Computational schemes and numerical stability conditions of a modified version of Marker and Cell method are studied and a new computing program is developed using second-order upstream differencing representations of the momentum conservation equations and a SOR iterative method for solving a Poisson equation for the pressure, which is applicable to 3-D wave making problems of steadily advancing floating bodies in deep water. Computed results are given for nonlinear bow-waves of wedge models.

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The effect of bow-bulbs on reduction of wave resistance is studied through some kinds of experiment with wedge models and a ship model of fine hull form. The stress is focused on their effects on wave configuration and flow velocities in the near-field. The effect of frame-lines of hull forms on both linear and nonlinear wave resistance components is also studied with a ship model of fine practical hull form. An approximate method of estimating the two resistance components is proposed and applied to hull form improvement.

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Development of Stern-End-Bulb (abbreviated as SEB hereinafter) for five actual ships in three groups is described. Design of optimum SEB form is discussed for these different ships through model resistance test. Effect of SEB on performance in waves and on maneuverability is studied. Good effect of SEB has been confirmed at Sea Trial and by voyage data analysed on actual ships.

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In this paper, the boundary layer around a rotating circular cylinder in an axial uniform flow is discussed both theoretically and experimentally. The problem has not been exactly dealt with because of its difficulty, although it is one of the most fundamental and important problems in the field of the three dimensional boundary layer theory.
Theoretical investigations are made with the use of the finite element method solving the Navier-Stokes equations and experiments are carried out in the circulating water tunnel. The Laser Doppler Velocimeter is used to measure the velocities in the boundary layer. The results obtained by numerical and experimental investigations are qualitatively in good accordance with each other.
Conclusions obtained in this paper are summarized as follows ;
1° The boundary layer around a rotating circular cylinder is analogous to that of a yawed flat plate in relatively wide range of the rotation parameter ;
2° The rotation causes the point of inflexion in the axial velocity profile, which may make the flow turbulent ;
3° The boundary layer around a slowly oscillating circular cylinder is analyzed approximately, which is effective for the estimation of the viscous damping force of the lateral oscillation of a ship in advance.

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The authors have presented a new approach to solve the viscous flow around the stern end including the wake. The particular iterative procedure has been developed to satisfy precisely the condition on the boundary surface between the outer potential flow region and the inner viscous flow region, namely the boundary layer and wake (abbrv. BLW). The procedure makes the continuous solution of BLW to be obtainable avoiding the divergence of it at the stern end. The computational process is composed of two main parts, one of which is the potential flow calculation by the modified Hess & Smith method with the correction of the blow-out effect of BLW and the other is the boundary layer calculation by the integral method considering the cross flow of Okuno's reversed cross flow model. The numerical results for two examples, Series 60 (C_B=0.60) and HSVA tanker (C_B=0.85), have indicated the possibility of solution of the stern end flow continuing the wake without any divergence within the field of the boundary layer theory.

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In order to calculate frictional resistance increase due to surface roughness of a ship, a two-dimensional turbulent boundary layer theory for rough surface was applied to potential streamlines over the hull surface. In the calculation, Karlsson's roughness functions for full-scale ships were used. The calculated results were compared with those calculated by replacing a ship with a flat plate, and compared with the experimental data. The frictional resistance increase calculated by the present method is a little larger than that of flat plate approximation. Further, a fairly good correlation between calculated results and experimental data was obtained when they were plotted with respect to the mean apparent amplitude.

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By using the mathematical hull form and the simple sink propeller model, the mechanism of the free surface effect on the propulsive performance of a ship is elucidated. This sink propeller model is different from the actuator disk model, because the strength of the sink is, determined by the boundary condition at the propeller plane. The hull form is represented by the Michell source distribution. Following results are obtained.
1) This propeller model explains the propeller characteristics under the free surface.
2) The hull wake increases the thrust and the propeller wave wake decreases the thrust.
3) Increase of wave pattern resistance expresses a part of the thrust diminution.
4) It is preferable to analyse the propulsive performance of a ship in the ballast condition by using the propeller characteristics which was obtained at the same F (=V/√gI) .
5) The wave pattern resistance of the self-propelled ship depends on the distance between the hull and the propeller and on Froude number and immersion.
6) As Froude number increases, the wake fraction and the thrust deduction fraction generally undulate under the free surface effect.
7) The ratio of the increase of wave pattern resistance to the thrust of the model ship is nearly same as that of the full-scale ship.

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A new propulsion test method i. e., propeller loading test system which is based on the theoretical consideration about hydrodynamic interaction problem, has been developed in the Ship Research Institute.
The propulsive performance factors of a ship are presented as the function of propeller thrust loading in this method.
By making use the interaction calculation of the proposed method, it is possible to estimate the propulsive performance before the tank test.
Three ship models of stern form variation were designed. Applying the new method for the models, tank tests were performed. And the test results were examined by means of this test system.
Effectiveness of use of the method is demonstrated in this report from view points of stern form improvement and detailed analysis of propulsive factors is also presented.

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A semi-submerged ship with small water-plane area will easily change its trim and dipping by small disturbances unless it is controlled by fins. This character of semi-submerged ships is unfavourable for the propulsive performance test, because it is difficult to make coincidence of the both running conditions in the resistance and self-propulsion tests. To avoid the above mentioned difficulty in the propulsive performance test, the authors adopted the locked model testing system as the first step for completion of the free running system with fin control.
In this study, a new propulsive performance test, tentatively named “Self-propulsion test in thrust shifting”, was proposed. In this method, the resistances of a model ship can be determined from the relation between thrusts and towing forces obtained by the self-propulsion test in thrust shifting. The new self-propulsion test was performed for a locked model and the attempts were successful.
According to the results of the experiments, the shallow draft semi-submerged ships will contribute to saving energy. Furthermore, the authors found out that the surface force and the bearing force generated by the propeller operations behind hulls played an important role in the ship behaviour in calm water.

