In this paper, a method of analysis for steady viscous flow past a body in an infinite domain is proposed on a matching method of inner and outer solutions which may be regarded as an extension of the method of superposition proposed by the present authors.
Viscous flow under consideration are described by the Navier-Stokes equations and the equation of continuity together with appropriate boundary conditions on the body surface and at infinity. It is, however, difficult to solve this nonlinear boundary value problem in an infinite domain, although the finite-element and finite-difference methods are effective tools for solving the Navier-Stokes equations in a restricted domain. If the far field solutions of the governing equations are given properly, the domain of numerical analysis for the Navier -Stokes equations is reduced to the finite one by the use of the method of matching inner and outer solutions.
Assuming that the disturbance caused by an obstacle is small, Oseen linearized the Navier-Stokes equations, and the resulting equations can be solved in an analytical form. Oseen's approximation becomes highly accurate at a far distance from the body. Moreover, in the case of two-dimensions, Imai proposed an asymptotic solution on the basis of the Navier-Stokes equations by the successive approximation.
In the present method, the infinite domain of analysis is divided into the inner and outer domain by introducing a fictitious surface. Oseen and Imai's approximate solutions can be used for the outer domain. The inner solution is given by solving the Navier-Stokes equations by the finite-element method and is matched on a fictitious surface with the outer solution. The present method is applied to two-dimensional and axi-symmetric problems including the practical analysis of the force acting on the mushroom anchor in the mud which can be regarded as viscous fluid. The validity of the present method is illustrated by numerical studios on the flows past a circular cylinder and a sphere whose results are in fairly good agreement with experiments by the previous authors.

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It is confirmed that a wave pattern and a wave making resistance at large Reynold's number are determined by the potential component of the flow field, and that the effect of the rotational component is negligible, by means of a linearized theory for ship waves in a viscous fluid under assumptions of Oseen's equation and equivalent laminar wake. In order to know a modified potential flow, boundary layer and viscous wake, as well as wave pattern, are measured. It is discovered that turbulence occurs beside and behind a ship near the free surface, and that it originates another sort of viscous wake. Making use of measured displacement thickness, the wave pattern and the wave making resistance are calculated and compared with measured values. A qualitative but plausible agreement is obtained.

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Non-linear properties of wave making resistance of wide-beam ships are studied with the sound examination of their physical phenomena to show the working limit of “linear” and “low speed” wave making resistance theories.
Vast experiments on series models of wide beam ships are undertaken including wave pattern analyses, flow field analyses and momentum loss measurements. Calculations of wave resistance, wave profiles and disturbance velocity distributions are carried out. From the examination of these analyses following three conclusions are obtained.
1) Effect of beam and draft upon wave making resistance of wide beam ships does not subject to the law derived from any present wave resistance theories. It is mainly attributed to the existence of non-dispersive waves tentatively called “free surface shock wave” in reference 2) and 3).
2) Free surface shock waves contribute to wave making resistance as a significant portion of momentum loss measured behind the ships.
3) The low speed theory developed by Baba is not always effective for hull form design. Its application should be limited within certain dimensions of hulls even in low Froude number region.

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The low speed wave resistance theory developed by Baba⁴⁾ and Maruo⁵⁾ seems to be a promising theory to predict the wave resistance of conventional ships, because it includes the nonlinear effect of the free surface condition. The wave resistance curves calculated by the low speed theory, however, have large humps and hollows, and they do not agree with the measured^{7) 10)} .
In this paper, a refinement of the low speed theory is discussed by imposing the more accurate hull surface condition. The wavy source distribution added to satisfy the hull sruface condition is obtained numerically, and the wave resistance, the hull side wave profiles and the velocities around the hull surface are evaluated. The results coincide fairly well with the measured values, especially the humps and the hollows of the calculated wave resistance curves are remarkably reduced.
It is ascertained that the added source distribution plays an important role to improve the low speed wave resistance theory, in spite that its strength is one-order smaller than that of the double model source.

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Concerning development of propulsive performances for high-speed-catamarans, the most significant influence can be given by reduction of the wetted surface area. For this purpose, concept of the air cushion catamaran has been proposed by the authors in 1976, however, augmentation of the wave resistance due to cushion pressure has been remained in obscurity.
The intent of this paper is twofold. One of the purpose is to establish an experimental method for determination of the wave resistance due to cushion pressure. The other purpose is an evaluation of the resistance characteristics of air cushion catamarans. As a conclusion, it is shown that a remarkable power saving can be expected by developments of air cushion catamarans.

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This paper presents a method to predict ship wake from measured model wake by applying the theory of two-dimensional turbulent wake. From basic investigations on two-dimensional wing, the following physical properties of turbulent wake were made clear with respect to the scale effect on viscous wake.
(1) The width of wake is in proportion to the momentum thickness and not to the scale of model and ship.
(2) Velocity distribution in wake varies downstream as a function of non-dimensional distance divided by momentum thickness.
(3) The value of the wake peak is affected significantly by the difference of the velocity profile at the stern frame between model and ship.
In the well-known Sasajima-Tanaka's method only the first item of above is taken into account for scaling the viscous wake.
The method for predicting ship wake was developed in view of the above properties. Applicability of the method to the wake of ship was examined by use of the geosim models of a cargo ship and it was shown that the method presented here provides reasonable results and can be applied as a practical means for predicting ship wake.

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Assuming that no appreciable separation of either two-dimensional or three-dimensional type occurs at the stern of a body or a ship, the scale effects of the boundary layer and wake have been studied with the purpose of finding the Rn-dependency of the wake distribution at propeller location. The Rn-dependency on pressure resistance has been also investigated.
It is pointed out the scale effects of the velocity distribution of the boundary layer and wake as well as the pressure resistance may be slightly different from each other and also between a two-dimensional body, a body of revolution, and a ship. The upper and lower limits of Rn-dependency are described for the wake distribution and the pressure resistance.

