The accuracy of the finite-difference method TUMMAC-II developed in the first report is attempted to be raised by applying the concept of two-step Lax-Wendroff scheme to the computation of convective terms of the momentum equations. The advantages and disadvantages are studied through test computations. The wave configuration and wave resistance of the forebodies of two simple hull forms, with a sharp and a blunt bow, are computed at several speed of advance and the avail-ability of the TUMMAC-II method to hull form design is discussed.

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Characteristics of nonlinear waves generated by a 2-D advancing body of rectangular configuration are experimentally studied. Flow visualization, recording of unsteady wave profile and pressure measurement are conducted at three speed of advance. The degree of accuracy attained by the numerical method developed in the first report is examined by comparison to experimental results. Some interesting and complicated characteristics such as periodicity of bow waves and turbulence of stern waves are shown and discussed.

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A non-linear effect due to self-interaction like in the Stokes' wave is discussed on propagation of the Kelvin's ship wave from the view point of the perturbation method under the assumption of thin ship. The main purpose of this paper is to improve the expression of the phase function of the Kelvin's ship wave by considering the varying magnitude of the first order solution in the thin ship theory, whose decreasing rate is R^-1/2 inside the cusp line of the Kelvin's wave or R^1/3 on it, where R is the distance from the source of the wave. It is shown that the difference of the phase function from the first order solution increases in correspondence with log R inside the cusp line and with R^-1/3 on it. Calculated bow wave pattern of Wigley model is compared with an experimental result and the result of the thin ship theory.

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Mathieu-function-expansion method is proposed for evaluating and improving performance of ship hull forms. Medium speed ships, the design Froude number somewhere between 0.20 and 0.25, are mainly discussed.
The present method is based on minimum wave resistance theory (Maruo and Bessho, 1963) for infinite draft wall-sided ships. When the half breadth curve is expanded by Mathieu functions, the coefficient of the higher order term has by far the greater effect upon the value of the wave resistance than the coefficients of the lower order terms. Using this fact the performance of the ship hull form is evaluated from the standpoint of the wave resistance and the information, how to improve the ship hull form is gotton.
The tank tests are carried out to verify it and the results show that the present method is very powerful for improvement of practical ship hull forms.

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In the previous paper, the hydrodynamical characteristics of sand roughened surface and painted one were discussed and it was found that the differences of characteristics between two types of roughness were remarkable.
Trying to explain these differences, the simple wavy roughened surfaces are investigated experimentally in this report.
The main conclusions obtained are as follows ;
(a) In the fully developed state, the resistance curves of wavy roughened surfaces are nearly parallel to that of smooth one (Fig. 2 ; W-1, 2, 4, 5, 6, 7), and these features are the same as painted surfaces.
(b) However, the wavy roughness having steeper slope than about 1/10 shows the sand roughness characteristics (Fig. 2 ; W-3) and the slope seems to be a critical value (Fig. 2 ; W-2, 3).
(c) In the fully developed region, the roughness functions of wavy roughened surfaces take constant values (Fig. 5, Fig. 6), whose magnitudes are nearly in propotion to the roughness heights (Fig. 7).
(d) The empirical equations of roughness functions are introduced (Eq. (5), (6), (7)).
(e) For three dimensional wavy roughened surface, only one case is tested and the result is shown in Fig. 3.
Finally, as an application the ΔC_F of a tanker whose skin plates are covered with various roughnesses are calculated (Fig. 9).

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The three-dimensional unsteady boundary layer theory is applied to the problem of ship viscous wake-decrease and resistance-increase in waves. The laminar boundary layer equation is expanded with the assumption of small oscillation amplitude and high frequency, so that the steady part of the second-order solutions thus implies the effect of the oscillatory flow.
The wake decreases due to the ship pitching motion and the incident wave are calculated showing a qualitatively good agreement with Nakamura and Naito's experiments. The calculation also gives an estimation of the viscous resistance increase in waves, which is, however, quite small compared to the wave resistance increase in waves.
Although the present analysis is based on the laminar boundary layer, it represents the basic mechanism of the viscous effects of the ship hydrodynamic forces in waves.

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In this paper explanations are made on experimental procedures of self-propulsion tests of a semi-displacement craft model with a combined propulsion system of twin screw propellers and a waterjet at center. First, self-propulsion tests only by a pair of screw propellers were conducted and then tests by the combined propulsion system were conducted. By using both test results self-propulsion factors, inlet drag and trim change associated with the installation of waterjet propulsor were determined. As a result it was found that the thrust deduction factor for waterjet system in operating condition was small negative value.