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In the previous report, a possibility of wave devouring propulsion was discussed qualitatively under the assumption that wave energy is ideally converted into thrust. Furthermore, as a realization of wave devouring propulsion, thrust generation by an oscillatory hydrofoil was discussed on the basis of Wu's theory. And free surface effects which had been neglected in Wu's theory were introduced approximately, and the importance of the free surface effects was pointed out with the results for a linear Wells turbine (non-oscillatory hydrofoil).
In the present report, a possibility of the idealized wave devouring propulsion is treated more quantitatively, and the advance speed effect on the wave drift force is correctly introduced under the assumption of the perfect absorption of wave energy.
As a main subject of the present report, a concept of power free motions of a hydrofoil in a wave is explained as a basis of passive-type wave devouring propulsion, and it is discussed how to choose an optimized motion among the power free motions. And the importance of the optimized motion is strongly demonstrated. Similar results have already been obtained for thrust constant motions by Wu.
The effect of depth of submergence on wave devouring efficiency of a linear Wells turbine is also discussed, and a possibility of an optimum depth of submergence is suggested.

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In the previous papers¹⁾³⁾ the authors presented experimental and theoretical data on propeller open characteristics, propulsive performance characteristics, cavitation characteristics, propeller-induced fluctuating pressures and blade stresses of MAU type Conventional Propeller (CP) (MPNO. 80-3), conventional 90° Highly Skewed Propeller (HSP) (MPNO. 80-4) and theoretically designed 72° HSP (MPNO. 80-5).
Presented paper studies flows on HSP blade at ahead and astern conditions and crash astern performance of the ship equipped with HSP.
First, flow visualization tests which examined flows on the blades of CP, 90° HSP and 72° HSP were carried out using depth tuft method and oil film method in order to check up the applicability of propeller theory for estimating performance characteristics of HSP and the difference between flows on the blades of CP and HSP.
Second, crash astern performance simulation for a prototype container ship (SR 183) equipped with CP or 72° HSP was carried out using theoretical method in order to compare crash, astern performance of the ship with CP and that of the ship with HSP.
From results of the study, the following conclusions were obtained;
(1) Near propeller design point, propeller theory is applicable for performance analysis of HSP.
(2) At ahead-reverse condition, propeller theory is not applicable for performance analysis of HSP. At astern-reverse condition, performance analysis of HSP by propeller theory can not be carried out when skew angle and propeller load are excessively large.
(3) Near propeller design point, flow on HSP blade is similar to that on CP blade.
(4) At astern-reverse condition flow on HSP blade is different from that on CP blade. Boundary layer flow on CP face is almost full of turbulent flow. But when skew angle and propeller load are excessively large, the wide range near blade root comes to dead flow zone.
(5) Crash astern performance of the ship with HSP is inferior to that of the ship with CP, though it falls less than backward thrust.
(6) The best way to raise crash astern performance of the ship with HSP is to increase the number of reverse revolution within the allowable range on blade stress.

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Present linearized theories can not predict cavity flow around a hydrofoil with rounded nose. The authors propose a non-linear theory for a partially cavitating hydrofoil with arbitrary profile where cavity does not generate from the leading edge of the hydrofoil. Transient cavity flow model is adopted in the present theory. According to Hess and Smith's method for a two-dimensional steady flow, line sources and vortex are distributed on the surface of hydrofoil and that of cavity to treat the hydrofoil and cavity thickness exactly. Boundary conditions are as follows :
(1) flow direction is parallel to the surface on wetted portion of the hydrofoil
(2) flow velocity is constant on the cavity surface except for the collapsing region
(3) position of cavity tip coincides with laminar separation point or transition point of boundary layer on cavitating hydrofoil
The solution is derived by an iterative procedure. In the cavity collapsing region, cavity shape and collapsing length are determined by solving Rayleigh's equation for a single spherical bubble and connected to the constant velocity region. The laminar separation point and transition point are derived from theoretical calculation.
Experiments were made with a hydrofoil with symmetrical section whose chord was 150 mm and thickness was 12 mm. The position of cavity tip and end, cavity volume and cavity shape were measured. The results of present theory were found to be in good agreement with experimental results.

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As a practical method to calculate ship motions in waves, so-called strip methods now prevail through the world. According to the investigations which have been performed up to now, it is conceived that the wave exciting forces related to heave, pitch, sway and yaw motions can be evaluated by the strip method with accuracy enough for practical use, but, on the contrary, there is room for further investigating whether the strip method is valid for estimating precisely the wave exciting roll moment. Recently, Tasai and others manifested that when a ship has no advance speed the wave exciting roll moment acting on it was able to be evaluated well by New Strip Method if two-dimensional hydrodynamic forces were determined appropriately, for example, by the close-fit method. In this paper as well, the particular problem mentioned above is dealt with for the case where a ship has advance speed. As the result of the present investigation, it is concluded that Ordinary Strip Method (O. S. M.) yields good estimation of the wave exciting roll moment. However, if the wave exciting roll moment is required to be predicted more accurately, a method advocated by Salvesen, Tuck and Faltinsen (S. T. F.) is recommended rather than Ordinary Strip Method. Lastly, effects of the presence of heel of the hull on the amount of wave exciting forces are discussed on the basis of theoretical values of wave exciting forces obtained by the strip method. In consequence, it is shown that the wave exciting roll moment is affected to a great extent by the presence of heel of the hull compared with others.

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A theoretical derivation, according to the interpolation slender body theory, is presented for the diffraction problem of a fixed ship, moving with forward velocity in regular head waves.
Assuming that U=O (ε^1/2), ω₀= O (ε^-1/4+b) (0<b<1/4), the boundary value problem is linearized in the outer and inner regions respectively. The inner solution, governed by two-dimensional Laplace equation, involves an interaction effect between the steady forward motion and the unsteady incident wave motion. A similar matching procedure, as for the radiation problem, is used to determine the unknown source strength and the homogeneous component in the inner solution.
Computations and measurements are carried out for the wave exciting force of a slender ship model, with cross sections defined by Lewis forms. Comparing the results, it appears that the present method gives good predictions, including the interactions between sections along the length.