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This paper presents the results of model tests performed in the towing tank to investigate the effect of afterbody shapes and also highly skewed propellers on propulsion and propeller excited vibratory forces.
The variations of the afterbody shapes were investigated for three model series based on a shallow draft C_b=0.7 gas carrier. One of the three is the parent model, which has a conventional single screw mariner stern. The other two models have a U-shaped stern form with somewhat different degrees of U-shape. The wake measurements have shown that a remarkable reduction of the non-uniformity of wake was attained by both U-shaped sterns.
The highly skewed propellers also showed remarkable effectiveness in reducing the propeller excited vibratory forces.
Both the highly skewed propellers and U-shaped sterns applied to this type of ship gave no appreciable effect on propulsive performance.

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In this paper, the authors investigate viscous effects on the characteristics of two-dimensional hydrofoils.
The pressure distribution on a foil section in non-cavitating flow should be considered before its cavitation characteristics study. Theoretical results which neglect viscous effects do not always agree with experimental ones, especially at a high angle of attack or at thin hydrofoils. Moreover, recently Arakeri et al. reported that laminar separation bubble played an important roll on the cavitation inception.
From these considerations, it is very important to study on the viscous effects of the foil sections-specially on the mechanism of separation bubble. Separation bubble is classified into two types. One is called “short bubble” which can reattach to hydrofoil surface (non-burst type). The other is called “long-bubble” which can't reattach to the foil (burst type).
The authors investigated their nature and mechanism in detail, and verified the effects of separation bubbles on the hydrofoil characteristics. An empirical classification method of the separation was proposed, which can be used to evaluate the viscous effect of any hydrofoil sections. Then, experiments were performed to support this empirical method on 5 hydrofoil sections. A good agreement between empirical method and experiments was obtained.

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In this paper the authors describe investigations of the detailed cavitation structure, those are cavity length and its fluctuation, cavity shape and volume, void ratio in the cavity and velocity and pressure distribution around a cavitated foil. The following six foil sections were tested :
Non-burst type : NACA 0015, NACA 16-015, NACA 4415
Burst type : MAU 0.6r, MAU 0.9r, 4% thickness Plano-Convex
Results are as follows :
(1) At a bursted foil, a vortex cavitation occurs first in the shear layer of the leading edge separation zone, when the cavitation number is greater than-C_Pmin of the foil. This vortex cavitation is very similar to the cloud cavitation. Decreasing pressure, it changes to the ordinary sheet cavitation.
(2) Sheet cavity is trapped in the separated zone, which does not coincide with the lowest pressure zone. Consequently a region, whose pressure is lower than vapour pressure, does exist at the upstream of the sheet cavity on a foil.
(3) Cavitation characteristics of foils can be classified into two categories according to whether the laminer separation bubble will burst or not. Cavity length of a bursted thin foil can be calculated by the linear closed cavity model theory. On the contrary, the cavity length of a non-bursted foil agrees with the result of “lift equivalent method” (empirical method).
(4) Cavity volume can also be classified by the condition of burst or non-burst. Empirical formulas are proposed from the present experiment.

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The role of cavitation nuclei on sheet cavitation inception was investigated experimentally for three axisymmetric test bodies, by using a nuclei generator.
With no added nuclei, the incipient cavitation number σ_i showed a large scattering, whereas, when nuclei were added, the scattering became fairly small and σ_i converged to the upper limit of σ_i with no added nuclei. It also coincided with the desinent cavitation number σ_d.
By using Laser Doppler Velocimeter, the velocity distribution on axisymmetric bodies were measured, and good agreement was obtained with calculated results. The pressure coefficient at separation point c_ps was also measured by LDV and was compared with σ_i, which confirmed the result obtained by Casey that σ_i is equal to, or slightly less than (-c_ps).
A hypothesis for the mechanism of sheet cavity inception was made, taking account of the surface tension of nuclei and the pressure fluctuation at the reattachment zone of a separated flow. It explained, at least qualitatively, the dependence of σ_i on u_∞ and the relation between σ_i and (-c_ps).
By controlling the amount of added nuclei, the radius of nuclei which contribute to the sheet cavity inception was estimated to be about 20μm.

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In a cavitation tunnel, it is difficult to produce so intense cavitation that may cause erosion on the back of a propeller blade or a hydrofoil. To make cavitation erosion experiment possible, some special experimental techniques should be derived such as aluminium erosion test, paint test etc.
Authors have studied the effect of cavitation number, fluid velocity, size and material of hydrofoil on the cavitation erosion by aluminium erosion test and paint test.
This paper reports the result of those tests for three types of two-dimensional hydrofoils (NACA-0015, NACA-16015, and NACA-4415). The erosion intensity is more influenced by the unsteadiness of cavity than the difference of hydrofoils. When the fluctuation of cavity is little, a peak of erosion is clearly observed at a little downstream position of the cavity end. On the contrary, when the fluctuation is large, the erosion peak becomes lower, but the range and intensity of erosion becomes wider and more intense.
This paper also treats the calculation of erosion pit formation by the axisymmetric elastic-plastic analysis using the finite element method. The rim of a pit, which is sometimes observed at an actual case, can be successfully reproduced by the calculation of the simple compressive load on the solid surface.
Based on those analysis, a new estimating method is proposed to scale the erosion amount for various materials.
Finally the influence of mechanical properties of material on the erosion is discussed.

