piercing struts are studied by a numerical simulation method solving 3-D laminar incompressible Navier-Stokes and continuity equations. The simulation shows that vorticity is generated on the curved free surface to satisfy a no-shearing stress condition. The vorticity, whose strength is proportional to the free surface curvature, leads the generation of the vortical motions beneath the free surface in front of a bow. To investigate curvature effect of the body, three different struts having NACA 0005, NACA 0008 and NACA 0012 sections are used. The effect of free surface boundary conditions and grid density around the free surface are also discussed.

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Computational results of a two-dimensional gravity current in a lock-exchange flow is presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density when a lock gate was opened. The computations were performed in a two-dimensional channel by solving the incompressible Navier-Stokes equation for an inhomogeneous fluid, the continuity equation and the transport equation for solute by the finite volume method. For accurate representation of small density difference, the density variation relative to the characteristic density difference was used as one of primitive variables. The finite volume formulation holds the conservative property with respect to mass at the boundaries as well as at the density interface so that the total mass of the two fluids with different density remains constant. Some of standard numerical schemes were used to examine their performance to the density jump of the interface. The computed gravity current moves steadily in an initial phase, and the front speed decreases with distance in a self-similar phase when an internal bore on the interface reflected from the back of the lock reaches the front of the current. The effects of the bottom boundary layer on the internal structure of the current is investigated from numerical experiments with no slip and free-slip boundary conditions. The volume of the diluted fluid in a gravity current by the entrainment of ambient fluid is evaluated as a function of time to quantify the mixing. The result indicates that at low Reynolds numbers the subsequent mixing occurs in the early stage of the evolution of the gravity current in a lock-exchange flow.

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This paper describes the experimental result of cloud cavitation on a two-dimensional foil. Cloud cavitation was observed by a high speed camera and a high speed video camera to know the mechanism of cloud cavitation. Ink was injected to investigate the reserve flow (re-entrant jet) at the bottom of the sheet cavity. The flow around the sheet cavity was measured by a laser doppler velocimeter. By applying conditional sampling technique on the flow measurement, unsteady flow field was examined with the motion of cloud cavitation.
A small square bar was attached on the foil surface and the effect on the cloud cavitation was investigated.
The conclusion are as follows :
(1) The shedding of cloud cavitation is caused by re-entrant jet.
(2) The re-entrant jet starts at the rear center of a sheet cavity and spreads to the leading edge.The re-entrant jet disturbs the sheet cavity and the sheet cavity collapses into a mass of bubbly cavities. When the re-entrant jet reaches the cavity leading edge, the shedding of cloud cavity occurs.
(3) A bar attached on the foil surface reduces the re-entrant flow, resulting in the reduction of cloud cavitation shedding. A ditch on the foil surface gives the similar effect on the cloud cavitation.

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This paper describes the successful application of a theoretical supercavitating propeller design method to racing boat propellers. Two propellers were designed, manufactured and tested on a newly developed full-scale boat.
The first one, the SC-2 propeller, was designed at an advance ratio of 1.371 and a cavitation number of 0.3, and tested at the Kiryu racing site together with two target propellers, the SC-1 propeller which was previously designed by a Bp-chart method, and a commercial racing boat propeller, the “Record Propeller”. No remarkable difference in the measured speeds of the racing boat equipped with each propeller was observed at full throttle condition, while the performance of the SC-2 propeller was superior to that of the SC-1 propeller at the prescribed design conditions in tests in two cavitation tunnels.
The second propeller, the SC-3 propeller, was designed by changing the propeller diameter from 165 mm to 175 mm to make the diameter more optimum at an advance ratio of 1.197. The blades of this propeller were designed to be as thin and narrow as possible to get the optimum lift-drag ratio at each radial position within the limitation of having the same strength requirement as that for the SC-1 propeller. At the propeller root, aerofoil blade sections were applied from the view points of strength and efficiency.
The second propeller was also tested at the racing site with the SC-1, the SC-2 and another famous commercial propeller, the “Rolla Propeller”. The racing boat with the SC-3 propeller ran at the highest speed of about 97 km/h in the full-scale test. At the racetrack, a running test around two turning buoys 300 m apart gave the following results ; the racing boat with the SC-3 propeller completed a lap within 33.8 seconds which was 1.4 seconds faster than that with the “Rolla Propeller”. The test in cavitation tunnels endorsed the higher performance of the SC-3 propeller than those of other propellers.

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We present a simple surface panel method to predict steady marine propeller performance. This method uses source distributions (Hess and Smith type) on the wing surface and discrete vortex distributions arranged on the camber surface according to Lan's quasi-continuous vortex lattice method (QCM). Then these singularities are determined at a time by solving simultaneously both the wing surface and the camber surface conditions that the normal velocity should be zero. Since these singularities satisfy automatically the Kutta condition, we need not use any iterative procedure. We named this method SQCM (Source and QCM).
We show numerical results for four kinds propellers (DTRC 4119, DTRC 4842, Seiunmaru conventional and highly skewed propellers) in this paper. Pressure distributions obtained by the present method are in good agreement with the experimental data and other numerical results. Though the viscous effects are not taken into consideration in the present calculations, the calculated thrust and torque coefficients agree qualitatively with experimental results.