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The second-order forces acting on a fixed or free-floating two-dimensional body at a free surface are calculated on the basis of the perturbation theory.
The first and second-order boundary value problems are solved by the Boundary Element Method (BEM) which includes both boundaries of the body and the free surfaces. The pressure distribution including the quadratic terms of the Bernoulli equation is evaluated from the solution. The hydrodynamic forces acting on the body are obtained by the integration along the instantaneous wetted contour of the body. Finally, motions of the body in waves are determined by the solution of the equation of the motion up to the second order.
Experiments are carried out for the diffraction problems of a fixed or free-floating Lewis-form cylinder in steep regular waves.
Those results are discussed in comparison with the numerical calculations. The steady heeling angles of the free-floating cylinder in waves are observed in the experiments as are predicted by the calculation.

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In the first and second report, comparisons between tank experiments and theoretical calculations were carried out mainly in following waves where encounter frequency is very low. At ω_e_??_0 transfer functions of vertical wave load from experiment showed a considerable difference compared with results of theoretical calculation methods. And this difference is understood that there was certain problem in calculation of diffraction force and radiation force, especially in following waves.
In this paper, we made a reconsideration of accurate estimation on longitudinal ship motions and vertical wave loads taking account Mizoguchi's method for diffraction force and moment and using Maruo's three dimensional correction for only added-mass in radiation component. This calculation method for diffraction force and moment is a complementary approach in Newman's diffraction solution, considering no effect of the forward velocity on the hydrodynamic coefficients mentioned in our second report. By applying this method, experimental values of longitudinal ship motions and vertical wave loads can be explained satisfactorily not only in following sea, but in all the wave directions and all Froude numbers within the range for practical use.

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The stability derivatives of a ship travelling in a following sea vary as functions of its longitudinal position in waves. As the primary cause of broaching-to phenomena, the loss of directional stability which a ship suffers when it is situated on the down slope of the following wave is pointed out. In order to examine the variation of directional stability in detail, to what extent the stability derivatives are affected by ship's position in waves should be more clarified both theoretically and experimentally. For this purpose, forced oscillation tests were carried out in following waves which was generated in an usual manner, that is to say, by the flap-type wave maker, and the stability derivatives were measured with both a rectangular flat plate which is a substitute for a ship, and a model with a realistic hull form. Simultaneously, stability derivatives of a rectangular flat plate with an aspect ratio equal to 0.2 were calculated by the numerical method advocated by Chapman. As the result of comparison between theoretical prediction and experimental results, it was shown that the numerical calculation performed for the flat plate can predict qualitatively the variation of stability derivatives of a ship due to its position in waves.

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In this paper, the emphasis is laid upon yaw-sway-roll-rudder coupled motion of a container ship in following seas.
We take the case that the component of ship speed in the direction of wave propagation is equal to the wave celerity, i. e., the encounter frequency is nil. The linearized equations of sway, yaw and roll coupled motion in still water are generalized to use by adding the terms. of wave exciting forces.
The hydrodynamic force coefficients varying with ship's relative position to wave system, are obtained by captive model tests in regular following waves generated by means of a wave making board. Using the experimental results, dynamic stability of a ship in following seas is discussed.
It reveals the possibility and physical mechanism of an unstable yaw-roll behavior due to the fact that :
1) the wave exciting yaw moment acts as a negative restoring moment ;
2) hydrodynamic forces acting upon a ship in following seas give less damping compared with in still water ;
3) small metacentric height encourages a heavy yaw-roll coupling.
However, such unstable behavior in following seas can be stabilized by adding an adequate control parameters of autopilot steering system.

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When travelling in heavy following sea a ship is accelerated on the front slope of a wave and her velocity may become nearly the same as the wave celerity. This phenomenon is called surf-riding and may cause broaching-to, which is very dangerous situation for small craft. The present paper relates to the surf-riding.
First, the resistance variation in wave, an important factor of the surf-riding, was treated with both theoretically and experimentally. The usefulness of theory on the Froude-Krylov hypothesis was examined by the proposed theoretical method on the boundary value problem and the captive model experiments.
Second, the motion involving the surf-riding phenomenon was realized and recorded in a towing tank. The results show a fairly good agreement with a digital simulation based upon the theory and captive model experiments. Finally the author proposed a diagram indicating the possibility of surf-riding for a given wave and ship on the basis of the present studies. This simulation study proved useful to predict surf-riding of a given ship.

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Performance of a hydrofoil sailing boat equipped with two surface-piercing dihedral foils and an inverted “T” foil has already been analyzed in the previous paper. The estimated sailing performance in terms of a static balance calculation agreed reasonably well with results of sea test using a boat of 5.08m LOA.
In the present investigation, dynamic performance and stability of the boat are examined as an extension of the previous work. The equilibrium state for the sailing is determined by solving six simultaneous non-linear equations as a function of wind velocity, wind direction and the angle between the boom and boat centerline, which is called sail trim angle. Then the dynamic stability around equilibrium state is examined on the basis of linear theory for small disturbances by assuming a constant heading angle against the true wind direction. Finally motions around the equilibrium state is computed by numerical simulation to compare with the results of stability analysis.
The sailing performance of the boat is affected by sail trim angle. The smaller the angle, the higher become the boat speed with the less stability in the sailing state and vice versa. The stable sailing become difficult with increasing the wind velocity. These analysis for the dynamic stability agree well with the results of the numerical simulation.

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The author proposed the entirely new ship's autopilot system using a stochastic autoregressive model (AR autopilot) and corroborated that the system worked well in the actual sea test by a small training ship (about 310 g. ton). Many sea tests of the AR autopilot has been carried out by the same ship since the first trial.
Emphasis of the tests was put on (1) the effects that the change of gains gives to the course keeping quality, (2) the robustness to the change of the disturbance, (3) the method to eliminate the offset from the desired course and so on.
In this paper, the author analysed in detail the results gained at the above sea tests from the view points of the course keeping quality of the AR autopilot.

