In the previous paper the numerical method of analysis of imcompressible viscous fluid problems was proposed. As velocities and pressure are adopted as the unknown values, it is believed that this appraoch may be very effective in analysis of the three dimensional flow problems. As it was demonstrated, the main feature of that method is the use of the lower order shape function in evaluation of element stiffness matrices.
Following the same line the two dimensional viscous flow problems are solved by using stream function in this paper. In the present analysis element matrices were derived from the hybrid variational principle of Hellinger-Reissner type which was used by K. Kondou in his plate bending analysis.
Using newly derived elements, the flow in a square cavity and the flow around a circular, cylinder are solved as examples. In the former problem the flow patterns are analyzed up to Reynolds number of 3200 and in the latter one the drag coefficients are calculated.
Results obtained in these analyses duly showed validity of the present method in comparison with the existing finite element or finite difference method.

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Stability of wake field with a pair of longitudinal vortices is discussed by a simplified in-viscid flow model. The model is composed of an axisymmetric jet, a vortex doublet inside it as the limiting configuration of a pair of vortices, and a cross flow to keep the vortex doublet inside the jet. The theoretical analysis based on the linear instability theory shows that the whole flow field is unstable and the flow due to vortices weakens the instability of jet at the side of the cylindrical jet surface facing the cross flow but magnifies it at the back side of the surface.

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Separation patterns are classified into three types (regular, singular and combination types) by the property of the differential equation, the solution of which gives limiting streamlines.
A criterion for the three-dimensional separation line is deduced from the negation of the Lipschitz's condition. The criterion is applied to the existing limiting streamlines over a ellipsoid of revolution at incidence, and also to the calculated ones on a ship hull.
The results show that the present criterion is available for the prediction of the three-dimensional separation line.

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Outer and inner expansions are formulated on the basis of “Rational Strip Theory” for slender floating body motions due solely to the incident wave. More precisely, since the detail of a slender body is lost in a farfield, farfield potentials are assumedly represented by lines of pulsating source and/or doublet, and their densities are determined by matching with nearfield potentials. This scheme readily results in three dimensional diffraction as well as radiation potentials which are valid in a farfield. Unlike non-rational strip theories, wave pattern, exciting force, drifting force, etc are all available in a three dimensional sense, since throughout the analysis all problems are discussed in terms of three dimensional velocity potentials. Measurements of wave heights and exciting forces manifest the respective validities of the farfield diffraction and radiation potentials obtained here, and substantiate that these potentials are dependable, at least, up to a wavelength as long as the body.

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The diffraction problem appeared in the ship-wave interaction problem is treated by making use of the slender body theory under the short wave assumption. A solution which is valid in the bow near field as well as in the midship near field is derived and it turns out to be able to descrive the 3-D effect of the interaction of incident waves with a ship hull. This solution is thougth to be the extention of Faltinsen's³⁾ in the meaning that it is valid at the vicinity of bow and also the extention of Maruo's⁴⁾ in the meaning that it can treat not only zero forward speed case but also forward speed case.
The wave load distribution calculated by the present method shows strong x-dependance, which can easily be attributed to the cumulative effect of the slowly varying source density function which is a representation of the effect of the interaction between incident waves and ship hull.
By use of Green's theorem, the wave load can be calculated by the asymptotic behavior of the solution for the generalized radiation problem in which the 2-D Helmholtz equation is the governing field equation.
Some heuristic numerical results are presented for a ship with circular cross section.

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Two methods are in common use for solving the numerical problem of a body oscillating in the presence of a free surface : (1) a multipole-expansion method and (2) an integral equation method. The latter generally breaks down at and near a set of discrete frequencies, namely, the eigenfrequencies of the complementary, hypothetical problem for the flow inside the body. Ohmatsu (1975) has shown how to avoid this difficulty by modifying the interior problem. In the present paper, an even simpler procedure is presented for accomplishing the same result. A minor change is made in the Green function, in such a way that the interior problem never has an eigenfrequency near the frequency under consideration. Any existing computer program based on the approach of Frank (1967) can be modified easily to incorporate the change of Green function. The modification is based on a procedure suggested by Ursell (1953).