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In this paper, the applications of surface vortex lattice method to marine propellers in non-uniform flow are considered.
The surface vortex lattice method based on the general vortex lattice method is possible to simulate the flow around a lifting body including thickness and volume effects by distributing horse-shoe vortices and surface source distributions on the both side surfaces of the blades. The advantage of this method compared to other panel methods is the fact that the Kutta-condition is satisfied automatically in not only steady condition but also unsteady condition by convecting the trailing and the shed vortices. The geometry of the wake using the linear wake model having the geometrical pitch of blades and all shed vortices are convected to new positions step by step with a small time interval.
Three propellers are used to confirm the accuracy of the results of the present method. At first, the fluctuation of the thrust and the torque coefficients of a propeller in harmonic wake are calculated to compare the time derivative term with the results by VLM. And next, the pressure distribution on the blade concerning to two full scale propellers are calculated by the present method.
The results of these calculations are good agreements with experimental results and other theoretical calculations

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In this paper a surface panel method formulation for analysis of a marine propeller for different wake models is described. The method is based on Green's theorem which is composed of the combination of dipoles and sources distribution on the blade, hub and also, dipole distribution on the trailing vortex wake to represent the potential flow around the propeller.
Investigation of three kinds of wake models (linear wake model, devised wake model based on slip ratio and new wake model based on thrust loading coefficient) for a marine propeller are presented. New wake model based on thrust loading coefficient uses the momentum theory technique in conjunction with iterative procedure to generate the wake model. Using a momentum theory, the ratio of propeller wake radius at the infinite downstream to the blade radius can be obtained. The first solution is obtained based on linear wake model. The iteration process is repeated until the results are converged. The calculated results are in good agreement compared with experimental data and other methods.

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In the previous paper the author and a co-author analyzed the principal mechanism of propulsion of a ship by “Ro” so as to make an automatic rowing machine of a 1/3 scale model of “Ro”, and carried out open tests and self-propulsion tests of “Ro” rowed by the automatic rowing machine in the towing tank of Yokohama National University. The results of such experiments made clear the hydrodynamic characteristics of “Ro”, such as possibility of high efficiency more than 70% by skillful rowing.
In the present paper, the hydrodynamic characteristics of some sections of “Ro” measured in the wind tunnel are reported in C_L and C_D diagrams in the first stage and the numerical results calculated by the blade element theory of “Ro”, which has been developed originally by the author, using the characteristic diagrams of sections obtained by the wind tunnel experiments are reported in the second stage. Conclusively such calculated results are compared with the experimental results measured by the above-mentioned automatic rowing machine of “Ro”. Calculations are showing good tendency matching with experiments, but the quantitative agreement between the two is not necessarily good.

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A Computational Fluid Dynamics (CFD) study on the jet-stream propulsion of rigidly oscillating and undulating bodies has been undertaken, by the unsteady solutions to the two-dimensional incompressible Navier-Stokes equations in conservative form, which are discretized with the finite volume method, using the pseudo-compressibility technique. Computational validation confirmed that the present method was capable to reasonably predict highly unsteady flows of biological problems. Numerical study on an oscillating hydrofoil (NACA 0012) reveals that there exists a problem of optimal propeller efficiency in generating the jet-stream in wake, but within a narrow region of the Strouhal numbers. Further analysis on a tadpole-shaped object and a fish-like body swimming in realistic kinematics, shows that the kinematics effectively produces a jet-stream propulsion with much higher propulsive efficiency than that of achieved by the oscillating hydrofoil. Investigation of Reynolds number effect for the undulatory swimming indicates that the propeller efficiency increases with increasing Reynolds number with no Re ceiling in generating the jet-stream.

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Predictions of hydrodynamic forces acting on a sailing yacht are very important, especially in the hull form design of racing yachts as used in America's cup. However those accurate predictions are very difficult, because the sailing yacht has complex geometry with a large fin keel, and the free surface problem must be solved under the condition with leeway angles.
In the present study, hydrodynamic forces acting on sailing yachts are computed by means of a surface panel method. Morino's method, which is well known as one of the useful surface panel methods for lifting bodies, can be extended to the free surface problem around an advancing body with leeway angles under the linearized free surface condition. According to this formulation, numerical examples are given for two sailing yacht hull forms, KIT 34 and NCAC 12 m class, in which computed results of wave making resistance without leeway, hydrodynamic forces with leeway and side wave profiles with and without leeway are compared with the experimental results. In order to investigate the wave making effect of the fin keel, these computations are shown for both conditions with and without the fin keel.

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In this paper, components of the drag force which acts on the hydrofoil are evaluated by momentum theorem taking account of the wave generation and the trailing vortices. Then, it is possible to compute the total drag without the interference of induced drag and wave-making resistance as far as vortex model has normal image system which satisfies the rigid wall conditions at the free surface.
Also, it was shown that the lifting line approximation for calculating wave-making resistance is not valid in the case of low speed by using of wave amplitude functions of lifting surface. And, asymptotic behavior of wave pattern generated by vortex system at the high speed is analyzed. As a result, flow field is represented by inverse image system and above-mentioned approximation is useful for the limiting case of high speed.

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In order to investigate capsizing caused by low cycle resonance of ships running in irregular astern seas, an analytical approach has been conducted for computing the fluctuation of metacentric height in irregular astern seas and the power spectrum of metacentric height has been obtained from the time histories of it. The unstable regions of low cycle resonance have been discussed for a container ship and a purse seiner on the basis of Mathieu's equation.