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In this paper, an attempt was made to establish the optimum propeller design method in non-uniform flow, especially considering unsteady cavitation. For that purpose, the optimization method of blade section profile was investigated, which was known to be closely connected with cavitation characteristics.
Based on the following two ideas, a tentative design method was proposed, using the conventional MAU-propeller design chart and Koyama's lifting surface theory.
(1) To adjust each r/R section's camber height so as to absorb the non-uniformity of wake in the radial direction.
(2) To optimize each r/R section's thickness distribution so as to improve the chordwise unsteady cavitation characteristics.
The propeller designed by this method was called NTR-type, and it was able to change its section profile against a given wake pattern.
A conventional MAU-propeller and two NTR-propellers having different section profiles were designed for a certain wake pattern, which was expected to cause violent cavitation. And the following experiments were performed on these three propellers, to verify the design ideas of NTR-propeller, and to investigate the effects of the blade section profile on unsteady cavitation characteristics.
(1) propeller open test and cavitation test in uniform flow
(2) cavitation test in non-uniform flow (cavitation observation, cavity volume measurement, fluctuating pressure measurement, paint test, noise measurement)
From these test results, it was verified that the cavitation performance of NTR-propeller was superior compared with that of the MAU-propeller. And the improvement of the blade section profile near the tip was found to be more effective in the reduction of fluctuating pressure amplitude.

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In this paper, a synthetic method for evaluating the seakeeping performance of a ship in waves is studied.
For the prediction and evaluation of irregular phenomena to be correlated each other, the multi-dimensional Rayleigh's joint probability density function and the cumulative distribution function are approximated.
According to this approximated function, it is able to calculate easily the occurrence probability of the factors on seakeeping performance.
We proposed an evaluation method and an index to be defined by the seakeeping performance reliability, that is considered as the dangerousness and the relative dangerousness of the factors on seakeeping performance in waves.
The use of this method and index will be effective to install the sensors which are necessary to evaluate the states of ships at sea.
Some examples of the calculations by this method for 175 m length single screw container ship equipped with diesel engine are also presented.

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In the preceding report, we have confirmed theoretically and experimentally that there exists appropriate fins to suppress heaving and/or pitching motion at designated wave length in head sea. However, the area of such fin becomes fairly large so that practical application may be difficult.
This report deals with this point, that is, upon which particulars of ship form the fin area depends and the possibility to reduce its area. For this purpose, we derive nine models from the container ship considered in the preceding report preserving its prismatic curve unchanged and changing its water plane area, moreover, for comparison sake, take up Series 60's cargo and tanker and a destroyer model.
At first, fin particulars to suppress pitching motion at each wave length are calculated and selecting appropriate one of fins so obtained, the wave-exciting force and moment, heaving and pitching motions and resistance increase in head sea are calculated in both cases with and without fin. The effect of antipitching fin obtained is satisfactory like as in the former report. The necessary fin area becomes smaller, the water plane area smaller.

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In the previous paper, the authors presented a method for calculating vertical motions and vertical wave loads of a high-speed craft which travels in regular head sea, and verified its validity comparing the computed motions and wave loads with the results of model tests. Furthermore in this paper, the above-stated method is applied to an existing high-speed craft of medium size in order to clarify the fundamental characteristics of vertical motions and wave loads of the medium-sized craft. The illustrative calculation is performed extensively for various cases of wave length, wave height and advance speed.
As a result, it is found that the magnitudes of the vertical acceleration at the bow and the vertical bending moment correlate definitely to each other. This fact approves the propriety of the current design practice : the highest possible bending moment that is required to be predetermined for structural design of the hull is prescribed well as a function of the vertical acceleration at the bow.
Besides, remarkable dependence of the maximum bending moment on the advance speed of a craft is demonstrated successfully by dividing the vertical bending moment into three parts and then clarifying the effects of advance speed on each part.

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In the theoretical estimation of the long term distribution of the ship's wave induced variables, it is well known that the estimated extreme values are significantly affected by the supposed wave conditions and the ship operating conditions. However, there are few reports which investigate the statistical characteristics of the wave conditions. Furthermore, there is no report which concern with the varying of ship operating conditions of every each ship, which may appear as so-called the captain's spectra.
Authors studied the statistical characteristics of the wave conditions which are observed by 35 voluntary ships in the North Pacific Ocean during the period of 6 years (1976-1981). From this study, it was clarified that meteorological phenomena such as winds and waves in the ocean had wider scatter band than which was estimate by the usual simple population with constant parameter. Authors proposed the probabilistic model of the population of such phenomena which had a complex distribution with random variable population parameters.
In this report, authors study the statistical characteristics of the extreme values of wave induced variable of the ship with the supposed wave condition having the population of the complex distribution.
The general formulation of the extreme distribution taking number of N samples from the population of the complex distribution is shown, and the asymptotic distribution is proposed. From the analysis of the distribution of the maximum wave height observed by 35 voluntary ships, it is found that the mean value of the distribution is proportional to the logarithmics of the sample size and the standard deviation is nearly constant. The properties of the statis-tical characteristics of the theoretical maximum distribution agree with the observed distribu-tion. On the other hand, the distribution of the usual simple population with constant parameter is found to be inaccurate.
The maximum wave height and its probability of each wave period interval have direct effects upon the estimation of the extreme values of the wave induced variables. Authors' study on the distribution of the maximum wave height shows that the theoretical maximum distribution of the population with the complex distribution well agree with the observed maximum distribution of each wave period. From above result, it is clarified that the coefficient of variation of the maximum wave load is 14% to 18% and its value increase proportional to the ship length. This value is larger than the value from the usual supposed wave conditions of the population with constant parameters.