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Dr. Hanaoka's theory and Prof. Nishiyama's theory are well known as a linearized theory of cavity flow past a hydrofoil in which a source-sink method is applied. Comparing with experimental data of thick hydrofoils, the calculated thickness of cavities is about two times of experiment, although close agreement is obtained within comparative calculations.
Authors have attempted to calculate the characteristics of partially cavitated thick hydrofoils by solving the non-linear equation expressing the velocity on a thick hydrofoil in which a shape of cavity is included as an unknown parameter.
Herewith, the method for solving the non-linear equation is presented, and numerical calculation results are compared with experimental data for a shape of cavity and pressure distribution on a partially cavitated hydrofoil.

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So far it has been known little about the problem for a 2-D general shaped body on free surface which makes arbitrary motion in time from t=0, though the problem might have broad application in ship hydrodynamics.
As in the counterpart problem in the frequency domain appeared in the “strip method” or the “slender ship theory”, the problem in the time domain may have many solving methods. Among them the integral equation method seems to be most powerful. However, in solving the problem by source distribution method, one peculiar phenomenon occurs, that is, the irregular frequency effect in the time dependent source. This peculiarity is analysed theoretically by investigating the counterpart problem in the frequency domain.
A procedure to avoid this peculiarity is presented, which is inherited from the results of Sayer & Ursell⁴⁾ and Ogilvie & Shin.⁵⁾ And a few attempts to the problem, making use of the integral equation methods, are illustrated in theories and numerical calculations.

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In the preceeding paper¹⁾ the author proposed an inviscid model of discrete-vortex shedding for the oscillating fluid flow around the flat plate. It was proved to be useful for understanding and evaluation of the nonlinear dependence of the hydrodynamic forces on the amplitude of motion.
This method is applied to the flow around the periodically rotating flat plate. Then the added moment of inertia and moment of drag coefficients are compared with the experimental values which were also obtained by the author. The results show very good agreement.

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In the former report we obtained the so called equivalent linearized roll damping coefficients by the experiment of forced irregular roll with large amplitude. In this report, we applied the obtained coefficient for predicting ship roll time history in high irregular waves using various method and compared with the results obtained from experiments performed in the towing tank.
And after that it is shown that the calculation of roll time history by the equivalent linearized method (E. T. method) will be preferable for predicting the order statistic of roll amplitude especially maximum roll angle.

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In this paper, a synthetic method for predicting the speed loss of a ship in waves by taking account of the main engine characteristics is shown. In determining the ship speed in waves, two factors are considered : the nominal speed loss due to added resistance caused by wind and waves and the deliberate speed loss by the captain's command in order to prevent severe ship motions.
An example of the calculations by this method for 175m length single screw high speed container ship equipped with diesel engine is also presented.

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In recent years, spip owners have been very much interested in the method of achieving the more economical operation of their ships than ever. This paper states the service speed, which cannot be disregarded in trying to solve the above matter. The service speed is for tankers on the route between Persian Gulf and Japan, and the method of presuming the service speed is mentioned here under. First, each element such as fouling, aging, current and wind frequency is extracted from the ships logbook data and the wave spectrum equivalent to that at the actual navigating conditions is predected from loss of speed of actual ship and theoritical added resistance due to wave.
Further, introduce fouling area into the concept of effective depth and nondimensional added resistance values due to fouling are within some limit with no relation to ship's size.
Aging affect docking interval and we propose that equivalent sand roughness which was estimated from analysis of each ship's added resistance is applied to calculated added resistance due to aging.
At last, each calculated element is assembled and the service speed on each voyage of a certain ship is figured out by presumption.
This method of presuming the service speed is proven effective by means of comparing it with the actual data.

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The procedure of calculations by the use of pulsating pressure distributions on a free surface is applied to three dimensional motions of a box-shaped floating structure of shallow draft in regular waves. Integral equations are solved numerically, and added mass, damping coefficient and wave exciting force are computed. The dependence of them on various length-to-beam ratios is shown.
Motions and hydrodynamic pressures in regular waves are also computed, and the results of the computation are compared with those of the experiment in which a model of the box-shaped structure, corresponding to a floating dock, responds freely to the waves. It is observed that the computed values are in excellent agreement with the measured ones.

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This paper deals with a method estimating theoretically effects of breadth and depth of restricted waters on the radiation forces, the wave exciting forces and the amplitudes of ship motions in regular head waves.
The approach used here is based on the strip theory and the slender body theory. Hydrodynamic forces on a ship model without the tank wall effect are assumed to be given by the strip theory and the reflections of waves generated by a ship model oscillation from the tank walls are assumed to be estimated by applying the slender body theory. In the next place, the amplitudes of ship motions in regular head waves are obtained by using those hydrodynamic forces. Finally correlation works between the theoretical results and experimental ones are done. It becomes clear from this investigation that the theoretical results obtained by this method are in good agreement with the experimental ones except for a damping coefficient for heave in very shallow water.

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Recently, the size of floating structures has become greater, and in the near future, huge floating structures, such as offshore floating plants and floating airports, seem to be brought into practical use. In the cases of these structures, elastic deformation due to waves may be of the order which cannot be neglected in comparison with the motion as rigid body.
In this paper, the author dealt with the problem of wave-induced behavior of huge floating structures theoretically, regarding them as the so-called “uniform beam on elastic foundation”. Model tests were carried out selecting two prototypes, and fairly good agreement was obtained between measured results and calculated ones. The theoretical calculations were also made for series prototypes to examine the effects of the length and rigidity on the behavior.
As the result, it became clear that the effect of elasticity should be taken into consideration to evaluate the wave-induced response of floating flat structures far larger in size than the existing ones.