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In the previous paper, the author reported on a theoretical study of the effect of side-wall interference which has deleterious influences upon the results of experiments in regular head waves.
In this paper, the author reports experimental studies which were carried out to verify the appropriateness of the theoretical study. Model experiments were carried out in two towing tanks of different sizes. One of them was a narrow tank (B_T/L = 1.5), and the other a wide one (B_T/L = 3.9). The results of the experiments at the two towing tanks were compared with each other and with numerical results calculated previously.
Furthermore, wave patterns, generated by a pulsating point source which travels with constant speed, were obtained to study the contribution of Kelvin ship waves which are disturbed by periodic ship motions. This contribution was considered to be small and was neglected in the earlier analytical approach.

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Pressure measurement on blade surface of rotating MAU type propeller and cavitation tests were carried out in non-uniform flow.
The measuring accuracy of the adapted pressure microsensor was not satisfactorily high regarding the stationary component. However, as far as the unsteady component is concerned, its accuracy appears sufficient for supporting the usefulness of unsteady lifting surface theory.
In this calculation, it is also found out that circumferential wake component plays an important role for precise prediction of phase-shift.

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A new propeller series (KB-type) was developed on the basis of the results with MAU type propeller (REPORT I & II) by applying three-dimensional cavitation bucket chart. Noticeable improvement in cavitation characteristics was obtained with the KB-type propeller without sacrificing the overall efficiency of MAU type propeller.

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In this paper, the authers describe an experimental investigation of the cavitation damage on a two-dimensional hydrofoil -NACA 16-021 section made of pure aluminum-tested in a venturi type cavitation tunnel.
Linearized theory of cavity flow was used along with the equation of bubble radius to predict the cavitation erosion intensity.
The following conclusions are obtained :
1) Weight losses caused by cavitation erosion could be devided into 3 zones : Incubation, Accumulation and Attenuation zone, respectively. On the other hand, surface roughness increased linearly with the exposure time to cavitation even in the incubation period.
2) Measurement of the surface roughness is an useful method to evaluate cavitation damage.
3) The maximum erosion rate appears at a certain cavitation number. The same tendency can be obtained by the above mentioned theoretical analysis.
4) The paint test results agree with that of the measurement of surface roughness increase.
5) The plastic deformation caused by cavity collapses was simulated using the two-dimensional elastic-plastic analysis by FEM. The calculated result shows a qualitative agreement with the exprimental results. But the raised rim around a pit which is observed on the eroded surface, is not obtained by the FEM calculation.

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A procedure to predict the effective wake distribution, which is important for the design of a wake-adapted propeller and for the calculation of propeller vibratory forces, is presented for an axisymmetric flow. The prediction is made by means of streamline tracing under the assumptions that the fluid is inviscid and the propeller-induced velocity field is irrotational. For practical convenience, the interaction of a propeller and boundary layer around stern is not considered.
The velocity measurements of the flow in front of a working propeller in open-water and in wake field of a body of revolution were carried out in the towing tank by use of 5-hole pitot probe. The propeller was arranged away from the body of revolution enough to avoid the interaction between them.
A close agreement is obtained between measured and predicted velocity profiles upstream of a propeller. It is found that the rate of the contraction of the nominal wake varies in radial direction when the propeller is operating. The circulation distribution of the propeller in radial direction for the predicted effective wake distribution is slightly changed from that for the nominal wake distribution.

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When a ship with a propeller advances in the sea with winds and waves, she usually loses in speed compared with the case in calm sea under the condition of constant output-power of the main engine. In this paper a method is presented that, in the case where the ship is moved almost straight in regular head waves, the propulsive performance is evaluated by using the calculated results of the pitching and heaving motions. Then, the relations among the ship speed, the rate of revolutions of the propeller and the delivered horse power are shown in numerical examples.

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A method of prediction of hydrodynamic forces and moments acting on a ship in heaving and pitching oscillations is presented. It is based on a revision of the slender ship theory, which can interpolate between the original slender ship theory at low frequencies and the strip theory at high frequencies. Numerical computations are carried out for Series 60 models and results are compared with experiments by Gerritsma and Beukelman. Much better agreement between computed and measured results is observed when compared with results of the strip theory.

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A method for predicting the roll damping of a ship at forward speed is proposed. The roll damping is assumed to be divided into five components, that is, the frictional, the wave making, the eddy making and the lift components of the hull, and the bilge keel one. It is found that the eddy making component of the hull decreases rapidly with forward speed, while the wave making and the lift components increase. The formulas for these three components are deduced from some theoretical considerations and the experimental results.
The frictional component is estimated by Kato-Tamiya's method. The bilge keel component is assumed, to be constant at forward speed, and is estimated by the formula which the authors have proposed recently.
The values predicted by the present method are in fairly good agreement with the experimental ones for ship models at forward speed.