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It is well known that the semi-submerged ship possesses excellent seakeeping qualities in seaways, because of its long natural periods due to the small waterplane area. However, the small waterplane area also causes instability in the longitudinal attitude or large oscillations in following seas. Equipment of some control fins is desirable for making the ship stable at high speed and for reducing the oscillations at resonance.
In this paper, the three components of hydrodynamic forces acting on the fin-body configuration were measured firstly by wind tunnel test and towing tank test. These data were analyzed putting emphasis on fin-body interactions and free surface effects.
The free running test on the radio controlled SWATH type model were carried out secondly in the seakeeping basin. The trim, sinkage and oscillations in regular waves were measured in various conditions with fin control.
The main conclusions obtained in the present study are summarized as follows ;
1) The fin-body interaction and downwash effect of the forward fin to the aft fin can be evaluated by the method of Pitts et al.
2) The free surface effect on the lift of fin can be estimated by taking into consideration of the flow field around the body which changes with the advance speed.
3) The lift generated by the oscillating fin or the lift acting on the fixed fin in regular waves can be evaluated quasi-steadily by using the method mentioned in 1).
4) At the free running test on our SWATH ship model, a large bow down phenomenon was observed near Froude number 0.4. This instability can be anticipated by the moment measuring test in towing tank.
5) The usefulness of fin control for reducing the oscillations in waves was approved by the free running test.

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A new multi-hull-type floating wave energy converter, which consists of multi floating bodies with asymmetrical cross section and the bars connecting these bodies, is proposed and fundamental studies on this converter are conducted. Wave energy absorbed by this converter is induced from the motions of the floating bodies and the connecting bars in waves.
The authors developed the method to calculate the hydrodynamic forces and moments acting on this converter by using Okusu method, in which the hydrodynamic interaction between the floating bodies are taken into account. Here they derived the equation of the motions of floating bodies and connecting bars in waves by balancing the hydrodynamic forces on floating bodies with the forces on connecting bars.
For the twin-hull-type floating wave energy converter which consists of two salter duck type bodies and a connecting bar, hydrodynamic forces, motions, efficiencies of wave energy absorption etc. were calculated as model experiments were carried out.
It is found that the results of calculation by this method are in agreement with the ones by model experiments and the twin-hull-type floating wave energy converter is capable of absorbing more stable wave energy than that of the single-hull-type.

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Characteristics of a fixed terminator of oscillating water column are described in this paper. It is one of the most promising wave power absorbers, as well as a floating-body-type such as Salters Duck, performances of which were shown in the previous papers. The experimental data both in regular and in irregular waves are compared with calculations based on a linear water wave theory with equivalent floating body approximation. The calculations agree very well with experiments in case of deep water depth and low frequencies. The ability to absorb wave energy is as excellent as Salters Duck both in regular and in irregular waves.

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On the study of the wave induced variable of a ship, the full scale measurement have been developed a many useful and remarkable success. Because of the measuring period is short in such measurement, the wave condition encountered by the ship may deviate from that to be encountered in her life time. So, it is feared that the estimated extreme value of the response from the result of the measurement will include error which is not to be neglected.
Authors research the observed wave conditions of 62 voluntary merchant ships in North Pacific Ocean for three years (1976-78). It is clarified by our research that in the case of such short term operation the difference of wave condition between ships according to variability of service condition is remarkable in comparison with the difference between random samples from the same population.
Regarding each wave condition observed by a voluntary ship as that observed by a ship on which the response is measured, the reliability of the extreme value over her life time estimated from result of the measurement are studied. The estimated values scatter over wide range, and moreover, the reliability of the value falls off as the length of the ship becomes longer. So, it is concluded that to estimate the correct extreme value of the wave induced variable from the measurement for such years may be difficult especially in the case of a large ship. Authors analyse the effect of wave condition on the extreme, and suggest a new method to estimate the extreme from the result of the measurement with higher reliability.

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Long term automatic full-scale measurements of a container ship 'Beishu Maru' (24, 000 tDW) on the Pacific North West course have been operated for 52 months. For three item of pitching angle, rolling angle and wave bending stress of upper deck, the values of root mean square, maximum peak and minimum trough and zero-cross mean period for 30 minutes have been measured and, recorded on punch tape in every three hours. The environmental condition data by the favour of ship's crew are to be studied comparing with those ship's response.
In the first paper we have reported the statistical distribution of environmental conditions and corresponding operating conditions. In this second report, general frequency distributions cumulative probabilities and distributions of mean periods of ship's response have been studied. Intensive analysis of the data of rough sea conditions are to be reported in the next paper.

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Mild steels have mainly been used as ship structural members in the shipyards of Japan except for particular longitudinal members in spite that qualified high tensile steels have been prevailed. In these years, however, there has been a growing tendency using high tensile steels from the economical requirement. Report of the 200 th Research Committee of Shipbuilding Research Association of Japan stated that the amount of high tensile steels used in ship structures would much increase in the near future. Investigation from the standpoint of design aspects as well as from that of economical aspects will be greatly appreciated in these circumstances.
In this paper, the problems of allowable stresses and the decrease of compressive strength of high tensile steel plates subjected to compression is studied. Firstly the ultimate compressive strength of deck and bottom panels when compressive loadings are loaded to ship structures due to the longitudinal bending moment is analysed. Secondly the probability of failure of panels was calculated based on the reliability analysis after the examination of statistical data on longitudinal bending moments.
The analytical method which was developed by the authors using the concepts of limit analysis in the finite deformation was applied to obtain the compressive strength of panels. In order to get probability of failure, a great many statistical data are required. In this paper, the yield stress of materials and initial deflections of panels are considered to be probabilistic variables as factors of strength R, and still water bending stresses and wave induced bending stresses are also assumed to be probabilistic ones as factors of applied stress S.
Reliability analysis method which was originally introduced by Freudenthal et al. and developed by Yasukawa et al. were applied here.
The following results were obtained from the calculations carried out in this paper.
1) When a high tensile steel plate is used as a deck panel instead of a mild steel plate, it is quite natural that the thickness of a high tensile steel plate may be thinner than that of a mild steel one. However, it can be concluded that the allowable stresses of a high tensile steel plate depends on not only yield stresses of materials but also breadth-thickness ratio (b/t) of the plate.
According to the result obtained by the reliability analysis, the ratio of allowable stress of plate used MS and that of plate used HY 32 is given in equation (9).
2) When plates of the same value b/t are used for the bottom and deck plating, the probability of failure of the former is a little smaller than that of the latter. Especially for the bottom plating, it can be said that the longitudinal systems have the advantage of the transverse systems from the aspect of longitudinal compressive strength.