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This paper describes both experimental and theoretical investigations on sloshing motion of liquid in cargo tank and resulting tank wall pressure.
Motion of liquid is numerically simulated by the MAC method, where the effects of tank oscillation are expressed as apparent forces with a moving coordinate system in order to simplify the boundary conditions.
The calculation successes to explain the suppression and the resonance shift of liquid motion caused by chamfers. The calculated time histories and amplitudes of sloshing pressure also show good agreement with experimental values. The present method estimates sloshing pressures more precisely than the linearized theory in design procedure of tank structures.

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The authors have made extensive investigations on the wind effects on the maneuverability of ships with large superstructure, such as LNGCs and PCCs, from both experimental and theoretical aspects. This paper, as the first report of the above mentioned investigations, presents the results of the experimental study with the wind force simulating device. Using a 5.0 meter long and self-propelled LNGC model, and utilizing the wind force simulating device on the model deck as shown in Fig. 1, extensive free-running model tests were carried out for two kinds of typical ship maneuvering motions in wind, namely the course keeping motion and the turning motion both under steady wind condition. In addition to the model tests mentioned above, simulation calculations were carried out with mathematical model for the ship maneuvering motions in wind as described in Appendix. The computed results show satisfactory agreement with the model test results for various wind conditions as shown in Figs. 615. Through the present study, the following conclusions are obtained.
(1) The experimental approach with the wind force simulating device is one of the promising and useful ways for the evaluation of the ship maneuverability in wind.
(2) The simulation calculation based on the mathematical model as proposed in the present paper can give fairly good prediction for the ship maneuvering motions in wind.

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A mathematical model has been already established for describing maneuvering motions of ships with relatively large advance speeds. But this model is not applicable to the motions in low speeds, though such motions are of vital importance for ships' safety in harbours. In the present report, an attempt is made to modify the above mathematical model so that it can also express maneuvering motions in low speeds.
Utilizing the large-amplitude planar motion mechanism, detailed captive model tests were carried out for two tanker models and a boxtype vassel. To cover various aspects of maneuvering motions, wide combinations of longitudinal and lateral speeds and yawing velocity were employed in the tests. The test results, mainly of a tanker model, are introduced and the method is discussed to describe hydrodynamic forces in simple forms. Starting from the established mathematical model in relatively large advance speeds, some terms of the model are modified from necessity so that it can express hydrodynamic forces in wide combinations of three motions. After these efforts, a new mathematical model is summarised finally. It is needless to say that the model was led, being based on open-water characteristics of hull, propeller, rudder and interaction effects among them.

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The present paper deals with a study on the mechanism of capsizing phenomena of a semi-submersible platform in regular beam waves. Especially, the author's attension is paid to analysis of larger steady tilt of the platform under the excitation caused by the wave-induced vertical steady force on the lower hulls.
Firstly, the steady wave force and moment on the submerged cylinder were investigated. As the result of this study, the steady heeling moment due to vertical steady force on the lower hulls were obtained by both theory and experiment.
Secondly, the time histories of the platform motions predicted by the computer simulation are shown and are compared with the experimental results with good agreement.
Finally, the insights of stability of a semi-submersible platform in regular waves are examined by means of graphical illustrations.
In conclusion, it is clarified that the larger angle of steady tilt is strongly influenced by the wave-induced vertical steady force on the lower hulls. Especially, when the platform has small metacentric height and/or the higher position of fairleader, the angle of tilt increases drastically.

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Nowadays, the theoretical calculation method based on Hooft's Method is widely applied on semi-submersible rig motions in waves. In regarding about this method on the usual ocean wave frequency range, the extensive studies obtaining a good agreement between experimental and calculated results of the rig motion were carried out in recent years. However, on the very long wave period, and more, when the semi-submersible is placed on a large water depth by mooring systems, the researchs in such field are still little at the present moment. Moreover, experimental results on these described conditions is very rare.
This paper is concerned with a comparison between the results of the experiment and the new practical calculation method that is proposed here and obtained the good results. Mainly, this research deals on the study of the effect of the water depth and the mooring system on the semi-submersible rig motion in the wide wave frequency range.
Three model scale were chosen to the experiment. And using a very small model of 1/300 scale has made possible to obtain the response of the rig motion in a wide range of wave frequency, including the roll and pitch natural periods located in a very low frequency. A newly developed remote measurement system based on the opto-eletric device has a possibility to measure precisely the motions of the small model.
The geometry of the used model and its condition is the same one used by the SR-192 Committee in Japan and coincides with the model applied on the comparative calculation of semi-submersible rig motion by I. T. T. C. Ocean Engineering Committee.
This research treated the unmoored condition of the semi-submerible motion too, however, in this paper we will explain mainly the moored condition. Moreover, the steady part of the motion as drift it will be leaved to the next oportunity