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In the previous paper, characteristics of snap loading were studied by the experimental and theoretical investigations on vertically taut moored platforms subjected to regular waves. Since then, the wave exciting tests on vertically or splayed taut moored platform models have been conducted to clarify the more general dynamic characteristics.
In this paper, the characteristics on motions of the platforms and the wire tensions are discussed from the comparison of the experimental results with the theoretical linear frequency domain analyses on the models mentioned above. As a consequence of this discussion, possibility of occurence of several kinds of remarkable nonlinear responses besides snap loading are pointed out, which are quite different from ones obtained from the linear frequency domain analyses. These are considered to be divided into three kinds : nonlinearities at primary resonance, sub-harmonic resonance and super-harmonic resonance. Some considerations are finally given for the approximate estimations of these nonlinear responses.

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The performance of Salters Duck as an energy extractor from ocean waves is studied. numerically on the basis of linear theory of surface waves and floating bodies, and experimentally by making use of hydraulic power transmitting devices. Quantities of engineering interest such as hydrodynamic forces, induced motions, efficiencies for extracting energy from ocen waves, transmitted waves and drifting forces are presented and discussed for fixed and for rolling only. The authors showed that the linear theory would be held for extracting energy from ocean waves as the first approximations.

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It is well known that there exists the hydrodynamic interaction between ship's hull and rudder which may have a remarkable effect on ship maneuvering. By many experimental investigations of lateral force acting on a ship during maneuver, it is found that the hydrodynamic force which is induced on the main hull of a ship by steering its rudder comes up to about 30% of rudder force. At present, however, the effect of presence of main hull on the rudder force is not yet made clear. The main aim of this paper is to deal with the latter problem.
Assuming that the hull and the rudder can be replaced by a low aspect ratio rectangular wing and its flap which is separated from the wing, the integral equations based on nonlinear lifting surface theory are derived, and the results of numerical calculation are compared with the experimental data. The calculation values of normal force acting on rudder and main hull agree fairly well with the experimental ones. Furthermore, by comparing tine hydrodynamic forces of rudder and main hull obtained in hull-rudder system with those obtained when rudder and main hull exist independently, the authors discuss the hull to rudder interaction.
Consequently, it is shown that additional hydrodynamic force due to steering is induced on the main hull, but on the contrary, the rudder effectiveness is reduced compared with that in open water.

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It has been passed more than ten years since so-called unusual phenomena in manoeuvrability were first reported by Nomoto. At the early stage of research, the phenomena were regarded as the unusual scale effect, because it appeared only in model ships. According to the tendency of growing the fullness of ships, however, these phenomena slided even into real ships. Besides, quite many types or varieties were appeared from the results of free-running tests.
For these several years authors have treated many cases appeared on either model ships or real ships, carrying out free-running tests, captive model tests or full-scale trials. Some of these results were published.
Through the detailed examination of these experiences, the comprehensive explanation of the phenomena is made as the main purpose in this paper.
It is known from the captive model tests that in model ships with the phenomena the measured hydrodynamic forces contain two different characteristic forces : one is the ordinary force proportional to the motion of ships and the other is the abnormal force which appears only in ships with the phenomena. This abnormal force is found to originate from the flow separation at either side of the stern by the flow observation and divided into two main types ; binary type and breakline type (see Fig. 5).
Although this abnormal force is the direct cause of the phenomena, such many types of the phenomena don't seem to be derived from only the two types of the abnormal force. Another factor closely relative to the phenomena is directional stability of ships. Almost all the unusual phenomena ever found are shown to be well explained by the combinations of directional stability with two types of abnormal force.

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In this paper, a new mathematical model describing manoeuvring motions of a ship is presented according to the detailed investigation of captive model tests. This model, based on the method proposed by the subcommittee of JTTC named Group-MMG, is composed of individual characteristics of hull, propeller and rudder and their interactions.
First, the model for longitudinal hydrodynamic forces is dealt with.
Second, the method to describe the hydrodynamic forces concerning to rudder is treated. A simple model consisting of open characteristics of rudder, inflow angle and velocity at rudder is proposed.
Two problems as to lateral hydrodynamic forces acting on hull are then argued. One of them is the matter of nonlinear terms and, from the practical point of view, third order terms with rate of turn and swaying velocity are recommended. The other factor is the fin effect of propeller, and it is verified not to be negligible for manoeuvrability.
Last, comparing the free-running results with estimated manoeuvres calculated by the present model, satisfactory coincidence is obtained. Consequently, the proposed model describing manoeuvring motions of a ship is found promising.

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The numerical solutions of the existing lifting surface theories do not converge at the parabolic wing tip on account of the singularity. The restriction in the existing theories can be removed by using the new integral equation presented by Dr. Hanaoka.
In the first reports, employing the new integral equation, the range of validity of propeller lifting surface theory was extended to include the tip of blade, for the case of the steady propeller.
Marine propellers operate in non-uniform flow, so the calculation for the unsteady propeller is important. In the second report, calculation is performed for the unsteady propeller, employing the new integral equation.
Following facts are revealed by the results of the numerical investigation. (1) Accurate solutions for the hydrodynamic load distribution near the blade tip of unsteady propellers are obtained by the present method. The method is useful for the calculation of cavitation. (2) For the case of an usual propeller, the existing mode function method is valid in wide range up to 0.9 radius. The method is useful for the calculation of unsteady propeller forces. (3) The effect of p^*≠p, that is, the effect of non-linearity in the steady theory on the characteristics of the unsteady propeller, is not small except the region near the tip of blade. The effect should not be neglected for the calculation of unsteady propeller forces. (4) A modification of the present method to shorten the computing time, is attempted. There is possibility of further study on the modification.