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In this paper, a study was made on buckling and plastic behavior of a corner bracket which is attached to the beam and frame. In order to make the beam most effective, one requirement is that the bracket should neither elastically buckle nor plastically collapse, before the beam reaches the plastic collapsing state, forming the plastic hinges at the toes of brackets and the center of the beam which is assumed to be subjected to uniformly distributed loads. A method of calculation is proposed to determine the necessary thickness of the bracket so as to fulfil the requirement.
The procedure of calculation is as follows : (1) to calculate the plastic collapse load of the beam, (2) to determine the stress distribution in the bracket under the plastic collapse load. of the beam, (3) to choose the requirement either elastic buckling for thinner plate or ultimate strength for thicker plate of the bracket, and (4) to determine the necessary thickness so as to satisfy the requirement.
Elastic-plastic large deflection analysis by FEM was carried out on several beams with brackets whose thicknesses were determined by the proposed method and the results demonstrated that the method was simple and useful. The necessary thickness calculated by the method was compared with that by the NK rule.

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It is important to estimate the ultimate bending moment of a ship hull girder, because it is the real resistant value to the maximum wave bending moment. The ultimate bending moment of the cross-section of a hull girder was calculated by the in-plane strength of stiffened plates. Therefore, it is necessary to calculate the ultimate strength of stiffened plates. The author's 1st and 2 nd reports presented an approximate analytical method which was in good. agreement with experimental results. In the design stage, however, it is difficult to determine the initial imperfections of the real ship structures.
This paper estimates the initial imperfections of ship structures and studies the ultimate strength of typical stiffened plates used for the longitudinal stiffening of ships. Initial deflection, residual stress and water pressure are the main influences on the ultimate strength of a hull. Two approximate formulas are developed for calculating the ultimate strength of stiffened plates from the elastic buckling stress and the yielding stress. One is a formula for long rectangular plates and the other is a formula for one way stiffened plates. These formulas are in good agreement with past experimental results and have confirmed efficiency in designing ship hull structures.

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In the previous paper the rigid flat plate element was derived for the discrete limit analysis of thin shell structures of arbitrary shape, and numerical results under the assumption of small deformations were shown on the standard elasto-plastic problems. In general the effect of geometrical nonlinearity such as large deformations and buckling behaviors is one of the main factors which determine the ultimate strength of thin-walled structures, however, the method for the general treatment of geometrical nonlinearity is not necessarily given in the conventional plastic analysis.
In the present report the general computational algorithm for the discrete limit analysis of thin-walled plate and shell structures is presented, by using the flat rigid plate element of triangular shape. The present algorithm is characterized by the following statements :
(1) The discrete analysis on the limit strength is possible for arbitrary thin-walled structural members, in which the effects of geometrical as well as material nonlinearities are taken into account.
(2) In the application to the structural stability problems a family of simulation models with low degrees of freedom can be derived, including Shanley model in the plastic buckling problem of columns and Yoshimura buckle pattern observed in the non-axisymmetric buckling behavior of circular cylindrical shells, which can be effectively used in qualitative investigations on the instability phenomena of thin-walled structural members.
(3) The formulation expressed in terms of stresses and strains is adopted instead of resultant forces, so that all kinds of constitutive equations can be easily introduced and the application to general material-nonlinear problems such as visco-elasto-plastic problems is possible.

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A semi-submersible ship is composed of three parts ; a superstructure, lower-hulls, and columns. Stiffened cylindrical shells are used as columns in order to decrease structural weight. Most of these cylindrical shells have several axial stiffeners connected with girders of a superstructure and/or with rings of a lower-hull. The local collapse of stiffeners under concentrated axial compression load transmitted through girders or rings often becomes one of the most important problems of those structures.
This paper presents a simplified method for estimating the collapse loads of stiffeners which are axially connected with cylindrical shells and are subjected to concentrated axial compression load. Two kinds of collapse mode are considered, i) plastic collapse, and ii) collapse after elastic buckling. In the case i), the collapse loads are defined by the effective width of cylindrical shells obtained from experimental results, and in the case ii), effective lower-bound solution of buckling load is obtained by a simplified equation.

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The deformations and bending stresses of a mooring leg and a riser pipe of an assumed tension leg platform model are analyzed by two kinds of analytical methods under the condition of the severe irregular waves. One is a simulation in the time domain in which the drag term of the Morison's equation are left as the nonlinear term. The other is a linear response analysis in the frequency domain which is based on the linearization of the non linear drag term. From the comparison of the power spectral density functions and the related statistics derived from the two kinds of methods, the applicability and characteristics of the simpler latter method are discussed. In addition to these, the effects of bending on the structural responses of the mooring legs and risers of the tension leg platforms are studied.

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In this paper, a response analysis method of taut moored platforms is developed under the assumption that the superstructure behaves as flexible and the validity of this method is confirmed by comparison of the calculated results with the experiments carried out for this purpose. A series of calculations by this method can clarify the structural response characteristics of the taut moored platforms including the effects of the flexibility of the superstructure on the leg tensions. Simultaneously, the questionable phenomena reported in the previous paper can be explained by this method.

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In general, it may be said that semi-submersible offshore drilling units are designed under some conditions, such as design conditions and design criteria. The former include conditions of operation site, and the latter consist of requirements for operation and restriction of regulatory bodies, and both can be largely considered as a necessary conditions for initial designing of semi-submersibles.
However, it is necessary to work out some sufficient conditions for creating economical and reliable semi-submersibles. In this paper the author explain the above necessary and sufficient conditions obtained through fabrication and operation of Hakuryu series of semi-submersibes, and pick up some problems which we have to consider in the initial design stage for creating a new type of semi-submersibles.