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In this paper the theory of optimal control is developed in a form in which non absorbing modes of motion may be included in any system. The theory is developed for wave energy absorption by phase controlled systems and ones where only a simple resistive damping may be applied.
The theory is applied to two attenuators based on the Kaimei (an attenuator) concept. Firstly, a system of vertically oscillating pistons are considered which is intended to model a device with bottom opening oscillating water columns, and secondly horizontally moving pistons are considered. The latter system is analogous to a device containing side opening oscillating water columns.
Results are shown for both devices when constrained so that only the column motions are possible and for the case where the systems float freely. In addition, power extraction systems corresponding to phase control and resistive damping alone are considered. The conclusions from the study are unexpected in that floating attenuators perform better than fixed ones. Less surprising is the fact that phase controlled systems are considerably more effective than simple damped ones. Overall the results supported a bottom opening floating attenuator to be superior to other configurations although to what extent this conclusion is dependent upon the actual device geometries chosen is difficult to deduce.

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At the docking of a three-dimensional moving vehicle to a fixed base in deep water, an automatic system is indispensable to assure reliable and safe operation, and authors proposed an automatic docking system using ropes for such situation. In the first report, the investigation was focused on the practical feasibility of real time state estimation which is the most significant at the docking, and it is shown that a near optimum filter can be effectively utilized to estimate the state variables of the moving vehicle, based on which the vehicle can be controlled by the ropes.
In the first report, proportional control law was applied to check controllability of the system by the ropes, although it is not sufficient for the docking which requires accurate access to the docking point along the desirable trajectory avoiding collision or unexpected oscillations. Therefore, an optimal control technique is introduced to improve control performance of the system, and practical feasibility, especially that of real time computation is investigated.
Considering the system requirements and computational feasibility, the system equations are linearized and linear regulator algorithm is applied for the docking control. The system performance is investigated by simulation study, and the following results are obtained.
1) Proposed control algorithm based on the optimal regulator can control the system fast and stably compared with the proportional control law by selecting adequate control parameters through the simulation study.
2) It is shown that real time control by conventional mini-computers is possible if only there are enough memory capacity for storing feedback control coefficients computed in advance. The off-line optimizing computation is not so difficult for this problem formulation, and it can be also computed by a small computer.
3) The system can control the vehicle stably when it approaches within ±5×5 m area in horizontal plane and 10 m above the base. This is easily realized by conventional control system using ultrasonic positioning systems.
4) When the vehicle is controlled based on the filter outputs, i. e., estimated state variables, overall control accuracy of the system is the same order as the filtering accuracy, which is sufficient for the docking requirements.

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For a traffic control system for ships passing through the control region arbitrarily, optimization techniques can be effectively utilized to get smooth and safe courses avoiding dangerous encounters where miss distance and destination error for each ship are evaluated as a criterion function. In the paper, the control algorithm shown in the previous paper is applied to more real situations to investigate the applicability and limitation of the algorithm, where
1) ships have their own priority levels,
2) fixed point obstacle exists in the region, and
3) ships are passing continuously through the control area.
Through the investigation, it is shown that the control system can be applied to those situations with slight modification of the algorithm and proper parameter selection, and the following results are obtained.
1) Priority of ships can be taken into account in the control algorithm by selecting weighting parameters evaluating the destination errors according to the priority level of the ships. An obstacle in the region can also be considered as a stationary ship with extreme priority.
2) In order to realize reasonable priority reporting, a concept to collect priority charge from each ship equal to the expected gain, i. e., the decrease of the course deviation loss by adopting the reported priority instead of equal priority, is proposed. If the base priorities are chosen adequately according to the average cost of ship type or its objective, this charging system makes it possible to optimize total expected cost including the charge in the minimax sense when ships report the priorities based on actual cost.
3) Control performance is evaluated by simulation study for the third situation, and the proposed algorithm can control 97% of total time interval clearing 1 km miss distance only by changing the direction, when ships pass 12 km × 12 km region arbitrarily with 4 minutes average arrival time. Average delay time by the course deviation is about 0.15 min. Comparing this result with that of the control system on parallel route crossings proposed by Kobayashi and Koyama, the delay time is decreased as the ship speed is kept in this case.

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The controlled thermal environments in enclosed space during natural convection, such as a reefer hold of refrigerating cargo ship, are unnegligibly affected by thermal radiation. The quantity of heat transfer by thermal radiation depends upon surface temperature, emissivity and geometric configuration factor of surrounding walls.
In order to investigate the effects of heat radiation to thermal environment, the radiative flux and heat flow between surrounding walls are measured in an air conditioned chamber installed a wall with lusterless black surface during allowing to warm or cool. Further, three dimensional analyses of heat transfer taking account of heat radiation are carried out for the model of the chamber used for measurements and the results of theory and experiment are compared.
The relations between the emissivity of surface and the heat radiative flux or the distribution of air temperature in enclosed space are clarified by the results of calculation.