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In the previous papers authors studied capsizing phenomena of a small pleasure boat in beam seas. Small ships, which usually have large breadth/draft ratio, are apt to sway with a large amplitude in waves and to drift at a high velocity in wind. It was clarified that the large lateral motion can lead to a large drag force and moment because their complicated under-water hull forms can easily make flow separation. In a heeled condition the rolling moment by the separated flow works asymmetrically to the direction of sway motion, being larger when the ship moves to the direction of heeling than to the other direction. This asymmetries helps to enlarge the heeling angle and finally to capsize.
In this paper a large amplitude forced sway motion test was conducted to investigate the effect of hull forms to the non-linear sway force and moment. Three two-dimensional round-chine models with dead-rise angle of 10, 20, 30 degrees were used. Totally the test was carried out on nine hull forms, using the three round-chine models with/without hard-chine pieces and skegs. It is clarified that a conventional linear integral equation method can almost evaluate the acceleration component of sway force and moment, but cannot evaluate the damping component, because drag component occupies the main or non-negligible part of sway damping. It is also clarified that the rolling moment by the sway motion gets very asymmetric when flow separation occurs locally at the vicinity of the bottom center or of the chine. The asymmetry becomes small when the separated flow covers the whole bottom, which happens on the models with skeg or with large dead-rise angle.
This paper also deals with the force and moment of drift motion at a constant speed. The characteristics of the heeling moment is similar to that of sway motion. The moment works to increase the heel angle when the ships moves to the direction of heeling. But, it becomes small if the model makes a large separation region.

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A new numerical approach based on the 3-D panel method was presented for the estimation of the wave forces acting on a half-immersed spheroid advancing in oblique short waves in the 3rd report. This numerical approach consisted of the spline approximation of the ship surface and the velocity potential distribution on it, and the integral equation directly with respect to the velocity potential itself. It was clear that this method improved the predicted results of the wave forces on the spheroid in oblique short waves.
In this paper, the numerical approach is applied to estimate the wave forces and the pressure distribution on a realistic blunt ship advancing in oblique short waves. Moreover, the steady disturbance on a realistic blunt ship surface was taken into account.
The numerical results of the present method are compared with the experimental results and the numerical results of strip method. The results of the present method are in good agreements with the experimetal ones about radiation forces and pressure distributions on the ship surface.

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A new theory is presented for the radiation problem of heave and pitch modes of a slender ship advancing at arbitrary forward speed. The theory has no restrictions on the order of forward speed and oscillation frequency, embracing both of unified theory developed by Newman and high-speed slender-body theory (HSSBT). The inner velocity potential consists of a particular solution, which is the same as that of HSSBT, and a homogeneous component, which is constructed by the superposition of the real-flow velocity potential and the reverse-flow reverse-time velocity potential.
Since precise computations of HSSBT are prerequisite for the present theory, the calculation procedure adopted for HSSBT is described, converting the formulation into an equivalent initial-value problem in the time domain and applying the higher-order boundary-element method at each time step.
Numerical results of added-mass and damping coefficients based on the present theory are shown for a modified Wigley model and compared with corresponding experiments and other computed results by the strip method, HSSBT, and 3-D Rankine-panel method.

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A full nonlinear method to simulate three dimensional body motions in waves is presented. This is a time domain method to simulate Euler's equation of ideal fluid motion coupled with the equation of solid body motions.
Introducing Prandtl's nonlinear acceleration potential, whose gradient gives acceleration of the fluid, Euler's differential equation of the ideal fluid motion is converted to the integral equation of the acceleration potential. The boundary condition of the acceleration potential on the body surface is systematically derived from the kinematic relation between the acceleration of the solid body and the acceleration of the fluid on the body surface. Since this kinematic boundary condition is a function of the body acceleration, the boundary values on the floating body can not be evaluated explicitly. To overcome this point, the unknown acceleration of the free floating body is eliminated by substituting the equation of body motion into kinematic condition, then implicit body surface boundary condition is derived. This is the kinematic and dynamic condition which guarantees dynamic equilibrium of forces between ideal fluid and the solid body at any instance. With the free-surface boundary condition of the acceleration potential, the formulation of the boundary value problem for the acceleration field is completed.
Although this formulation of the acceleration field is mathematically correct, this is not appropriate to numerical computation, because Prandtl's nonlinear acceleration potential does not satisfy Laplace's equation. Therefore, the nonlinear part is shifted from the governing equation to the boundary condition, then the alternative formulation for the numerical computation is derived. The computational flow of the nonlinear simulation method based on this alternative formulation is also given. In order to show the accuracy of this new method, two dimensional numerical results are presented. They show that the conservation of mass, momentum and energy are satisfied excellently.

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Free-fall lifeboats provide a safe alternative to conventional lifeboats for emergency evacuation from ships and offshore platforms. The international regulations require that a lifeboat for free-fall launching shall be capable of rendering protection against harmful accelerations when it is launched with its full complement of persons and equipment from at least the maximum designed height. Through model and full scale tests, much has been studied about the behaviour of these lifeboats. These tests, however, are very expensive to conduct and the complete behaviour of the boat is sometimes difficult to discern. A mathematical model, therefore, can be very much effective to quantitatively evaluate the kinematics of the free-fall lifeboat.
The hydrodynamic impact of the boat at water entry is a complex problem and is responsible mostly for the acceleration on board. Presented in this paper is a mathematical model where impact has been evaluated for a realistic lifeboat hull on the basis of the concept of a momentum theory, and the falling motion of the boat has been computed by solving the motion differential equations in the time domain. From the numerical simulation, trajectories of the boat and time histories of accelerations in different positions and directions are obtained. Model experiment has also been conducted to verify the numerical results and good agreement has been obtained between the numerical and experimental results.