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Model experiments were carried out on an ore and two container carriers in head and oblique regular waves. Relative water elevation around the bow and shipping water passing through the forecastle deck end were measured to analyze the behaviour of the shipping water on deck. Criterion for deck wetness was also examined by the O. S. M. calculations and the model experiments. Severity index to shipping water onto deck of the ship was proposed.

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Wave forces exerted on circular cylinders in regular waves are investigated. The circular cylinders are fixed horizontally below the water surface.
Experimental results are compared with values calculated by linear theory and the other data obtained differently.
Main conclusions obtained are as follows :
1) In case of small period parameters, inertia coefficients obtained by experiments show good agreement with theoretical values calculated by linear theory. But for large period parameters, the experimental values are much smaller than the theoretical ones.
2) For large period parameters, drag coefficients derived in the present investigation approximately coincide with those obtained in experiments on hydrodynamic forces acting on circular cylinders in oscillatory flow. But there is much difference between them in case of not so large period parameters.

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This paper is mainly aimed to study the phenomena of slowly varying oscillations of moored vessels and to state the procedures for predicting their values in wind and waves.
Model tests were conducted at IHI's ship model basin on the motions of a floating vessel moored by coil springs in regular and transient water waves, and theoretical calculations of dynamic behaviors of a moored vessel including slowly varying transient sway motions were also carried out. As a result of the studies, the following conclusions were reached;
1. Slowly varying oscillations of moored vessels exist as transient sway motions for a long period in regular beam seas, which are directly propotional to the steady-state displacement due to the wave drifting forces.
2. The calculation and the test results are in fairly good agreement showing the procedures for predicting slowly varying transient sway motions in regular beam seas.
3. Slowly varying transient sway motions also exist in transient water waves after the time when the transient water waves pass through.

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There have been frequently occured miserable accidents of capsize for small fishing boats in the northern sea area near Japan, which were attended in the most cases with loss of human lives. Such accidents occured on the salmon fishing boats in high percentage in comparison with others.
The purpose of this paper is to investigate the important factors affecting to capsize for such a small fishing boat as well as the effectiveness of the mean for preventing the accidents, through the model experiments in heavy seas.
In the experiments, the 1/7 scale model was navigated in regular and irregular waves of high steepness generated in the model basin so that the capsize of the model could be expected to occur at some special conditions of the model and sea.
The model ship was equipped with the weight shifting device for simulating cargo shift which could occur by heavy rolling motion of ship and would promote the capsize, while, on the other hand the inflatable rubber bulges were also attached on the both sides of the model hull which will lend an additional buoyancy and the righting moment to the ship in the emergency cases.
A great number of running was carried out in the experiments under the various ship conditions as well as sea conditions, and as the results some capsizing phenomena were observed in case of poor stability condition. It was deduced through analysis of the experiments that the trapped water on deck with cargo shift act most effectively to capsize the vessel in beam and quartering seas, while the inflated bulges were so efficient to prevent the capsize that no capsize was observed when the inflation of the bulges was timed in spite of the trapped water and weight shift.
The theoretical analysis of ship motions, such as rolling, accelerations and relative motions in irregular waves can explain well the experiment results of capsizing phenomena which attracted attention to the danger of navigation in quartering seas having high steepness.

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In this paper, various types of the long-term distribution of extremes are re-examined by the analysis of the actual ship's data. Authors try to applicate the following probability distributions.
1) Logarithmic normal distribution with upper limit.
2) Gumbel's extreme distribution with upper limit.
(Type III), used by Watanabe^{2), 3)}.
3) Weibull distribution, used by Nordenström⁴⁾ etc.
Moreover, the estimated extreme values of ship motions are compared with the long-term prediction values calculated by the theoretical method.
Data used in this paper are measured by the several full container ships, in North Pacific Ocean, in winter. Consequently, next results are obtained.
a) Long-term distribution can be expressed properly by the logarithmic normal distribution with upper limit or the Gumbel distribution with upper limit.
b) The logarithmic normal distributions without upper limit give clearely large estimated values compared with the actual ship data. Then, this distribution is not suitable for the estimation of long-term ship motions in ocean waves.
c) Obtained extreme values in 100 years, are about ±9 degrees on pitch angle, about ±0.96 g on bow vertical acceleration, about ±31 deg. on roll angle.
d) Long-term predictions taking into consideration on the ship operations, coincide with the long-term extreme value estimated from the measured data of short terms.