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An optimum design problem is treated to determine a frame structure minimizing the structural cost or weight under the constraints on the allowable failure probabilities of critical sections specified in the structure. The configuration of the structure and loading conditions together with their probabilistic nature are assumed to be given. The design variables are the geometrical dimensions of the elements. The failure criterion of the critical section is expressed as a function of the strength of the element and the internal force, which is generated by a matrix method. The optimum design problem is reduced to a nonlinear programming problem. The solution to the optimization problem is obtained by applying the sequential linear programming, and numerical examples are given to illustrate the applicability of the proposed method.

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A statistical result of damages such as cracks, dents and corrosions observed in ship hull is presented which is obtained from the databank of ships registered with Nippon Kaiji Kyokai during recent five years.
The probabilistic density functions of failures, represented both by the number of failures and number of failed ships are given for several causes of damages such as vibration, improper design, mishandling etc. The dependence of failures on the age of ships are analysed in the form of Weibull's and other distributions. The rate of failure and average life of ships are discussed.

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Various structural inspection procedures are applied to detect environmental, accidental and fatigue damage in response to requirements on structural safety. A regular inspection program takes care of environmental deterioration and accidental damage. As fatigue damage most likely occurs in an aging structure, another inspection program is necessary to preserve a fatigue failure of the structure.
It is said that a fleet leader sampling inspection is effective due to the fact that high-time structures corresponding to the fleet leaders might have fatigue cracks with high probability. Meanwhile, operators who have those structures are required to spend time and cost for the inspections. A rotational sampling inspection which was recently recommended consists of inspections of a fraction of candidate fleet until all candidate structures are inspected at least once. Therefore, as many operators participate in the program of inspecting candidate structures, the undesirable situation mentioned above is avoidable.
This report is devoted to discuss the two sampling inspection methods with the aid of a model developed adequately to generate actual circumstances and the Monte Carlo technique. It is mentioned that a method such as the Bayesian method to estimate parameters from data obtained by inspections is not adopted in this model.
The following results are remarked from the numerical example :
1) According to the proposed model that the secondary inspections are performed if the primary inspections detect fatigue cracks, the damage detection capability of the rotational inspection is better than that of the fleet leader inspection.
2) The number of failed airplanes is not affected by the shapes of the fleet time distribution governing number of service flights for each airplane. The distribution in this model is assumed to be represented by the Beta distribution.

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Fracture toughness, size of weld defect, fabrication error etc. which control brittle fracture of welded structure are generally thought to be probabilistically distributed factors. It is easy to evaluate deterministically whether fracture occurs or not by using fracture mechanics and the worst values of various factors. However, there exists some ambiguity in determination of the worst values.
Reliability analysis of spherical tank for the model case was performed by means of fracture mechanics and Monte Calro simulation under postulation of distribution functions for various factors.
The present report describes the postulated probabilistic distributions, model of simulation and formulation of analysis which are used in reliability analysis of the tank. It is recognized that Monte Calro simulation is effective method for reliability analysis of the tank.
From the results of simulation, it is shown that 1) probability of failure P_f of the tank is 10^-310^-4 and 2) average value of δ_c, distribution parameter α_δc, of δ_c, average size of retained weld defect etc. have significant effect on P_f, but angular distortion and misalignment of butt welded joint have trivial effect on P_f.
It is pointed out that the following information and data accumulation are important to reliability analysis of welded structure. That is 1) probabilistic distribution parameters, especially in NDI detection probability and δ_c distribution function. 2) probabilistic information in what kind of microstructure the tip of weld defects exist. 3) information about difference of δ_c value between for natural crack and for fatigue crack.

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Impact of a wedge body dropping on a water surface is analyzed by means of the boundary element method. Wagner's theory predicts maximum pressure in good agreement with experimental results in case of larger deadrise angle β>15°. In case of small deadrise angle, however, there is a large discrepancy between experiments and the theory, which gives an infinitely large pressure in the limiting case β→0°. In reality, pressure is reduced due to air cushioning effects. The present paper concerns with the behavior of the wedge of an intermediate deadrise angle, 1°≤β≤5°, and air cushioning effects are shown to be neglected for β>3°.
In the present calculation, the water is idealized by boundary elements, and the instantaneous configuration of free surface and the wedge body are determined by considering the fluidsolid intersection. Numerical and experimental results show the variation of maximum pressure along the width depending on the dropping conditions, which is in contrast to Wagner's theory predicting uniform distribution.
The relation between the maximum pressure caused by dropping at constant speed and that by dropping freely is also shown as a function of wetted width and impact velocity.
In order to improve accuracy of numerical results, the splash condition should be included in the analysis, which will be left to further study.

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A container ship suffered serious structural damage in her fore body due to slamming in heavy seas in the North Pacific Ocean in January, 1977. She was in the fully laden condition and voyaged to Kobe from Oakland, California, U. S. A. A long brittle crack propagated in the fore and aft direction in shell plating of the flare part on the starbord side. The inner structures, such as longitudinals, web frames and side stringers, on the side shell of the same side were collapsed, and deck and shell plating on the port side was buckled. Furthermore, No. 2 Hatch was distorted in a parallelepiped. In the present paper, the damages are investigated from the view point of ship hydroelasticity with the aid of fracture mechanics. The results obtained suggest the importance of ship handling as well as structural design for preventing serious damages in large container ships.