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To design a very large floating structure, such as a floating airport, we have to estimate the hydroelastic response on any point of the very large floating structure exactly. We developed the estimating method of the hydroelastic response of a very large pontoon type floating structure. In this method, to obtain the hydrodynamic forces we used the pressure distribution method with Shallow draft assumption, considering the elastic motion of a floating body. The elastic response of very large floating structure was estimated by using the modal analysis of 2-D beam model.
On the other hand, to observe the elastic response of a large pontoon type structure we carried out experiments in head sea and head+beam sea condition. The experimental model was a pontoon type large elastic floating body. This model consists of many box type rigid floats that were connected by longitudinal and lateral elastic beams. To measure vertical motions of multiple points of the elastic model we applied the optical and image processing system. We could measure the elastic motions and deformations of the model in 2-directional waves.
To validate the corresponding of numerical estimating method we compare the numerical results with experimental results. From these results, we found good agreement and confirmed the accuracy of this numerical estimating method of the hydroelastic of a very large pontoon type floating structure. Furthermore, we discussed the hydroelastic responses and bending moments in shorter wave length with changing stiffness of the floating structure.

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A huge box-shaped floating structure is now being proposed as one of the candidates of an offshore airport. According to the plan, the length and the width will be 5000 m and 1000 m respectively while the thickness of the structure is expected to be about 5 m. But, never in history has there existed such a structure, so we have many unknown factors about the behaviors of such structures in waves. Among them, one that is unique to such structures is large elastic deformations that will be induced by the dynamic effects of waves, because the horizontal dimension is extraordinary large compared to its thickness.
Experiments on elastic deformations of such structures are quite difficult because, if both the horizontal and vertical dimensions are equally scaled, the resultant model should be as thin as less than 10 mm. Hence, the development of theoretical techniques to be able to predict elastic behaviors without experiments is quite important. For the structures considered in this study, the local displacements due to elastic deformations may be comparable to or even larger than the displacements due to rigid-body motions. Therefore in the predictions of hydrodynamic forces on the structure, the elastic deformations should be taken into account. On the other hand, the elastic deformations are in turn affected by the hydrodynamic forces. Thus the elastic deformations and the hydrodynamic forces interact with each other, which is called a hydroelastic interaction.
The main purpose of this paper is to propose a new theoretical technique that can incorporate such hydroelastic interactions in the predictions of dynamic behaviours of a pontoon-type huge floating structure in waves. We compare the numerical results based on the presented theory with experimental data, which are obtained by making use of a flexible model in a water tank and discuss the effectiveness of our theory.

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In the first report, the basic concept of a longlife-oriented new type floating offshore airport was proposed and its fundamental response characteristics such as static stability, response due to an impact load were investigated. This second report deals with the deflections and bending moments among waves with special considerations of its deck stiffness and effects of loss one unit due to replacing.
The response to regular head waves are studied numerically and verified by experiments. The hydrodynamic forces induced by wave are calculated by using 3D singularity distribution method taking the symmetry of structure into accounts. On the other hand, the structural analysis is conducted by using the application of FEM approach. Then, the hydroelastic responses, namely deflection and bending moment in waves are determined by combining the above two analyses.
The influence of deck stiffness on deflection and moment are discussed through a series calculations. Also the loss of unit in replacing condition is investigated, and some suggestions for such type floating airport are proposed consequently.

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This paper presents statistical analyses for second-order responses of tension-leg platform.
Second-order responses of moored vessels in random seas include two kinds of elements, difference-frequency response and sum-frequency response. It is well known that difference-frequency response leads to slow drift oscillation. Sum-frequency response is generally eliminated for an analysis of slack mooring.
In the case of heaving motion of tension-leg platform, sum-frequency response is large because of its high natural frequency, and it leads to springing response. Non-normality of two kinds of responses are investigated, and compared these two responses for surging, heaving and pitching modes.
Main results are as follows :
1) Sum-frequency response of exciting force is a little larger than difference frequency response of it. Both of them have large non-normality.
2) Sum-frequency response of heaving and pitching motions are much larger than difference, and surging shows opposite result. These three large responses have behavior similar to normal distribution.
3) Gamma-distribution approximation and DVI method can be applied to sum-frequency response.
4) Non-normality increases and standard deviation becomes small as damping increases.

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Recent tension leg platform (TLP) model tests have revealed strong transient resonant responses during extreme wave frequency responses. It is said that these responses, termed ringing, are associated with large-crested, near breaking wave events. In this paper, as a first step of giving light on the occurrence mechanism of such nonlinear phenomenon, first-order, second-order sum frequency and higher order wave force measurement tests are carried out in regular and irregular waves. At the same time, wave height distributions of the wave field inside the TLP are also measured to investigate the correlation between the occurrence condition of higher-order wave force and the wave height deformation. The first and second order wave force measurement tests are used to validate the predictions based on a newly developed first-order and second-order diffraction theory for an arbitrary three dimensional floating bodies. As a result, not only first-order wave forces but also second order sum frequency forces can be predicted from the second-order diffraction theory except for high frequency range (kL >6, k : wave number, L : distance between columns of TLP). However, a significant third-order surge force occurs when kL becomes larger than 4.4 and has the same characteristics as the first-order force. Furthermore, nonlinear force higher than second order occurs even in irregular waves when a crest pairing of waves occurs inside TLP. Such forces seem to be caused by what the surface elevation inside TLP become more steep and nonlinear, as compared with the incident wave, by a hydrodynamic nonlinear interaction between columns.