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Floating storage system has been recently proposed as a new method for stockpiling emergency petroleum reserves.
In this system, floating storage barges are moored to mooring and loading dolphins by way of rubber fender.
For mooring design of these barges, analysis is essential for the behavior of the barge in connection with mooring facilities having non-linear resilient characteristics.
In this paper, non-linear mathematical model of moored floating storage barge is investigated by various basic approaches and some results of numerical simulations are introduced.
Results of these investigations show as follows :
(1) Numerical simulation by non-linear mathematical model is available for mooring design of a floating barge.
(2) Adopted fender is effective for energy absorption without excessive fender reaction forces.

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Many researches have been reported on sloshing forces of liquid in a ship tank. But most of them have focused on results of experiments and only a few researches have been reported about methods of evaluation of sloshing load on actual ships. In the previous report, the results of the model tests focused on sloshing phenomena of a nearly fully loaded tank which has a large flat tank top were presented. In this report, the authors present the method of evaluation of impulsive pressure on actual ships taking into account the characteristics of the phenomena, that is, scattering of impulsive pressure in regular ship motion and non-linear relation between the amplitude of ship motion and impulsive pressure.
The following assumptions were made :
(1) The probability distribution of impulsive pressure in regular ship motion conforms to Weibull distribution.
(2) The magnitude of pressure varies in a relation between 0 and 2nd power of amplitude.

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A method of predicting the non-linear stresses such as the von Mises' equivalent stress on the longitudinal members of a ship in sea waves is proposed, by assuming that total normal stress and total shearing stress would be regarded as completely dependent randam variables.
The application of this method is made for a large oil tanker in short-and long-term sea waves. The short-and long-term trends of the equivalent stresses on the longitudinal members are investigated in relation to heading angle.

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In this paper, the compressive strength of long rectangular plates (aspect ratio α=3 and α=4) under increasing compression and constant hydrostatic pressure, is studied theoretically and experimentally as a basic study on the compressive strength of a ship's bottom plating. The theoretical calculations are performed by following two methods assuming that the plate behaves elastically up to the collapse.
a) The method assuming that the plate collapses when the normal stress in the direction of compression at the longitudinal edges of the plate will become equal to yield stress of the material.
b) The method assuming that the plate collapses when the plate will satisfy the condition of plastic collapse based on plastic analysis in which collapse mechanism is assumed and the large deformation theory is considered.
From these results of theoretical calculations and experiments, conclusion is summarized as follows :
(1) The compressive strength for comparatively thin plates having the large value of (b/t) √σ_Y/E where collapse of the plate will occur in postbuckling state does not change so much with hydrostatic pressure, while for comparatively thick plates having the small value of (b/t) √σ_Y/E where collapse of the plate will occur in prebuckling state, the compressive strength changes remarkably with hydrostatic pressure.
(2) Calculated values of the compressive strength based on the method a) are generally larger than those based on the method b). The difference of the two becomes more remarkable for thicker plates having the small value of (b/t) √σ_Y/E under larger hydrostatic pressure.
(3) Experimental results of this study concerning with thin plates having comparatively large values of (b/t) √σ_Y/E agree generally with the tendency of theoretical results.

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The object of this research is to clarify the stiffening effect of relatively large-sized hat-shaped stiffeners on a plate which are often utilized in FRP ship constructions. In the previous reports, both the bending and buckling deformation of a fundamental single stiffener model was described and it was shown that the lower width of a hat-shaped stiffener is the most important parameter in view of the stiffening effect on a plate. It was also shown that a simple model considering the rotational spring constant of a stiffener web gives a good explanation of the local buckling mode as well as the bending deformation of a fundamental symmetric structural model.
One of the main structural characteristics of a hat-shaped stiffener is that the effect of its torsional rigidity cannot be neglected since it is attached to a plate along two separated lines and makes a closed section. In this report, an analytical model considering two joint lines of stiffener webs to a plate is proposed to modelize the stiffening effect of the torsional rigidity of a hat-shaped stiffener on the bending deformation of a plate.
In the first part of this report, the bending deformation of a unidirectionally stiffened plate is analyzed by means of Ritz method on a simply supported orthotropic plate with a single or double hat-shaped stiffeners under uniform lateral load and compared with detailed finite strip analyses. It is shown that the stiffening effect depends greatly on the position on a plate where a stiffener is attached and that the effective torsional rigidity is reduced by the cross-sectional deformation of a stiffener.
In the second part of this report, the bending deformation of a stiffened plate with multiple hat-shaped stiffeners is analyzed and compared with an equivalent orthotropic plate model using an effective torsional stiffness. It is made clear that the deformation behavior cannot be well explained by the conventional equivalent rigidity method on a stiffened plate with multiple hat-shaped stiffeners.

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When a plate structure is externally loaded, structural elements such as stiffened plates and panels are usually subjected to combined stresses. As practical examples of such combined stresses in ship structures, compression and shear, compression and lateral pressure and so on may be cited.
In our previous paper, the ultimate strength of a square plate subjected to compression and shear was analyzed as one of basic studies on the strength of the plates under combined stresses.
In this paper, the ultimate strength of rectangular plates subjected to compression and lateral pressure is investigated in order to know the strength of bottom plates of ship structures.
The analytical method from the previous paper is extended and applied to this problem. The analyses are carried out for the plates of various aspect ratios (β=1, 2 and 3). The obtained results are in good agreement with experimental ones conducted by Yoshiki·Yamamoto et al.
The following conclusions are obtained,
1) Lateral pressure reduces compressive strength of plates. Especially in case of square plates, the reduction of the compressive strength is almost uniform in spite of the variation of breadth-thickness ratio of plate.
2) As for a rectangular plate with the aspect ratio β=2 or 3, in case of small lateral pressure the collapse mode of the plate shows buckling pattern. On the other hand, in case of large pressure, the collapse mode becomes another pattern which is characterized by lateral pressure. From the above, the limit pressure p^*_c can be defined as the intersection of two curves which show the strength of the respective modes.
3) When a plate collapses in the mode of buckling pattern, the reduction of compressive strength due to lateral pressure is rather small. However in case of the collapse with the other pattern which is induced by lateral pressure, the reduction of that is considerably large because of the effect of the bending stress generated by the lateral pressure.