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Slamming responses and the effects of axial force on deck stress are discussed regarding a large bulk carrier. Axial force may not be neglected in full-formed ship like bulk carriers particularly in rough seas, because of the high wave height and her large pitching and/or heaving motions. In rough seas, moreover, slamming may occur, so the deck stress is raised due to both the whipping vibrations and the axial force.
In order to clarify the characteristics of slamming responses of a large bulk carrier in rough seas, model tests and numerical calculations are carried out : A series of tank tests for slamming is conducted in regular high waves with the use of an elastic model ship, and the deck strains are measured using strain gauges. On the other hand, numerical calculations are performed by virtue of a computer program for nonlinear ship responses in waves called TSLAM, to which a routine for calculation of axial force is newly added in the present paper.
Comparing the results of experiments with the calculations and performing the numerical calculations for an actual bulk carrier, following conclusions are obtained : The effects of axial force on deck stress cannot be neglected for large bulk carriers in rough seas and are significant in the fore-body. Pressure force due to pitching motion is dominant in the axial force.

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The bilinear Mindlin plate element developed by Hughes et al. can be used as a constant moment quadrilateral element by applying the reduced integration technique to both its bending and shearing strain energy. The inelastic plate bending analysis by using this element can be considered as an extension of the conventional plastic hinge method in the analysis of framed structures to the plate problems through a kind of lattice analogy.
In the present paper this element was applied to the bending collapse analysis of rectangular plates according to the tangent stiffness load-incremental procedure with the nonlayered approach for the treatment of plastic deformation. The obtained solutions were generally in good agreement with those by the theoretical plastic analysis, and the computing time required for the 64 elements representation was only 13 seconds by the domestic computer HITAC M-280H.
The present procedure is less inferior from the viewpoints of the efficiency and the accuracy to the various simplified methods previously developed for the nonlinear analysis of plate structures in spite of its conventional nature. Those simplified methods, especially the methods using the concept of plastic hinge lines, should be used as a specially purposed tool in the fields such as the computer simulation with low degrees of freedom on the limit strength of steel structures, the study on the structural crashworthiness and the analysis of concrete structures taking into account the propagation of crack lines.
The present method can be easily extended to the plastic analysis of general shell structures by the combined use with the constant strain plane element, however, in the inelastic stability analysis such as the plastic buckling problem the algorithm for the application of the nonlayered approach should be reconsidered.

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Recently it has become more and more important to ascertain residual safety in accidental case such as collision, grounding etc. of various kind of sophisticated ships or mobile offshore units. In order to localize an accidental damage of those structures, or to confine within a minor damage, it is very essential to quantify a structural resistance, especially relation between absorbed energy and penetration depth. And for this purpose, it is fundamentally important to point out when a outer shell get teared and inner frames or a deck plate get buckled. To observe and quantify those behaviors of steel structeres, many experimental crush tests have been tried.
In this report, to improve predicting method and get more precise estimation of damages, some considerations and basic test results are shown about fracture characteristics of materials used in similitude test and its effect on a law of similitude. It is since a plate thickness can affect not only geometrical dimension, but also material characteristics such as ductility and toughness.
Namely, conducting I-beam bend series test of geometrically similar specimen, it's shown that critical strain corresponding to plastic deformation instability of thin plate (2.3 mm thickness) is considerably larger than that of 20 mm thick plate. And the absorbed energy in each specimen at fracture is not consistent to the law of similitude, but deeply dependent on fracture characteristics of the material. That is, the absorbed work including fracture energy can't be estimated by a simple formula, third power to the scale factor of the model.
It is emphasized that model test results should be modified by calculating the critical strain to the onset of ductile fracture of used material and that its fracture mode, ductile appearance or brittle one, should be checked by a material strength test to be in a same type of that in original structures.

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The essential feature of this study is harmonic resonance of floating compliant structures which are elastically vibrating in regular waves.
The conceps of “characteristic bending moment” which is determined with no consideration about structural elasticity is introduced. It is proved to be efficient in estimating significant wave length condition (L/λ) for various vibration mode shape on which significant bending moment response appears.
The bending moment response is amplified by flexural vibration. The amplification factor of resonant bending moment is dependent primarily on the effectiveness factor of the flexural rigidity of the structure which is defined as EI (m_j/L⁴)/k.
Consequently, the amplitude of harmonically resonant bending moment is found to be estimated through the characteristic bending moment and the amplification factor.
Significant third harmonic resonance which is induced by non-linear wave force was observed in the experiment. Super-harmonic resonance in bending moment response is investigated through numerical calculation using higher order term of drag force which is expressed in Morison's equation.