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The development of ocean oil fields are now going to deeper and smaller oil fields. A FPSO (Floating, Production, Storage and Offloading) system is one of the most economical systems for the production of marginal fields and thus is in use worldwide. For the position keeping of a FPSO system, a single point mooring system is usually employed to economize the operation. However, the conventional single point mooring systems such as a catenary anchor leg mooring (CALM) or a turret mooring (TM) become less economical as the water depth increases because the system becomes heavier in order to sustain the large weight of mooring lines. In this paper, we apply a Counterweight Articulated Mooring (CAM) system, which was originally proposed for a mooring system in ice infested water, as the alternative single point mooring system for a FPSO that may be used in a medium-depth water (500 m).
Since a CAM system is mechanically much more complicated than conventional systems, we examine how the behaviours of a CAM system in waves can be predicted theoretically. A computer code is developed based on the constraint matrix method proposed by Langley for the analysis of a floating system composed of a number of structures.
Numerical results obtained by the developed code are compared with model test data. And the following conclusions are obtained through the present study.
(1) The numerical prediction of wave induced responses of a CAM system gives fairly accurate results.
(2) The low frequency responses in irregular waves are governed by the low frequency oscillations of a tanker, which should be predicted while properly accounting for the damping force.
(3) The connecting mechanism between a tanker and a yoke should be free rather than be fixed because the stress and the mooring lines' tensions are drastically decreased.

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When ship is moving in lateral direction at berthing in a harbour or when ship is moving with large drift angle at low speed, it is known that the component of cross flow drag dominates the hydrodynamic force acting on ship hull. It is important to develop prediction method for the cross flow drag from the view points of safe navigation of ships at low velocity in harbor or restricted water.
One of the authors has already proposed the prediction method for the cross flow drag acting on a ship hull based on the vortex shedding model. However, the prediction method requires to determine the parameter comparing with the results of model test in order to define the positions of the free vortices that are shedded from the ship hull. Additionally, value of the parameter α that reduce the strength of the free vortices is defined uniformly along the ship length in spite of the change of sectional form.
In this paper, we tried to improve the vortex shedding model by investigating the positions of separation points. We also investigated the longitudinal distribution of the parameter α. From these studies, it is shown that longitudinal distribution of the cross flow drag along the ship length can be predicted with comparatively high accuracy using the presented prediction method.

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The effect of measurement interval on the reliability of parameters estimated by the result of a full scale measurement of responses of ship to ocean waves is an important factor to consider in planning the measurement on a ship.
To clarify the effect, authors investigate records of wind velocity measured for ten years (1981-90) at seven meteorological observatories. The original record is divided into ten records of velocity measured for one year. As the original one is a record of wind velocity measured at intervals of three hours, we regard each one as a sample when measurement interval is three hours. For a sample we calculate such set of parameters as mean and standard deviation which corresponds to the distribution of elements. From ten values of a parameter, authors estimate sample distribution of it when the interval is three hours.
By the similar way the sample distributions of it when wind is measured for one year at intervals of 6, 9, 12, ...hours are estimated. Authors make it clear by investigation of the distribution that the scatter range of the distribution is constant in the case the interval is less than 9 hours. This means that the reliability of a parameter estimated by a result of measurement at intervals less than 9 hours is nearly equal to the value for 9 hours interval.
In order to study difference of the above character between the wind velocity and the response of ships to ocean waves, records of wave induced stress measured on a pure car carrier and a bulk carrier are investigated by the same method. By the study, the same relation between the interval and reliability is also found in the case of wave stress. The only difference between them is the critical interval for the stress amounts to above 12 hours.
It is concluded by the above study that the optimum interval of measurement of the response is 8-12 hours. The value may be increased by more detailed study.

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This paper discusses the influence on long-term predictions of ship response by using Global Wave Statistics data (GWS) with special emphasis given to its scatter diagram rounded by one thousandth (1/1000), and it presents a method for correcting round error of GWS. GWS standard scatter diagrams of significant wave height and zero-crossing wave period are corrected to a round number of 0.01/1000 by fitted with a model of the conditional log-normal distribution for zero-crossing wave period in some sea areas. The statistical characteristics of wave data for those sea areas are calculated, and long-term predictions of hydrodynamic pressure, relative bow ship motion and deck wetness are presented. On the basis of those numerical results, further investigation for standardizing the format of wave data are discussed.

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A computational method for analyzing response of large floating structures which are supported on multiple columns was proposed by a part of the authors. In this method, hydrodynamic interaction is taken into account as well as flexibility of the structures.
We extend this method to similar structures with braces and/or lower hulls. The applicability is confirmed through tank test results, using a model whose upper structure is supported on 45 columns with braces at the bottoms, and also by previous experimental results of a simpler model. First, we show that present method can fairly predict the responses of large floating structures in waves. Second, we show that the characteristics of responses can be explained by those of wave exciting forces or pressures to some extent. Hydrodynamic interaction effects in designing large floating structures are also discussed. It is concluded that hydrodynamic interaction effects are negligible from the viewpoint of designing when the ratio of the length between columns to the diameter of the column is over 4.

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When a offshore structure is constructed from several part-structures, the construction operations, such as mating, positioning and transportation of those structures to the objective point, must be carried out under various disturbances. This paper presents learning trajectory tracking control when the structures are repeatedly transported along the objective trajectory under unknown steady state disturbance.
Corresponding to premise mentioned above, a learning controller which consists of both feedback controller and feedforward controller is proposed. The controller improves its feedforward control force every time it tracks the same objective trajectory by learning unknown disturbances from the difference between the objective trajectory and previously realized trajectory.
In this study, simulation and basin test, using a model of a semi-submersible are conducted. The learning controller showed good performance in both results of simulation and basin test in the field of unknown disturbances.