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This paper deals with the theoretical and experimental studies of the dynamic tension and displacements of a chain subjected to forced oscillation at its upper end. The chain is anchored in the slack condition on the sea bed and is forced to oscillate vertically with considerably larger amplitude than the cases studied in the previous paper.
At first the mechanism of deforming dynamically the mooring line is discussed and then the relation between the dynamic load and deformation of line are formulated approximately. Finally the extended approximate method of calculating the dynamic tension of mooring chain of relatively large amplitude is obtained. The results of calculation by this method coincide fairly well with the experimental results.

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Main purpose of this investigation is to estimate fatigue life or allowable stress under random loading without using well known cumulative damage laws. Basis of the analysis is to obtain fatigue strength diagrams, namely S-N curves, under random loading, and to determine fatigue life or allowable stress directly from the above S-N curves.
Therefore, it is necessary to develop reasonable fatigue test method under random loading and to get S-N curves for random loading experimentally or analytically.
For this reason, it is required to study statistical characteristics of fatigue life under random loading and to compare with results of constant loading tests under various conditions, for example, kind of materials ; type of loading ; shape of specimen or model structure ; range of fatigue life, etc.
To achieve the above purpose, the following experiments were carried out and obtained statistical values of fatigue life and cumulative damage sum by Miner's Rule. The experiments are axial reversed fatigue tests with about 30 pieces of mild steel plain specimen in life range of about 3×10⁴ cycles, and loading conditions are (a) constant loading amplitude, and (b) load and strain controlled random loadings with exponential distribution.
From results of these tests, the following conclusions were obtained.
(1) It was found that probability distribution of fatigue life under the above loading conditions conformed with normal or logarithmic normal distribution approximately, by plotting tests on the probability paper and X² tests.
(2) Using F tests, it was clarified that scatter band of fatigue life under random loading was considerably narrower than that of constant loading and the band of the life under strain controlled random loading was little smaller than that of load controlled random loading.
(3) Probability distribution of cumulative damage sum is nearly equal to normal distribution.
(4) Cumulative damage sum is less than 1 and arithmetic mean value of the sum is O.222 for load controlled loading tests and 0.551 for strain controlled ones.

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In view of non-conservative prediction of cumulative fatigue life calculated by Miner's and Haibach's methods, the authors proposed in a previous paper a new model providing better and conservative prediction, although it was limited in application to only the bi-linear fatigue diagram in high cycle fatigue regime. If a fatigue diagram will be required to be expressed for a wide range of fatigue life from very low cycle to high cycle regimes, it is a convenient way to express the diagram by Stromeyer's expression.
The previously proposed model is developed in the present paper so as to be applicable to Stromeyer's as well as hi-linear expressions of a basic fatigue diagram in undamaged condition. The newly proposed model in this paper is based on a concept consisting of two assumptions ; (i) Fatigue damage will be accumulated as a power function of cycle ratio, and (ii) Fatigue strength at infinite fatigue life or at 107 cycles will decrease functionally according as accumulation of fatigue damage.

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It is well known that fatigue cracks remain closed during part of the load cycle under constant- and variable-amplitude loading. It seems that Elber's effective stress intensity factor range produced by a crack opening stress is in successfully good agreement with experimental fatigue crack propagation behaviour under various loading including constant-, block-, and spike-loading from a huge amount of tests. Recently, J. C. Newman introduced the interesting calculation model of the crack opening stress which was based on the Dugdale model, but was modified to leave plastically-deformed material along the crack surfaces as the crack advances.
However in his model, he neglected the stress re-distribution in the region of crack ahead in the calculation of crack opening load which leads to the occurrence of the re-distribution. Moreover, he also neglected the elastic deformation for the materials along the crack surfaces.
In this paper, Newman's calculation model is modified to solve the above problems. By the way, from the physical point of view, the idea that crack-opening stress is a limit stress for a fatigue crack propagation proposed by Elber comes to question. We considered that a fatigue crack does not propagate if a local part in the vicinity of a crack tip remains elastic, i. e., a plastic strain does not accumulate at a crack tip. This limit loading stress is named “consuming stress S_cs” which was confirmed to have nearly the same value as the crack opening stress by our calculation results. Various kind of case studies including constant-amplitude, spike and step down (for the threshold phenomenon) loading were carried out by using the model. These calculation results suggest the following phenomena.
(1) S_cs value increases rapidly just after fatigue crack initiates from a natural sharp defect. This result supports the phenomenon that fatigue crack can easily initiate from a sharp crack even if the length is small because of a large effective stress range.
(2) S_cs value reaches constant value approximately as a crack advances under constant-amplitude loading.
(3) S_cs value changes in accordance with the behaviour of acceleration and delayed retardation of a crack propagation after a spike over-loading.S_cs
(4) Phenomenon of threshold crack propagation seems to be able to be explained by the S_cs value under step down loading.

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It is well known that fatigue crack propagation (FCP) rate of welded joints is different from that of the base metal because of the existence of welding residual stress. However, the quantitative analysis for the effects of the residual stresses on FCP has not been made sufficiently.
In this paper, the predicting method of the FCP lives of welded joints, regarding the effect of the residual stress as that of the stress ratio, R (=K_min/K_max), on base metal, is proposed as follows.
(1) Stress ratio considering the residual stress of the welded joint, Rres, is obtained from the equation R_res= (K_min+K_res) / (K_max+K_res), where K_res is stress intensity factor caused by the release of the initial residual stress as the crack propagates.
(2) The FCP rate of the welded joint, (da/dN) res, is obtained by substituting R_res into U-R and da/dN-ΔK_eff relationships on base metal, where U is crack opening load ratio and ΔK_eff is U·ΔK.
(3) The FCP life of the welded joint, (N_p) _res, is obtained through integrating (da/dN) _res.
In order to examine the validity of the method, the FCP tests are carried out on welded joint and base metal of high tensile strength steel, using center cracked specimen.
As the result, the FCP behaviors of the welded joint is greatly different from that of the base metal, particularly under zero-compression loading. Even in that case, the predicted FCP behavior of the welded joint is in good agreement with the FCP test result. Thus, it is shown that the proposed method is valid enough to predict the FCP life of welded joint.