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A method is proposed to analyze the strength of jack-up rig using a model made by replacing its legs and platform with the beams and plane grid structure with equivalent stiffeness, respectively, and connecting them by equivalent springs. The expressions for the equivalent stiffeness of replaced line legs and those for the spring constant of connecting springs are introduced together with the method to calculate the axial force caused in each member of the actual legs from the axial forces, shearing forces, bending moments and torsional moments of line legs obtained by the present method. Then the accuracy of this method is studied by comparing the results calculated by this method with those calculated considering the legs as space frames and it has become clear that this method gives a practically sufficient results. Using the method of this paper, we can complete the analysis within a very short time as compared with the case where the analysis is carried out considering the legs as space frames. Therefore, this method seems to be very useful not only for the structural design of jack-up rigs but also for the investigation of many problems on the strength and vibration of them.

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The development of oil and gas is increasing in deeper and severer waters. Accordingly, it is getting very important to estimate the buckling and ultimate strength of offshore framed structures such as jackup rigs and platforms.
The following methods are introduced in this paper from the design point of view to estimate the buckling strength of braces and ultimate strength of offshore framed structures as both accurately and simply as possible. The method to estimate the buckling strength uses the simple column buckling equation with initial deflection in combination with the elastic buckling stress obtained from eigen value analysis of framed structures. Simplified non linear analysis method which consists of iterative procedure of structural model modification/linear analysis/ buckling and plastification criteria check is used to estimate the ultimate strength.
Four pieces of 3-dimentional 1/7 scale leg model of actual jackup rig were tested and compared with the above mentioned methods and obtained the following results. (1) The calculated buckling strength is within the error of 8% comparing to experimental results and the method to estimate the buckling strength seems accurate in spite of the simplicity of the buckling equation. (2) Simplified non linear method is found useful for design work by comparing the calculated and experimental results. (3) With using two kinds of brace material, one is high tensile steel and the other is mild, the effect of material on the buckling, the ultimate strength and the mechanism of failure is confirmed both by experiments and calculations.

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The failures in structures often develop from small cracks which initiated at the stress concentration parts such as structural discontinuity, welding toe of component etc.
Though strain gauge instrumentation is usually applied to the stress measurement at such parts, this method requires considerably complicated procedures and preparing time. Recent advances in the infrared technology have enabled to develop highly sensitive non-contacting instruments, for instance thermoelastic stress analysis.
This paper presents the results of some basic experiments for stress measurement using the thermoelastic stress analysis. The system produced stress maps which indicate the stress concentration around notches in test specimens and bracket end in structural model. The experimental maps showed well agreement with the results from F. E. M. or strain gauge measurements.

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Many studies have been made on application of results of fatigue tests on small smooth specimens to evaluation of the fatigue life in structural members based on the estimated strain behavior in stress-concentrated region. Most of the estimation formulae for strain behavior so far proposed have been derived from the analyses under monotonically increasing load. In order to evaluate the fatigue life reasonably, however, it is more desirable to know cyclic local strain range rather than monotonic strain behavior.
In the present study, therefore, it was tried to establish a simple method to estimate the local strain range under cyclic loading. Namely, elastic-plastic FEM analyses under cyclic loading were conducted on notched plates, and an investigation was made into effects of applied stress condition, stress concentration factor and material properties on the local strain range. As a result, the formulae to estimate shakedown limit and cyclic local strain range were derived.
A comparison was made between some results of fatigue tests on notched plates so far published and the fatigue life estimated using the formulae proposed in this study. Although the scatter band in the relation between estimated and measured fatigue lives is rather wide, it is concluded that the method proposed can be used to estimate well on the whole the fatigue lives in the wide range of 10²5 × 10⁶ cycles in notched steel plates of 4180 kgf/mm² strength levels.

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In this study, five types of load controlled fatigue tests were carried out under variable stress amplitude in order to clarify the stress-strain response and the fatigue strength of SS41 steel plate specimen. That is, those tests were constant stress amplitude test, step test, repeated high-to-low and repeated low-to-high block loading test and block random loading test. In each test, stress-strain loops were recorded by X-Y plotter from the start of cycling to visual crack initiation by using the strain gauges put them on the test piece.
As the test results, the following conclusions were obtained.
1) Stress-strain response for step tests, block loading and block random loading were different from that for constant stress amplitude, and cyclic softening for variable stress amplitude was greater than that for constant stress amplitude.
2) Especially cyclic softening under variable stress amplitude was remarkable for low stress level.
3) Fatigue life estimation by Miner's rule makes over estimation compared with the experimental values, and fatigue life of block random loading is slightly shorter than that of block loading under the same stress frequency distribution.
4) When the plastic strain amplitude was used as a determining factor of fatigue damage, the estimated fatigue lives fairly approached the experimental values.

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Fracture toughness tests and fatigue tests on welds of steels (ship structural steel and pressure vessel steel) were carried out in order to investigate the mechanisms and factors to govern the brittle fracture initiation during the fatigue crack propagation at low temperatures.
The welding residual stress was released and its distribution was altered according to the fatigue crack propagation. Although, if the effect of the residual stress was taken into consideration, the fatigue fracture toughness K_fc, was estimated as equivalent as the monotonic loading fracture toughness K_c, which were obtained under the same loading rate (K=dK/dt).
Thus, the fatigue fracture toughness can be obtained from the monotonic loading fracture toughness if it were known as a function of the loading rate and the distribution of released residual stress were also as a function of the crack length.
The safety assessment of a large component in a structure will be also estimated from the knowledge of the monotonic loading fracture toughness under given service conditions (temperature and loading rate), since the alternation of residual stress may be negligible in a large welded component due to the fatigue crack propagation.