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In designing a ship control system, the development of a versatile system is well anticipated for various ship and actuator type application. The authors develop a versatile control system based on nonlinear actuator force distribution method, and the effectiveness is confirmed by numerical simulation and tank test. In addition to reference control and nonlinear control functions, the disturbance compensation control for both determinate and undeterminate disturbances and a joystick manipulation function can be easily applied, so that the ship has such various control modes as auto speed keeping, auto piloting, auto position keeping, auto tracking, and berthing.
The developed system has a function expandability and a wide application for ship control system design. In the paper, the control logic, numerical simulation results and a part of tank tests are shown.

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Recently optimal regulator theory has been applied to the control of the manoeuvring motion of a ship. But it needs accurate mathematical model of the controlled object and it has not sufficient controllability to the nonlinearity of the controlled object. By these reason it was tried by one of authors to apply the Learning Feed-Forward Control (LFFC) system to the follow-up control to the desired value for the ship manoeuvring motion. The LFFC system is a kind of the neural network model. It is not a multi-layered perceptron type but a kind of an adaptive filter, and it has a dynamic quality. The system is tuned with the feedback-error-learning method proposed by Kawato and others. It was recognized that the LFFC system had a good controllability and the problem in the optimal regulator system mentioned above was solved.
The servo mechanism needs both an ability of the follow-up control to the desired value and that of the compensation of the influence from the disturbance. So in this paper it is tried to apply the LFFC system to the compensation of the influence from the disturbance to the ship manoeuvring motion. And for the basic study the following case is investigated with the computer simulation. That is, the heading angle of the ship is controlled with the bow thruster in the wind disturbance.
It becomes clear that the system has a good controllability to the compensation of the influence from the disturbance due to the self-tuning ability and a feed-forward loop.

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Research on the development of Super High-Speed Container Ship was already reported. In that research it was pointed out that there are some weak points on the transverse stability and turning ability. So, for overcoming these points, we considered vertical active fin under the middle bottom of the ship, and confirmed its effectiveness by model experiments in directional spectrum waves generated in the towing tank of Yokohama National University. Furthermore, we developed numerical simulation program for estimating coupled Roll-Sway-Yaw-Surge motion on a calm water and compared with experiments. One example showing the increasing the turning ability using vertical fin is also presented.

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An a posteriori error estimation method for the finite element solutions of two-dimensional elasto-plastic problems is proceeded based on the theory of element-wise error analysis in two and three dimensional elastical problems developed by the authors. The error is estimated element by element with an 8-node element and the finite element elasto-plastic solution is modified after getting the error force of FEM for each element with considering the continuity of stresses on the node which connects the adjacent elements. A special technique is presented to carry out the error modifying procedures after each increment step including loading and unloading steps. The unequilibrium of applied error force for each element is overcome with adding two low stiffness spring elements to each node of the element. The error energy norm and its distribution are obtained, and a very accurate stress solution compared with the 8-node results of FEM is gotten by acting estimated error force to each element in two numerical models.

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The structural analysis of large scale structures such as ship is usually carried out in several different stages, using different scales, and using different type of finite elements, varying from whole ship, cargo holds and to the detail structures. In conventional practice, the finite element models for different analyses are generated separately from different geometric models.
In this work, the method to generates finite element models for different analyses is considered. It is necessary to define the model so that it can exclude some parts of the structure which is not important in the analysis. Also, the model geometry need to change dimension depending on the analysis required, such as beam, shell, solid.
“Part Name”, which indicates whether the parts with that name are extracted in certain analysis, and “Part Type”, which indicates what type of finite elements are used to model the parts, are defined. Also, parentage relations between parts are defined. The techniques to transform geometry of the parts that are defined as shells into beams or into solids are developed. Finally, the interaction analysis techniques between beams, shells and solids are developed to generates parts that are used in mesh generation.
Using these techniques, the system is developed to generate finite element model for different structural analyses levels. The examples of generated finite element models of tanker structure in several analysis stages are shown.

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A new Finite Element by Source method (FES) is developed by the authors. FES which has flexible geometrical shape is composed by nodes distributed on the element boundary and sources distributed out of the element boundary. The relation between the density of sources and the boundary condition at the nodes is obtained from the combination of the fundamental solution such as Kelvin's solution for static elastic structural problems.
According to this procedure, we can perform numerical analysis dealing with complex configured structures such as ship with further less mesh comparing to the traditional Finite Element Method and we can obtain more accurate results.
This paper describes a fundamental theory and formulation of FES. Some examples for static elastic structural problem using 2D plane stress FES and 3D solid FES are also presented in this paper comparing to the theoretical solution or numerical results by using traditional FEM.

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It is known that the effect of fluid vibration upon structural one is very large, therefore fluid-structure coupling analysis method which combine the added mass matrix into FEM have been used since many years ago. But there has been no approach to such analysis method using experimental modal analysis. It is necessary to estimate vibration level on actual ships, and to examine the validity of the FE models.
In this paper, a new idea of reduced added mass matrix is defined and described completely, and the validity of the idea is verified by comparing with Matsuura's theory. Then combination analysis of the experimental modal analysis and BEM is described using the reduced added mass matrix, and the validity of the combination analysis method is verified by comparing with some experiments in the deep water and the shallow water. As the result of the validity, vibration level on actual ships in the deep water can be estimated by using this new method.