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Ships of the small draught/length ratio may suffer from serious structural damages due to slamming in heavy sea. The strength of a ship in such conditions can be investigated by studying its motion. In this paper the authors investigate theoretically the motion and longitudinal strength of a tanker in head sea taking account of the effects of nonlinearities such as the hull shape nonlinearity, bottom emergence, and hydrodynamic impact, and a series of tests was carried out in a basin, measuring the heaving and pitching angles, the acceleration at the bow, and the bottom pressure along the base line ; the experimental results were compared with calculations, which shows good agreement. Conclusions obtained are as follows : (1) The heaving and pitching amplitudes themselves are affected only slightly by slamming ; (2) the acceleration at the bow increases due to the effect of nonlinearity ; (3) the time history of the calculated pressure and the measured are similar in shape ; and (4) the sagging bending moment becomes very large in slamming conditions in the fore body in the case of large ships.

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Approximate calculations of amount of shipping water for two-dimensional ship model during one cycle of heaving motion were carried out. Using the approximate calculation method, wave bending moments of a large tanker including shipping water effect were presented, and effects of shipping water on the transverse strength of a single deck cargo ship were discussed.

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The present authors investigated the characteristics of force acting on the structural elements of a mooring anchor, such as fluke, shank and stabilizer fin. On the basis of experiments, stability coefficients were proposed in the first report [1] to evaluate the in-plane and transverse stability of the dragged anchor. In this paper, the stabilizing moment of the anchor around its shank is investigated in detail for all positions.
As a result, it is shown that an anchor of absolute roll stability can be realized by attaching a pair of large plate-face stabilizer fins.
Maximum holding power, inclination and depth of anchor dragged in sand bed are measured, and are compared with the results of calculation, which was formulated in the second report [2].

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In this paper, maneuverability indices of submarine longitudinal motion deducted from the mathematical model are correlated statistically with the pilot ratings obtained from the specified maneuvering test by several submarines.

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This paper presents the result of the study of the longitudinal motion of a circular type submarine equiped with flap type control planes.
Control plane effectivenesses of 24 different control plane configurations were investigated by use of control plane effectiveness derivatives obtained from 3-component test in a towing tank, and maneuverability indices deducted from the transfer functions.
As a result, it was concluded that the maneuverability of the circular type submarine with flap type control surfaces could be made equal or superior to that of the present day submarine, if we select a proper control plane configurations.

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In the former paper, the authors proposed an entirely new autopilot system using a stochastic autoregressive model. According to the model fitting procedure, we could design flexibly an optimal controller under an appropriate evaluation function.
In this paper, the experimental results that an on-line direct digital control using the model fitting procedure was applied to an actual ship are reported. For the sake of it, in chapter 2 and 3, the theory proposed in the former paper is outlined. In chapter 4, the hard and software developed for the realization of the on-line controlling of the ship are introduced. In subsequent chapters, the plan and the method of the actual sea tests are described and the results of the on-line direct digital controlling of the actual ship's course keeping motion are scrutinized.
The new concept used in this paper for identification of system through the autoregressive model, the AIC (Akaike's Information Criterion) proposed by Dr. Akaike is discussed briefly in Appendix.

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These days we sometimes have experienced or heard of full-bodied ships with so-called “unusual phenomena” in manoeuvrability, and the number of those ships seems to increase rapidly owing to the growing fullness of ships.
Herewith in this paper an example of such a phenomenon appeared in a fishery research vessel is dealt. Turning tests and zig-zag tests were held, using both the ship and the 1/10 scale model. Oblique towing tests, β-varying tests (changing drift angle gradually) and observation of the stern flow, furthermore, were held in a towing tank using the model.
Those experiments certify the existence of two separate flow fields around the hull and the occurrence of switching the two states. The large clearance above the propeller and the rudder as well as the full stern form permits the flow passing from starboard to port or vice versa through the clearance. By this flow, two types of unsymmetrical flow separation may occur. The alteration of the flow direction through the clearance accompanies the changes in the separation, the flow field and the force acting on the hull.
Basic characteristics of the “unusual phenomena” observed both in the ship and the model can be explained by the unsymmetrical separation and its alteration. The apparent difference between the ship and the model can be also treated by the conception of “switching line”. The “switching line” is defined as the critical state of motion at which the alternation of the flow occurs.
In consideration of those experiments, a center fin shutting the clearance was adapted to both the ship and the model. The results are fully satisfactory. In model tests the unsymmetrical separation is no longer observed. Therefore, the course stability recovers almost completely and the ship can keep the course without any difficulty.