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In order to obtain the precise failure process of structures, the importance has recently been recognized for the crack growth path of structures under tensile loading conditions. Several criteria had been proposed for the determination of the crack growth direction, i. e. the criteria of maximum hoop stress, minimum strain energy density, locally symmetric deformation, and maximum energy release rate. Using these criteria the finite initial branch angle of the crack growth can be predicted, if the stress intensity factor of the in-plane shear mode, K_II, exists at the pre-existing crack tip.
The abrupt crack curving is, however, often observed even if K_II≅0 at the crack tip, where severe bending or biaxial stress condition holds. Recently Cotterell and Rice examined this problem, and proposed the T-stress theory by using a small perturbation technique, in which they introduced the concept of stability for the crack growth path. T-stress is defined as the constant component of the normal stress acting parallel to the crack line, when the near tip stress field is expanded in terms of the distance from the crack tip. In their theory, if T>0, the crack growth path is unstable, i. e. the abrupt crack curving is expected, and vice versa. In case of biaxially stressed plate, this theory is successful in predicting the crack path stability, while the crack path is stable for the compact-tension specimen even though the T-stress is positive. Therefore the generality of the theory is still open to question.
In the present paper, based upon the crack path prediction obtained in the first report, the authors introduce the concept of intermediate range of stability for the crack growth path. This stability concept includes the length parameter corresponding to the crack growth, while only the immediate range of stability is considered by the theory of Cotterell and Rice. Numerical calculations are performed by using the finite element method, and the stability of the present theory is determined for various stress conditions at the crack tip. The numerical results clarify the difference of the present and Cotterell-Rice theories, and also confirm the stable crack growth path for the compact-tension type specimen.
Finally experiments are performed for the cases corresponding to the numerical calculations. The test specimens, which are made of PMMA, are prepared, and quasi-statically fractured under the monotonically increasing displacement with practically Mode I loading conditions. Various stable and unstable crack growth paths are observed, and the theoretical prediction of the stability for the crack growth path agrees quite well with the experimental results.

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Tapered Double Cantilever Beam Compression (TDCBC) test is proposed as a stress intensity factor K decreasing type testing method. In this test, Tapered Double Cantilever Beam (TDCB) specimen is compressed in the direction of the crack growth, and K-value decreases with increase in the crack length under constant load. The increase of the specimen width in the crack growth direction is effective for obtaining K-value decreasing tendency. The compression load is effective for the crack path directional stability. It is recommended that cracked side of two specimens be placed facing each other and compression load is transmitted through a pair of rollers between the specimens. This method is effective in minimizing the constraint in the crack opening displacement. The rollers have to be placed near the edges of the cracked side of the specimen in order to obtain positive K-value.
K-value was analyzed numerically and the effects of the specimen geometry and the loading position on K-value were examined. Approximate polynomials for K-value calculation of three kinds of the specimen shape are given. TDCBC static fracture test of PMMA was conducted and fracture characteristics were investigated. It was confirmed that brittle crack grows straightly and stably in the K-value decreasing zone and that K-value of the stably growing crack is almost constant.

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For the purpose to evaluate the arrestability against brittle fracture propagation, wide plate duplex Esso tests were carried out for two kinds of 9% Ni steel plates at temperatures below the liquid natural gas temperature, and for an Al-killed steel plate at a temperature below the liquid propane gas temperature.
Brittle cracks were all arrested just after passing the starter-specimen boundary under relatively high nominal stress levels, about 1/2 to 2/3 of the yield strength at ambient temperature.
A new approach to evaluate the stress intensity factors of running brittle crack was proposed on the basis of the dynamic measurement of specimen boundary displacements and the FEM stress analysis of side notched plates under prescribed displacement conditions.
The results of analysis were compared with those by conventional tangent formula or by the compliance method. The K values obtained in the present method have a tendency to saturate to a limited level for longer cracks. Some features of wide plate duplex tests were as well discussed.

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Controlled rolling processes (new-CR processes) of steel manufacturing have been remarkably developed in recent years. Several kinds of Al-killed steel plate for low temperature service are manufactured by means of these processes for trial. In this study, the authors examined the toughness properties of these plates with welding joints in view of applicability for low temperature use of ship or land storage tank.
As a result of this study, the following conclusions were obtained :
(1) The strength and toughness of new-CR steel plates are equivalent to those of normalized or quenched and tempered steel plates, conventionally used.
(2) Toughness properties of welded joints of new-CR plates are satisfactory in terms of K_IC, property analysis under ship or land tank conditions as well as charpy impact energy at -60°C : welding methods examined include metal inert gas arc welding and submerged arc welding, each with the practical heat input.

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The authors investigate the main strength characteristics of the 50kgf/mm² class newly developed controlled rolling steel plates especially for the welded joint made by high heat-input welding and also evaluate the fracture toughness of these plates, when they are used for ship's hull. And also investigate the crack arresting properties of the newly developed controlled rolling steel plates.
That is, this report shows the fracture toughness of Z direction (at the middle of plate thickness) and of the welded joint by high heat-input welding, and also proposes a method of estimating the values of fracture toughness of welded joint from V-notch Charpy absorbed energy.
When these plates are used as the material of ship's hull, it is possible to adopt the welding method of the highest class heat-input welding that has been used in the building stage of shipbuilding yard.
And after comparing K_ca characteristic between these plates and conventional process steel plates (Normalized or Quenched and Tempered), a possibility of using these newly developed controlled roiling steel plates as “crack arrester” for brittle fracture is discussed, supposing that necessary K_ca value for “crack arrester” should be greater than 600 kgf√mm/mm² (K_ca≥600 kgf, √mm/mm²).