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Dynamic characteristics of stiffened rectangular plates which are in contact with water is studied. The numerical analysis is performed by use of energy method where vibration modes of stiffened plate and fluid velocity potential are developed using harmonic wave series. Interaction of added mass of water of adjoining stiffened plates are investigated.

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This paper describes experimental studies on the horizontal impact of flat plates falling onto a still water surface with a trapped air condition. In order to make clear the effects of the mass of falling body, plate breadth, and impact velocity on the maximum impact pressure, we have carried out the experiment of plate breadths of 0.2, 0.4, 0.6 m, in addition to those of 0.25, 0.35 and 0.5 m done in 1983.The results of the data analysis confirmed the following effects ;
(1) The maximum pressure rises in proportion to the parameter K_m,
K_m=1/ (1+M_w/M)
where, M is the mass of the falling plate and M_w is its added mass of the water,
(2) The impact duration depends on B/V₀, where, B is the breadth of plate and V₀ is the impact velocity. Based on these facts, we have developed the following empirical formula to predict the maximum pressure and the impact duration Δt,
P_max=M_wK_mV₀/BΔt
M_w=π/8ρ_wB²
1/Δt=0.144 × 10³ (V₀/B) ^0.673
where, V₀ in m/s, B in m, Δt in s.
The agreement between experimental and predicted results is remarkably good. The formulae developed including the evaluation of the impact duration are suitable for the design of structures exposed to water impact.

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High speed ships like TSL (Techno Super Liner) have been developed recently for realization of modal-shift of transportation in Japan. The hull surfaces of these high speed ships are in contact with a rapid flow of water. These panels are so thin for light weight that the possibility of dynamic instability such as panel flutter phenomenon should be studied.
The purpose of the present study is to investigate the possibility of dynamic instability of the outer panels of the ships. Finite element approach for plates and boundary element approach for surrounding fluid are used for the analysis of the fluid-structure interaction problem. The numerical code ISAP-TSL developed is used for investigation of the effect of mass ratio, boundary conditions and plate shape on the critical speed of flow and the reduction of natural frequencies. Moreover the difference between the dynamic characteristics of a plate and those of a continuous plate is discussed from the numerical results as well.

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Recently huge floating structures such as floating airports with length of a few kilo-meters are under planning. Those structures are relatively very thin compared with their plane areas. The study on the structural behavior of such huge floating structures under dynamic loads like wave loads were carried out by Toki and Ende. Most of the researches so far, however, took up structures with footings instead of bare pontoon-typed structures which are more fundamental in shape. In this paper authors first summarized Toki's solution in a more comprehensible form with due corrections of minor mistakes.
Then authors applied the formulas to a pontoon-typed floating structure.
Finally authors replaced the same structure with an equivalent rectangular flat plate to apply finite element method.
The obtained modes and natural circular frequencies were compared with those of a beam analysis.

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In structural optimization, the computational cost increases rapidly as the number of design variables increases. In this paper, the multi-level optimization is proposed, which decreases computational cost. Moreover, the multi-level optimization is more natural way of carrying out optimal structural design in the distributed design practice in which different engineers design different parts of the structures.
The optimal designs of ship structure that minimize weight subjected to strength constraints are derived. The equivalent thicknesses of the stiffened plates are taken as global design variables that are used in overall optimization, and the detail sizes of stiffened plates are taken as local design variables that appear in single subsystem. The transformation of the constraints into objective function is carried out to include local design variables in the objective function, which is necessary for multi-level optimization.
By comparing the single level optimal design and multi level optimal design, it was shown that in the multi level optimization the number of iteration to reach optimal design decreases dramatically, and the computational cost also becomes quite small.

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In the case of a grounded ship, tears longer than half the ship's length may be found in its bottom. For this reason, a grounded tanker leaking heavy pollutants poses a serious threat to sea environments. Although researches on collision are intensive, very little is known about structural damage in the event of grounding.
This paper aims to contribute to the theoretical prediction of failures of bottom structures. The scenario under consideration is bottom raking. A method considering primary energy absorbing mechanisms is proposed to predict the structural strength against this kind of damage. Along the longitudinal direction, periodic structures extend nearly all the way from collision bulkhead at bow down to stern, so the resistance of bottom structures is assumed also to be periodic, with tearing and denting failures being predominant in the damage process, occurring alternately.
If a seabed reef impacts on a transverse structure, the bottom plate immediately behind the transverse structure tends to bulge out of its original plane, causing the denting of plate. Emphasis of this paper is on introducing and analyzing this failure mode. Through application of plasticity theory, a closed-form solution is derived for predicting the strength of a dented plate. By checking against existing experimental researches, the proposed kinematic models and the obtained formulas can be verified.
It is found that resistance of bottom plate is proportional to t^1.67 when it is dented, and proportional to t^1.5 when it is torn.

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This is the proposition of a theoretical model for the calculation of the collision strength of side structures. The emphasis of the analysis is on the behavior of side plate. Through introducing a new kinematic model, the deformation of side plate is modeled and formulated. It is found that deformation shape of the plate is a square. Webs are assumed to remain undeformed until it is compressed by the penetrating indentor. Beyond that, it fails into a multi-waved collapse shape, and the deformation of outer plate spreads to the neighbouring webs.
This progressive failure process is checked against FEM analysis and existing experimental researches, which show that the present method is effective.
Also, ship-ship collision problem, which assumes that both striking bow and struck side collapse during collision, is considered. At a particular penetration, either stricking bow or struck side is assumed to be rigid if it is stronger while the other is assumed to deform. Calculation based on this method shows that this method gives a more realistic predication of energy absorption during collision because it takes the deformation of stricking bow into consideration.