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本論文では, 面内力を受ける平板 (円孔, 楕円孔あるいはクラックを有する) の弾塑性解析を行なった.弾塑性解析の基礎概念として初期歪法を用いたため, 固有歪がその近傍に及ぼす影響係数を求める必要が生じた.そこで, 複素応力関数を用いて, 台形領域に存在する一様な固有歪の影響係数を求めた.解析中, 首尾一貫して複素応力関数を採用したため, 鏡像の原理および写像を導入することができ, 円孔, 楕円孔あるいはクラヅク上の自由境界条件を常に満足している解析関数を見出すことができた ((48) 式～ (56) 式).
開口近傍の応力の値は有限要素法の計算結果と比較して, かなり良い精度で得られることがわかった (Fig.18).
なお, 本方法の計算時間は, 円孔板 (無限板) の場合, 要素数86に対して, 固有歪の影響係数を作るのに約300秒, その後1ステップの平均所要時間は約1秒で計370秒 (70ステップ) を要した.一方, 有限要素法では, 約300自由度に対して, 75ステップの計算時間は約300秒で, 1ステップの平均所要時間は約4秒である.

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Geometric non-linearlity depends on the first derivative of the displacement field, so that it is very advantageous to use the lower displacement field with respect to cost and computing time.
In this paper, a new discrete plate bending element with the first order shape function is proposed, and their higher order derivatives are approximated by the finite difference expression which results in substantial simplification of energy integrals.
Furthermore, in this element a number of displacement parameter of one node is 1/3 of a well-known plate bending element and therefore considereable reduction of computing time can be expected.
From the results of numerical analysis it can be concluded that this model might be very powerful in non-linear in-plane as well as bending analysis of plates.

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Previously authors proposed a new discrete beam element with the first order displacement field, and in evaluation of the strain energy their higher order derivatives were approximated by the finite difference expression of the first order derivations.
In this paper, this new discrete element is applied to analysis of geometric and material non-linear problem of beam structures.
Total number of degrees of freedom of the present model is 2/3 of a well-known beam element and simplification of energy integrals etc. due to the use of the linear displacement field yield considerable reduction of computing time.
A series of results of analysis have duly proved validity of the present model.

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A new discrete model for elasto-viscoplastic analysis in beam and plate bending problems is proposed in this paper. This model can be used effectively in dynamic collapse analysis considering a strain rate effect.
As numerical examples transient response analysis of an elasto-viscoplastic beam and plate subjected to transverse impact and earthquake response analysis of a cantilever beam are carried out.

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Cylindrical oil storage tanks have been designed conventionally based on the brief calculation of elastic stress distribution on the components, because the shape of the tank is simple enough and the major part of hydrostatic load is supported by the foundation of the tank. Recently, some accidents of failure or damage have occured. Therefore, it has become necessary to re-investigate the safety against failure of the tank.
Stress and deformation of cylindrical tank have been analyzed numerically with the consideration of the behavior of the foundation, and it has been found that the complicated behavior of deformation caused by the local sinking of the foundation can be explained by the results of the analyses. This may be useful for the structural design. On the other hand, from the standpoint of welding or maintenance of the tanks, it is necessary to examine and to analyze the part, where is most probable to cause failure, with the consideration of material property, geometric discontinuity and fracture mode.
In this study, the model of Tee-joint which simulates the joint of cylindrical shell plate and annular bottom plate was examined and analyzed to research the deformation behavior of the joint and to investigate the criteria for design, welding and maintenance. As a result, it was found that the strain at the toe of weld on the annular plate, where fracture usually initiates under the bending load, is directly related to the change of angle between the shell plate and the annular plate. This relation does not depend on the material properties but on the plate thickness and loading condition.
From the relation obtained above, by setting the allowable strain for the toe of the weld, the critical deformation angle of Tee-joint is successfully estimated, which can be adopted. as a design standard or a maintenance standard of this type of tanks. Finally, the requirements for bending ability and Charpy impact energy of Tee-joint are determined in order to prevent from brittle fracture.
Futhermore, the completely penetrated groove welding of Tee-joint was compared with the fillet welding by means of experiment and numerical analysis. As a result, no difference was found between the both joints in regard to deformation ability and fracture stress. The incomplete penetration weld part which exists in the fillet welding joint has no influence on deformation and fracture behavior under the bending load. From this result, the conventional fillet welding may be satisfactory for the Tee-joint of the tanks.