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Among various offshore structures, semi-submersible rigs constructed of large diameter steel tubes have been given various types of reinforcement at their brace connections to insure their fatigue strength, which is one of the important problems directly related with the integrity of such structures
The rapid growth in development of marine resources has led to severer design conditions of a semi-submersible rig to be built for operation in deeper waters subject to higher waves and polar atmosphere. On the other hand, the pursuit of economy in the development is also an essential problem. This paper presents, as an approach to the above problems, a fatigue strength assessment method obtained through the development of a highly fatigue-resistant connection with considerations given to some problems involved therein.
For higher fatigue strength, one of the measures to be taken is to reduce stress concentration. With the new connection, it was possible to limit the stress concentration factor below 2 for welds at bracket toes, intersections, etc. From this fact, the fatigue life will be expected to sufficiently exceed the endurance period of 20 years.
Unexpectedly great influence on fatigue strength has been observed depending on the determination method of the stress frequency pattern and the wave direction, which are considered to be thoroughly clarified for future improvement of the design accuracy.

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There are many semi-submersible offshore structures working in deep waters in the world and many semi-submersible rigs have been built in Japan. Still more, a design of a semi-submersible rig with larger variable deck load has been required and planned for activities in deeper and far waters, and a design condition for a semi-submersible offshore structure has become more severe. Consequently, the importance of a fatigue strength evaluation has been increasing.
In this paper, first of all, a fatigue analysis is performed for a semi-submersible rig with 3, 400 tonage variable deck load by a direct calculation method. The direct calculation consists of a motion analysis in regular sine waves, a 3-dimensional frame work analysis and a long-term prediction of stress amplitudes induced in each members of the structure.
Subsequently, design wave conditions are proposed for the semi-submersible rig, and the results obtained by the design wave method are compared with the results of the direct calculation.
As a result, it is shown that the stress amplitudes calculated for the design wave conditions well correspond to the maximum expected values of stress amplitudes for the probability of 10-8 obtained by the long-term prediction, and the average shape parameter of the longterm distributions of the member stress amplitudes is 1. 1 when Weibull distributions are.applied to.

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In the preliminary studies which have been described in the first report, it is recognized that reliability analysis is a useful tool in order to estimate a reduction of safety due to the hot straining embritticment (HSE). As the main purpose in the report is to realize the unfavorable effect of HSE, the model adopted has only two surface flaws, the one detected and the other undetected.
There are, however, many flaws in actual welded joints, and adequate inspections and following repairs of detected flaws are repeated many times until flaws are not detected.
Expanding and modifying the method mentioned above, this paper presents analytical procedures to evaluate reliability of actual welded joints as a function of joint length under some simplicities. Applying the weakest link model, probabilities of failure for no repair, repair with or without HSE are calculated. It is pointed out that detected flaws should not be repaired if those sizes are smaller than a certain allowable value which depends on the statistics of critical COD, undetected flaws, thermal effects and so on.
In addition, Monte Carlo simulations which generate actual circumstances of welded joints as precisely as possible, are also performed in order to verify the proposed method, and it is shown that the analytical method is effective from the results of numerical examples.

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Weld defects such like blow holes, porosities, etc. are not likely to become high stress raisers compared with planar defects like incomplete fusion. But, if their size and number are very large, fatigue strength becomes lower. Radiographic test has often been used to assure the integrity of welded joints. However, grade of defects classified by JIS Code does not have sufficient correlation with actual fracture strength.
Then, both radiographic tests and fatigue tests were carried out for A 5083-0 aluminum butt welded joints with porosities. The correlation between JIS Code and defect rate in X-ray photograph, and the correlation between defect rate in X-ray photograph and defect-area rate in fracture surface were made clearer. In addition, allowable defect-area rates in fracture surface and their corresponding JIS grade of defects were determined for respective surface treatment of butt welded joints.

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In order to make oceanographic research activity more extensive, deep submergence research vehicle diving to the depth of 6000 m is being required in these days.
A pressure hull of the vehicle requires the material of high strength/weight ratio and good ability of manufacturing. In this point, 10 Ni-8 Co steel with the yield strength of 120 kgf/ mm² can be said the most promising candidate for the pressure hull at present.
To give 10 Ni-8 Co steel enough strength and toughness, heat treatment (double-quenching and tempering) is indispensable.
From this respect, the authors conducted experimentally heat-treatment of 10 Ni-8 Co spherical shell using a full scale model.
The report presents the description on the heat-treatment procedure, including the experimental results, which are necessary to establish the whole manufacturing procedure of a pressure hull being combined with the welding procedure already established.

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Welding deformations and residual stresses are major factors which affect the collapse strength of externally pressurized vessels. Deflections in spherical shell welded along the equator have been already investigated by some of the authors.
In many cases of actual structures, a penetrator is welded circumferentially to a spherical shell. In these cases, the spherical shell near the weld line and the penetrator tend to sink inward.
In the 1 St report, the deformations of spherical shell caused by the welding of penetrator were investigated. Experiments were carried out in order to clarify the characteristics of welding deformations under the effects of shell and penetrator dimensions and welding procedures.
In the 2 nd report, one-dimensional thermal elasto-plastic analysis using Rayleigh-Ritz method was carried out to solve this problem theoretically. It was clarified by the analysis that the parameter λ and λα, which correlate the rigidity of shell and penetrator, and the parameter (Q/h) β, which correlates welding thermal cycle, are governing the welding deflections.
In this report, a method of reducing the welding deformations in spherical shell structures is discussed. Some deflection control methods are considered based on the results obtained by the previous reports. It is proved by experiments that the “thermal-shrinkage-fit method” is effective to produce initial reverse deflection and the “restraint load method” is more effective to reduce welding deflections. The Welding deformations in spherical shells can be prevented almost perfectly by controlling the restraint load together with adopting the initial reverse deflection, and the effectiveness of this proposed method is confirmed by experiments.

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