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In this paper, elasto-plastic, flexural-torsional analysis of curved beams subjected to thrusts and bending moments applied in the plane of initial curvature is carried out by using Galerkin method. This method provides not only continuous distributions of stresses and displacements but also substantial cut of computing time compared with FEM because the size of final simultaneous equations could be considerably reduced.
The results of elastic analysis (lateral buckling loads, deflections of beams) are in fairly good agreement with those of S. P. Timoshenko and V. Z. Vlasov. From the results of elastoplastic analysis, it is clarified that initial imperfections such as initial deflections and residual stresses due to welding result in considerable reduction of lateral-torsional buckling strength.
The authors also suggest a simplified method to estimate elasto-plastic, lateral-torsional buckling load of curved beam with I-sections subjected to uniform bending.

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Previously, one of the authors developed the new mechanism of plastic hinge based on the plastic flow theory, derived the plastic stiffness matrices of elements and established the plastic hinge method for elastic-plastic analysis of space frame structures accompanied by large deflection. In this paper, the previous theory is further extended for analysis of plastic strength of plates based on the finite element method and a general theory is proposed. Applying this generalized plastic hinge method, several examples including elastic-plastic large deflection problems are analysed, and the effectiveness of this method is demonstrated.

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The sophisticated ships such as LNG or LPG carriers has been playing an important role in the clean energy campaign. To meet the strict qualifications against the crack failure and to make structural design much more rational and compatible with the actual defects in these ships, the so-called fracture mechanics analysis is appropriate and applicable.
The authors have tried to carry out the fracture mechanics analysis on the member of the ship hull structures. As an example taking the panel with the stiffener, the crack tip K-value etc. has been calculated and the crack propagation life is deduced by adopting the proper simplifications and expedients.
And to make the analysis simple and easy to execute for the similar structural members, the approximate calculation has been formulated. And the usefulness of the present approximation has confirmed by following the test results of the fatigue crack propagation rates and the stress distribution in the cracked stiffener.

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The finite strip method has been shown to be time-saving in computer analysis and efficient in analysis of axi-symmetrical structures and plate structures whose sections are uniform.
K. Yoshida et al. did numerical analysis by means of the combination of the finite strip method and finite element method, using the deflection function of Y. K. Cheung along the short side of a strip element, and showed the effectiveness of the finite strip method for bulkcarrier analysis.
In this paper, we developed the bulkcarrier analysis program of finite strip method, using the finite difference approximation for deflection along the short side of a strip element, as a simplified method for the purpose of initial design of a bulkcarrier. With this program, we got a good correlation between experimental results and analyzed ones of both actual and model ships of bulkcarriers.

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The present paper gives some results of static tests on the fracture of a ship-hull model in collision with a bridge pier. The test simulates the collision condition in which the bridge pier is hit by the forepart side of a ship. The collision is likely to occur in the actual state, but was not dealt with in the previous paper. The test in this paper shows that rather large forces are generated acting on the bridge pier.
Furthermore, we study the effectiveness of buffer equipments placed on the circumference of a bridge pier, on the basis of the tests on several kinds of buffer models penetrated by bow models. The composite-type of buffer model, in general, was found to do well from the viewpoint of the energy absorption efficiency. As a numerical example, the amount of the energy absorption was estimated for this type of buffer.

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In the previous paper¹⁾ , the motions of a 220m long and 45m wide square Plant Barge, towed from Japan to Brazil, were reported.
Here in this paper, the measured results on the longitudinal strength analyzed by means of statistical analysis and spectral analysis are reported. The stress variations due to 2-nodes vertical vibration were frequently observed. These power spectra were found to have two well-defined peaks of energy, one corresponding the low frequency wave-induced stress and the other the higher frequency vibration stress. Also, these short-term probability distributions were verified to be approximated by Gaussian distribution. As for the frequency response function of vertical bending moment, the obtained values by the measured power spectra of wave height and stress were good agreement with the experimental results in model test basin. The long-term distributions of extremes on stress, estimated by following three procedures based on the measured data of short term, were fairly coincident with each other.
(1) Cumulation of histograms
(2) Synthesis of short-term probability distributions
(3) Logarithmic normal distribution and Gumbel's extreme distribution with upper limit Moreover the investigation on the fatigue strength at the hatch corner disclosed that the damage factor very small.

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In the previous paper, the authors explained a proposed method for calculating the racking deformation in the hull cross section of a ship having few transverse bulkheads. By way of example, the authors analyzed the distribution of racking as the shearing deformation in the hull cross section of a Pure Car Carrier designed capable of carrying 3, 000 motor cars.
In this paper, the authors review the results of theoretical calculation and full scale measurements which they carried out on the racking deformation in hull cross sections of a Roll-on/Roll-off ship built at Nagasaki Shipyard & Engine Works of Mitsubishi Heavy Industries in order to evaluate the accuracy of the prediction made by the proposed calculation method.
The results of the theoretical calculation and actual measurements showed a fairly good agreement, and thus the proposed method of calculation was proved to be highly useful in accurately predicting the racking deformation in the hull cross section at the ship design stage.