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Various types of offshore structures including drilling rigs, platforms, etc. have been built. These days, they are requested to have better working performance in severer state of sea and weather, and as a recent trend, they are becoming larger in size and more complex.
However, they appeared just several decades ago, and the data to design them is not accumulated so much as general ships. These structures are to be designed under the rational and synthetic estimation of behaviors in sea, and the safety is also to be confirmed experimentally or analytically.
For that purpose, the authors have developed the total system of computer program for design and analysis for floating offshore structures. The system made it possible to realize the rational and consistent evaluation on the behaviors and the safety of them.
This system consists of an integrated group of individual programs which includes hydrostatic calculation, tank capacity calculation, trim and stability calculation for intact and damaged condition, analysis on the oscilating motion of the structures among regular waves and wave force calculation, the statistical analysis on each response of the structures among irregular waves, etc.
Furthermore, this system can be used individually or successively according to the needs in every stage of design or analysis.
In this paper, outline of this system is presented with examples of calculation using this system for the existing semi-submersible catamaran drilling rig, from which the reasonable results were gained.

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From the following points of view, periodic response of three dimensional floating framed structures is studied in this paper. What is worked on is three dimensional floating framed structures which consist of plural columns with immersed body and connecting members.
(1) The relationship between member force response and motion response should be clarified for the overall structural design.
(2) The amplitude and phase lag of member forces at member junctions are needed for the local structural design of junctions.
(3) The effects of flexibility of connecting members on the motion will be important for large scale floating framed structures in future.
A new analytical method based on the fundamental concepts studied by authors so far is developed to discuss the problems mentioned above. On the other hand, model tests of several types of three dimensional floating structures were conducted to evaluate the applicability and the accuracy of the new method. The calculations are compared with the experiments and several comments on estimation of member forces of connecting members are given from the calculated results.

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As one of the characteristics of ship hull structure, many holes are made on web plates for access and weight saving.
Many studies have already been made to investigate the declining of the buckling strength by the perforation. Nevetheless, the shear buckling failure of such a structure has not ceased to exist.
On this paper the instability of perforated plates having reinforcement is studied by means of FEM analysis and experimentation to determine the effect of stiffenings on the buckling strength. This study mainly deals with the simply supported plate with an oval hole subjected to shearing force. As for the reinforcing method, stiffener, spigot-plate and doubling are chosen.
The conclusions drawn are as follows;
1) As the reinforcing method, stiffener is most desirable in respect of elastic range.
2) On the presumption of the representative ratio of thickness to breadth for the web plate, yielding will take place before the buckling failure.
3) In case of the above, stiffener does not improve much the buckling strength and it is better to reinforce the perforated plate by doubling.

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In the previous report, the authors clarified the existence of the minimum stiffness ratio, γ^U_min, of a stiffener against the ultimate strength of a stiffened plate in similar to the buckling strength, γ^B_min. In this report, elastic large deflection analysis is performed on the stiffened plate, and the phenomenon of the secondary buckling after the primary buckling is indicated. Then, a series of experiment is conducted to confirm the phenomena predicted by the theory.
From these theoretical and experimental results, an approximate analytical method to determine γ^U_min is newly proposed as the intersection of the secondary buckling strength curve and ultimate strength curve of a locally failured plate, when there exists no initial deflection. When there exists initial deflection, the effective minimum stiffness ratio _effγ^U_min is defined as the intersection of a curve of the initial yielding of bending stress of a stiffener and that of membrane stress of a plate. This method can also be applied to determine γ^U_min of a stiffened plate with arbitary aspect ratio and arbitary number of stiffeners.
The effect of welding residual stresses on the buckling and ultimate strength is also discussed, together with on γ^U_min and _effγ^U_min and the minimum stiffness ratio against the buckling strength, γ^B_min.

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The present analysis deals with ultimate behaviors of a panel reinforced by a longitudinal rectangular stiffener under uniaxial compression. Their characteristics depend largely upon the flexural rigidity γ of the stiffener. There are two specific values γ₁, and γ₂ to classify the ultimate behaviors.
In the case of a weak stiffener (γ<γ₁), the behaviors of the stiffened panel is similar to those of an unstiffened panel. In the case of a strong stiffener (γ₂<γ), the joint line is supported effectively by the stiffener, and local deformations dominate even at the ultimate strength. If the rigidity of the stiffener is intermediate (γ₁<γ<γ₂), local buckling occurrs first, but later on overall deformations become large.
The panel reinforced by a one-sided stiffener shows rather complicated behaviors, since the effective neutral axis is influenced by local buckling and yielding in the stiffener.