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In the collision of hard and sharp bows breaking of ship side structures starts from the collided point of bow, while in the collision of soft and rounded bows breaking is likely to start from the supported point such as bulkhead or transverse web frame. In the case of breaking from collided point stretching of ship side structures is followed by crack propagation, so absorbed energy should be evaluated in consideration of crack propagation.
In this paper to develop an evaluation method for breaking from collided point, double hull panel models, which are typical as ship side structures of VLCC, were destructed with the indentation of rigid bow model which was pushed dynamically as well as statically. In the first crack initiation condition was investigated by FEM simulation using fine mesh solid element models and crack initiation was found to be estimated with the ductile damage parameter which consists of equivalent plastic strain and stress triaxiality. Then crack propagation condition was investigated by FEM simulation using coarse mesh shell element models. It was found that reduction of the reaction force due to crack propagation could be simulated by finding the elements adjacent to the crack and reducing the failure strain for those elements.

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This paper deals with development and application of a simple dynamical model which accurately simulate the buckling/plastic collapse behaviour of a plate subjected to cyclic inplane load accompanied by complex unloading and reloading. This model is based on the results of elastic large deflection analysis and rigid plastic mechanism analysis in analytical forms assuming a simple deflection mode.
The proposed model is implemented into a beam-column element as one of the fibre to analise buckling/plastic collapse behaviour of a continuous stiffened plating subjected to thrust. The beam-column element is composed of a stiffener and attached plating. The fibre representing the plating is assumed to behave according to the proposed simple dynamical model.
Applicabilities of the new plate model and the new beam-column element are demonstrated through comparison of the calculated results with those by the ordinary elastoplastic large deflection FEM analysis.

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A series of elastoplastic large deflection analyses of stiffened plates under thrust is performed using nonlinear finite element method, and the influence of cross-sectional geometries of stiffeners on the buckling/plastic collapse behaviour of stiffened plates is discussed. Interactions between stiffener and plate element are considered by modeling both the components with shell finite elements. It has been found that :
(1) Local buckling strength between stiffeners, inplane rigidity after the local buckling and ultimate strength are significantly increased by a flexural-torsional rigidity of stiffeners.
(2) Elastoplastic secondary buckling takes place after initial local buckling for all the stiffened plates considered here.
(3) Larger ultimate strength can be attained by stiffeners with web of smaller depth-to-thickness ratio. However, a load-carrying capacity after the ultimate strength tends to decrease more rapidly, because of the formation of overall buckling collapse mode.
(4) Stiffeners with web of larger depth-to-thickness ratio are likely to collapse in local torsional mode, resulting in a lower ultimate strength. However, the decrease of load-carrying capacity after the ultimate strength is not rapid, because of a wide spread of collapsed region over the plate.

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Thin walled structures such as ships and offshore structures are composed of many stiffened plate panels. To analyze these structures efficiently, “Idealized Structural Unit Method (ISUM)” was proposed by one of the authors. In the first report, eigen-function and plastic node method were introduced to calculate a plate panel, which exhibits complex behavior especially among some ISUM elements. Plastic node method is not so satisfactory in reference to computation time and accuracy for analysis of long rectangular plates. To improve them, new plate element is developed in this study, using selective eigen-functions for large deflection and sectional yield conditions at each integration points for plasticity. The stiffness of this element is calculated by numerical integration using the trapezoidal integration method. It is satisfactory that the number of integration points is only 5 × 5 for a entire square plate. This method can efficiently and accurately analyse the behavior of rectangular plates with initial imperfection such as initial deflection and welding residual stress. Necessary computation time is very short for any aspect ratios and the accuracy is very high in comparison with FEM. This element is a new efficient rectangular ISUM element.

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This paper presents a simplified analysis of the dynamic behavior of a large floating structure as a working model for decision making model in the structural design and discussion on the design of structure is also presented. The model of the structure in the analysis is a beam of finite length on elastic foundation with damping. This modelling is the most simple one but satisfactorily accurate to discuss the global behavior of the structure. Analytical solution of this model is derived and from the discussion, it is shown that the range of natural frequencies are higher than the heave natural frequencies. Quasi-static solution is compared with the dynamic calculations. At lower frequency, static solution gives relatively accurate prediction for the deflection and stress of the structure. With the analyses, design philosophy of the structure is discussed mainly from the view point of resonance avoidance design and selection of structural characteristic parameters.

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The water depth of the underwater development such as deepwater drilling and exploitation of submarine oil and mineral resources is becoming deeper so that the structures must be installed by remote control. In such a operation elastic response of a large-scale and flexible structure must be restrained by active control technology.
In water, uncertainties of parameters due to estimation error and non-linearity of hydrodynamic force make the control result worse. Adaptive control, which improves control gain by identifying parameters of system online, is expected to resolve this problem.
In this paper, control of structural response and rigid body motion is formulated adopting an adaptive control algorithm which renews optimal control gain while estimating parameters of system with recursive least squares algorithm. Comparisons of control result with optimal control are made. With respect to regulation control and tracking control of a flexible experimental model, simulations and experiments are performed. The rigid body motion and elastic response are more successfully controlled by adaptive control than optimal control. In adaptive control, the initial values of feedback gain and estimated parameters of system, which are improved during the course of control, are set up to optimal control gain, that is, the best estimated values at the starting of control, so that transient response and elastic deformation are well deteriorated.

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