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It is foreseen that the marine transport will make a remarkable growth recently in the domestic transport of general cargo due to the energy crisis, etc.
The authors introduce the newly developed marine transport system for general cargo and present the results of simulation study. The simulation is made for costwise and timewise comparison between the circuit transport system which is a distinctive feature of the newly developed system and the shuttle network transport system which stands for the conventional system.
The results show that the circuit transport system has an advantage in transport cost over the shuttle network transport system in wide variety of cargo distribution.

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A floating oil storage system developed by Mitsubishi Heavy Industries, Ltd. (MHI) is being examined as one of the national oil storage projects by the Japan National Oil Corporation, which will be constructed in Aokata Bay of Nakadorishima, one of the Goto Islands in Nagasaki Prefecture.
The system consists mainly of seven (7) oil storage barges capable of holding 835, 000 kiloliters of crude oil (about six million kiloliters in total), mooring dolphins and other facilities.
Procedure to determine the initial planning is as follows :
(1) Principle of how to develop the system was established.
(2) A site suitable for construction of the system was selected.
(3) Meteorological and sea design conditions of the site were investigated and then estimated for over a recurrence period of 100 years.
(4) Necessary technology was analyzed point by point and related experiments were carried out.
(5) Subsystems such as oil storage barge, mooring dolphin, safety device, etc. were designed.
(6) Finally the initial planning was made.
The most important matters at the initial planning are to establish the proper principle at first and to estimate meteorological and sea design conditions of the site.

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In thc previous paper the authors presented the problem of stress distributions around a hole or a crack which belongs to the very important one in the field of fracture mechanics. Basic equations were derived from complex stress functions and the calculations were carried out on the basis of the concept of thermo-elasticity theory.
In this paper, the problem is extended to that of an elasto-plastic stress field in an infinitely large isotropic matrix around a cuboidal element within which dilatational strains are distributed. Just as in the case of two-dimensional problem, the concept of thermo-elasticity is adopted.
Galerkin vector for unit inherent strains which exist in an infinitesimal volume element at a point is derived from the Galerkin vector for concentrated body forces in an infinite, isotropic, elastic medium.
When the distribution of the inherent strain in a cuboidal element is expressed by polynomial, the Galerkin vector will be obtained in terms of volume integrals in closed form to any order. Then, the displacement and stress fields are calculated from second and third derivatives of the Galerkin vector respectively.
The three dimensional elasto-plastic analysis is conducted using the “Initial Strain Method”, in which the localized zone with plastic strains is divided into a number of small cuboidal elements each of which has polynomial distribution of initial strains up to second order on the boundaries. The stress field as compensation for plastic behavior are then calculated by regarding the initial strains as inherent strains, and the values of plastic strains are determined by trial-and-error operation.
Numerical stress evaluation has been performed for several shapes of cuboids, within which dilatational strains are distributed.

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The residual stress due to circumferential welds in cylindrical shells is one of the most important problems concerning stress corrosion cracking in piping structures in service. Recently in Japan, many researches are carried out with regard to the above problems.
It is well known that the state of stress in welded cylinder may be quite different from that in butt welds of flat plates. This is because not only hoop stress but also bending stress in the axial direction is produced. This bending stress is induced because radial displacement caused by circumferential shrinkage occurs.
In this paper, one dimensional thermal elasto-plastic analysis using Rayleigh-Ritz method is applied to the axi-symmetric thermal stress problems of thin cylindrical shells. The adoption of deflection function which satisfies the geometrical boundary condition yields more accurate solution compared with that of FEM even in case of smaller degree of freedom.
The following conclusions are obtained from this analysis. The effectiveness of this analytical method and reliability of its results are confirmed by comparison with the experimental results. The influence of size of cylindrical shells and welding heat input on welding deflections and residual stresses is clarified. This influence is described by the use of parameter (Q/h) ·β. The estimation chart of deflections and residual stresses for a given cylindrical shell is also presented.

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In order to investigate the relationship between the fatigue strength and the reinforcement shapes for several types of welded joint, the axial load controlled fatigue tests were carried out employing SM 50 B, SM 58 Q and HT 80 QT steel plates. And the relationship above mentioned were analyzed statistically and discussed about each one group and between groupes that were classified according to materials, type of joints, dimensions of joints, etc.
It was found from these analyses that the variance of fatigue strength between several groupes was mainly attributed to the multiple effect of the stress concentration due to reinforcement shapes of the weld, together with the bending stress at the weld toe to the mismatch and the angular distortion of welded joints.
And the influence of welding conditions on the fatigue strength was also discussed and was shown the necessity of investigating the most suitable welding condition to ensure the lowering of the fatigue strength to the minimum value that was caused by the stress concentration at the toe of the weld.