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Some studies on optimization of structures are carried on by using of SMUT incorporated with matrix structural analysis. But this technique is difficult to achieve in practice because the cpu-time for calculation extremely increas as increasing of the structural members. Thus further works are needed to develop a satisfactory technique of optimizing the ship structures. In this paper following two techniques are investigated in order to improve SUMT.
(a) Linearization of constraints
It can be considered that the change of design variables at each iteration are generally small, then consider the Taylor series expansion of constraints about the starting point at the iteration up to linear terms. The constraints can be evaluated by the obtained linear formulas instead of by accurate analysis, number of structural analysis may be decreased.
(b) Multi-step optimization
Divide whole structure into sub-structures, some design variables can be diminished by assuming that similar structural members which compose a sub-structure have equal dimensions. Optimizing the whole structure on the left design variables, the dimensions of the structural member obtained by such an optimization can be considered as approximation for actual optimum design. Repeat the same procedure using the approximate design as starting point and increasing the number of sub-structures.
To compare the present methods to the normal one, several examples are performed by those methods. Application of linearization of constraints and multi-step optimization indicate that those techniques have good convergence property and computational efficiency, but it is shown that the multi-step technique is not effective for some cases.

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The behavior of the double-bottom structure of a ship stranding on a rock is studied to establish the analytical method for the strength. An experiment is performed by using a model of the double-bottom structure of approximately 1/7 scale and a rock model of a cylindrical shape. An analysis using the idealized structural unit method shows a good agreement with the experimental result.
A general analytical method to determine the strength of a ship at a stranding condition is proposed. An example calculation is performed for a cargo ship being about 120 m long and stranding on a rock with a cone shape. Furthermore, the nonlinear behavior of a girder element with a manhole is idealized for actual ships and the validity of the idealization is confirmed by an experiment.

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This paper deals with model tests and their analysis conducted to evaluate the structural strength of double bottom for two types of stranding. Striking : The bow of a ship strikes a rock, which horizontally penetrates the bottom structure. Grounding : The ship grounds on a rock, which vertically penetrates the bottom structure depending on sea condition. For the striking test, 1/4 scaled double bottom models of steel plates were made representing the bottom of usual cargo holds and more stiffened bottom of engine rooms, etc. The rock model is a rigid square piller with leading wedge of angle 90°. For the grounding test, 1/8 scaled double bottom model was made representing the bottom of engine room, etc. The rock model is a rigid cone with apex angle of 90°. The rock model was set on the head of a 600 ton Amsler universal testing machine, and forced to penetrate the bottom model set on the moving bed.
Following conclusions are obtained from analysis of test results.
(1) In striking situation, crushed (buckled or torn) members such as bottom plate, inner bottom plate, longitudinals and girders would have the collapse strength of 80% yielding of their material, while deflected and ruptured members such as floors would induce membrane force in proportion to rock's penetration and subsequently break at yielding of their material with 20% elongation (in case of mild steel). This assumption gives very good estimation for the relation between load and penetration of the bottom structure.
(2) In grounding situation, same assumption is also valid. In this case, crushed members are floors and girders, while ruptured members are bottom plate panels supported by floors and girders.
(3) The damage of an oil carrier of about 100 thousand tons with double bottom is estimated using calculation formulas acertained by the model test. On striking a rock at the bow during fully loaded running, rock's penetration would reach O.20.5 of ship length. On grounding on a locally projecting rock, the bottom plate would be ruptured at rock's reaction of 900 ton, and the rock would reach the inner bottom plate at that of 3, 600 ton.

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It is well known that the racking phenomenon is the most important structural design problem for a ship having few transverse bulkhead. This paper reviews the results of study on the method of calculation of the racking deformation in the cross section of such a ship.
First, the authors explain the method of estimation of deviation loads responsible for the racking. The authors define the deviation loads as differences between the actual loads and beam loads. The beam loads are assumed to be acting, proportionately to the resultant shear forces, on the cross section of each longitudinal strength member as an elastic thin walled beam.
Secondly, the authors examine the distribution of racking as the shearing deformations in cross sections of a Pure Car Carrier, which is capable of carrying 3000 motor cars, by somewhat simplified structural idealization.