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Considerations have been conducted of fracture transition behaviors of notched specimen extracted from 7 kinds of structural steels under dead loading. Three point bending COD specimens and center-notched tensile specimens are prepared for both monotonic loading and dead loading tests. The load-controlled testing machine is newly developed.
Fibrous crack extention initiates at a certain critical COD, δ_i which should be a material constant regardless of testing machines. Although no crack growth is observed by dead loading below δ_i, a certain value of increment of crack growth under constant load beyond δ_i-level can be observed. The reason of crack growth under dead loading can be explained by CTOD (CTOA)-behaviors observed in the vicinity of the growing fibrous crack by using scanning electron microscope.
At any δ-value above the critical COD level, (δ_u)_d or (δ_m)_d, the crack growth increase is not limited and instability immediately occurs in brittle manner at low temperature or in ductile manner at relatively higher temperature. The critical COD, (δ_u)_d or (δ_m)_d is considerably smaller than δ_u, or δ_m obtained by monotonic loading test. In particular, (δ_u)_d is equal to or a little higher than δ_i. The above results can be observed regardless of kind of steel and of loading mode. Moreover, (δ_u)_d-value obtained by bending COD test of deeply notched specimen is almostly equal to that by dead loading tensile test of deeply center-notched specimen. It can be clarified by bending COD test with extremely low strain rate that the critical COD is independent of strain rate, although the maximum bending load value is affected by strain rate.

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In this series of researches on evaluating the brittle fracture strength in structurally stress-concentrated regions, many kinds of crack tip opening displacement in model specimens were gathered as described in the 1 st to 3 rd report. It was also shown that these data could be arranged in a definite relation to applied strain on a crack and crack size, etc., and the validity of the COD design curve was confirmed.
Standing on the above approach, this report proposes a simplified estimation method of the strain distribution in structurally stress-concentrated regions and furthermore shows a series of strength evaluation techniques for such regions with consideration on the effect of welding residual stresses.

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This paper describes the crack arrest properties of 9% nickel steel and its weldment for LNG service applications.
Supposing the situations where the surface crack exists in the plate being uniformly applied a constant stress and kept at a constant temperature, a possibility of restricting the potentially extensive propagation of a brittle crack was discussed. The magnitude of stress intensity factor in the vicinity of the pre-existing surface crack shows the maximum value at the deepest crack tip located in the middle of plate thickness where the plane strain condition is maintained, and shows the minimum one at the both ends of surface crack in the plate surface where are in the plane stress condition. Therefore, there remains possibilities of crack arrest in the end of surface crack even if a brittle crack initiated and propagated in the bottom region of surface crack.
In this investigation, such run/arrest event was confirmed in the modified double tension test. This special testing technique is characterized by the specimen with the sharp notches simulating the pre-existing surface crack. The sharp notches have an adequate length and are located in the crack propagation part of specimen.
The crack arrest properties, K_a as the material constant were evaluated by the correlation of applied stress and arrest crack length obtained in the modified double tension test. The dimensionless stress intensity coefficient Y after Srawley's numerical analysis on single-edge crack model was used in the calculation of K_a. As a result, it was determined that the low tough 9% nickel steel used (_vE_-196=84 J) and its weldment had superior crack arrest properties of 220 and 259 MPa √m at -170°C respectively.

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In the previous paper, the run/arrest events of a brittle crack relied upon the mechanical discontinuities around the pre-existing surface crack in uniformly stressed plate at a constant temperature were confirmed by using the modified double tension test technique. And the crack arrest properties of low tough 9% nickel steel used and its weldment were determined.
In this investigation, the modified double tension tests were further conducted mainly on the low (P, S) type 9% nickel steel plates of 32, 23 and 16 mm thickness their weldments. As a result, the following conclusions were reached ;
(1) The critical stress values at which a brittle crack could be arrested at the end of saw cut notch simulated the pre-existing surface crack significantly increased with decreasing of plate thickness.
(2) Such effect of plate thickness is directing into the mechanism of crack arrest depend ing on the mechanical discontinuities.
(3) This fact indicates that the thickness-independent crack arrest toughness expressed in term of K_Ia as a material constant does never exist as to the run/arrest event of a brittle crack.
(4) The high toughness derived from the decrease in P, S content in steel brought a fairly increase in crack arrest properties, K_a of 9% nickel steels.
(5) Further improvement of crack arrest toughness was confirmed on the direct quenched and tempered 9% nickel steel.
(6) The crack arrest toughnesses K_a of low (P, S) type 9% nickel steel used and their weldments of 32 mm thickness were 514, 317 (fusion line) and 323 MPa√m (matching ferritic weld metal) at -170°C respectively.

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