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In view of safety design against fatigue failure in cylindrical storage tank of low temperature use, low cycle and low temperature fatigue bebaviour of shell to annular tee-fillet welded joint in tank was investigated experimentally and analytically, in case of liquefied propane gas tank, using a displacement-controlled bend test of model specimens.
The experiments and analyses were done either by strain and displacement measurements around weld toe in annular plate under cyclic deformation or by finite element analysis mainly to clarify quantitatively the effects of type of weld joint as well as dimensions of weld joint, including the effects of annular plate thickness, on the fatigue crack initiation life of tank.
Principal results obtained are as follows.
(1) In bend test of model specimen, a distribution of strain range in front of weld toe indicates that its maximum value is found at weld toe as far as the deformation range examined, although maximum value of strain distribution is found at 510mm distant from weld toe under large extent of deformation.
(2) Experiments and analyses show that there is no difference practically between fillet weld joint and full penetration joint in cyclic deformation as well as in fatigue strength.
(3) The expression of evaluating the fatigue crack initiation life in the displacement controlled bend test of model specimen was derived in terms of weld joint parameters, which is
N_c=2.3×10¹⁵·ρ^0.35/Δδ_p^3.78t^3.86 (SL) ^0.19 (unit in mm)
where N_c, ρ, Δδ_p, t, SL denotes fatigue crack initiation life, weld toe radius, displacement range at the loading point, annular plate thickness, and leg length of shell plate respectively.
(4) By introducing a parameter θ_S-A, an angle which defines an extent of deformation around weld toe, the fatigue crack initiation life in tank is predicted from the results on model specimen.
(5) The finite element analysis shows that as to the bend test on model specimen, the increase of annular plate thickness decreases the initiation life in displacement controlled test, and increases it in load controlled test. However, the incorporation of the results on model specimen to the behaviour in deformation of the tank indicates that these two expressions are essentially the same as far as the fatigue crack initiation in tank concerned. As of now, it seems that the thicker the annular plate becomes the longer the fatigue crack initiation life in this type of tank.

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In this study, it was investigated to evaluate the fatigue crack initiation life N_c, at a three-dimensional notch such as a toe of weld, which is in plane strain state, on the basis of fatigue test results using a smooth round-bar specimen at completely reversed constant strain amplitude. Finite element elasto-plastic analyses in plane stress state and in plane strain state were performed on a cruciform joint welded in complete penetration on condition of pulsating tensile loading. The analyzed cyclic stress and strain in-each stress state at the toe of weld were converted into the equivalent stress and strain in uniaxial stress state, using hysteresis loop of stress-strain relation and the conversion factors derived with the aid of total deformation plasticity theory. The converting stress and strain were applied to stress-strain function D, and then the crack initiation life at the toe of weld in plane stress state and in plane strain state could be evaluated from D-N_c, diagram obtained by the completely reversed strain fatigue test using a smooth round-bar specimen.
In order to confirm experimentally the present method of the fatigue life evaluation, moreover, fatigue tests were performed on two kinds of the cruciform joint specimens with short and long length along the weld bead, which corresponded to plane stress state and plane strain state respectively. A good agreement was found between the experimental life and that evaluated by the results of FEM in each stress state.

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In order to prevent cracking and to predict thermal stresses and distortions developed as a results of welding, it is necessary to know the details of thermal and mechanical response of weldments. While experimental measurements of the stresses and strains surrounding a weld heat source are very difficult due to high temperatures caused by welding, it has now become possible to analyse the transient stresses and strains in the immediate vicinity of the welded joints with an aid of the recent progress in analytical technique of the nonlinear problems by the finite element method.
Most of the former works in this field are concerned with the analyses of bead-on-plate welds. In an attempt to refine our knowledge and improve the degree of correlation with reality, more realistic analytical models are developed for calculating temperatures, stresses and strains resulting from butt-welds of mild steel plates by use of the finite element method taking changes of the thermal and mechanical properties of the material with temperatures into account. We solved the unstationary heat conduction problems first and based on the calculated temperature distributions, we analysed the uncoupled thermal stress problems with time depending varying boundary conditions. The material subjected to the welding thermal cycle is postulated to behave mechanically as an isotropic, elastoplastic and strain-hardening continuum obeying the Mises yield condition and the Prandtl-Reuss flow rule.
The elastoplastic stress distributions around a moving weld heat source, metal movements during welding and variation of forces and moments acting on tack welds are clearly presented. It has been shown that presence of root gaps play an important role in opening or closing behavior of groove and the magnitude of forces and moments acting on the tack welds ahead of the moving weld heat source. Some of the obtained results agree fairly well with experimental values.

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A simplified method for estimation of crack opening displacement δ in complex conditions is proposed in this paper. The expression for COD evaluation is a modification of the solution for the strip yield model, by Dugdale and Bilby et al., namely,
δ= 8σ_YC/πE 1n {sec (πσ/2σ_Y)}
where, σ, c, σ_Y and E are equivalent applied stress, equivalent crack length, epuivalent yield stress and equivalent Young's modulus, respectively. These values are affected by the crack profile, stress state etc., and are determined, basically, as follows, σ is determined so as to assume the same value as σ_Y when the cracked section attains general yielding conditions. c is determined by (K/σ)²/π in oder to satisfy the relation δ=K²/ (Eσ_Y) under small scale yielding conditions.σ_Y and E are determined by considering the effects of the plastic constraint, deformation mode etc.
The COD values of the cracks for which K values are known can be evaluated easily through the proposed method. It is verified that these COD values are, in general, larger and good approximations of the exact solutions by the strip yield model. The brittle fracture initiation stresses are estimated through COD concept using the proposed method and are compared with the experimental results. The relationships between COD and the overall strain in residual stress field and under bending stress are discussed using the proposed method.

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With reviewing weld defects in fabricated weldments, reasonable acceptance criteria should be made so that an optimum balance of safety and economy will be assured for the weldments.
In quest of the reasonable acceptance criteria, efforts are being made, as a worldwide trend, to work out some simple and practical acceptance formulae based on fracture mechanics. But the criteria are not perfect and contain a great deal to be wanted, due to the fact that the criteria were meant to be as simple as possible.
The purpose of this study is to clarify the uncertainties included in the present acceptance criteria and to describe the application of reliability theory to the assessment of significance of defects with respect to brittle fracture.

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