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Stresses in a LNG tank, which are random variables caused by various types of random wave induced loadings, should be treated statistically.
The Square Root Method (SRM) is a conventional method for the estimation of maximum expected values of the tank stress resulting from these types of loadings. This method gives an accurate solution in a special case where the loadings are statistically independent and stress response is linear with regard to the loadings. However, there are, in general, certain correlations between wave induced loadings and stresses, such as Von Mises' equivalent stress and principal stresses, which are non-linear quantities with regard to the loadings.
This paper explains and discusses an analysis procedure called “Total System Analysis” (TSA) procedure, which has been developed to accurately estimate longterm statistical values of tank stresses. This procedure is an extension of the concept of the commonly-used statistical analysis of the long-term prediction of response of ship's motions and wave induced loadings; the procedure treats non-linear stresses as well as linear ordinary stress components.
In establishing the procedure specific items such as the introduction of stress response functions, the problems of non-linear stresses and the approximation of probability density functions of tank stress local maxima (or minima) to Rayleigh distributions, etc. are discussed. These items are verified by numerical experiments by a computer.
A Hitachi Zosen CBI type spherical tank on a 130, 000 cubic meter LNG carrier has been analyzed by the TSA procedure ; the results show that the correlations between types of wave induced loadings have a large influence on the tank stress, tending to reduce it, and that the non-linear stresses including the influence of correlations between the stress components are smaller than those without the above influence.

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Fatigue tests on ship hull structures have been conducted by R. Weck and J. J. W. Nibbering and also in Japan by Mitsubishi Heavy Industries, Ltd. and other shipbuilders. On the basis of the results of these tests, this paper deals with a tentative plan of a fatigue design diagram centering on consideration of fatigue crack initiation life.
Structural members under consideration are transverse strength members with joints, longitudinal strength members with openings and longitudinals with scallops.
In calculating damage (D), the hot spot stress is used which is obtained by multiplying nominal stress by given stress concentration ratio K_t in cracked part of each structural member and stress increase ratio K_e due to decrease in effective width of face bars.
The diagram shows the lower limit of the relation between the hot spot stress and crack initiation life N_c. By using the diagram, frequency distribution of external force, and Miner's law, the possibility of fatigue failure of each structural member can be examined by whether damage (D) is greater than 1.0 or not.
The author has verified the appropriateness of the design diagram by comparing it with analysis results of fatigue failures in actual ship and the diagram has been compared with the fatigue test results of basic welded joints of simple shapes and the fatigue test results of smooth, simple shape specimens by constant strain amplitude.

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In this paper, authors report about the loads on ship caused by horizontally laid cylindrical heavy cargoes at rolling of ship. In such a case, a coil called “key coil” is usually used to prevent the motion of coils. The key coil is a coil which is laid in a narrower space than its diameter and held on a high position. Authors developed the calculating method for cases with and without a key coil, and their numerical results were compared with the experimental values. Results of this investigation can be summarised as follows :
(1) Loads on a side wall and a bottom can be obtained theoretically with a considerable accuracy.
(2) The key coil should be put apart from a side wall.
(3) If a coil which lies apart more than two coils from a side wall is used as a key coil, the design load F on a side wall can be given by a following expression,
F=2.5Wsinθ
where, W is a weight of a coil and θ is an angle of inclination.

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In the previous paper, the characteristic equation for the three dimensional beam structures contained the rigid bodies and mass particles was introduced by using of the solutions of four kinetic differential equations, i. e. two bendings, torsion, and tension-compression.
The orthogonality of the vector mode function composed of the four kinds of the shape functions was proved.
In this paper, we investigate in the modal analysis method of the general three dimensional beam structures contained the rigid bodies and mass particles.
We conduct the impact experiment, using the structure model constructed by a flat rigid deck with four legs same size as described in the previous paper.
The transient responses of the model subjected to the concentrated impact force at the deck and the leg are calculated by the proposed modal analysis method.
The theoretical results coinside with the experimental ones fairly well.

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A method for the calculation of the coupled vibration has been derived using the concept of modal synthesis. The modal parameters such as frequency, modal mass and modal damping and the vibration mode of the coupled vibration can be calculated by the present method using the modal parameters, vibration mode and mass distribution of uncoupled vibration. The applicability of the method is studied to the higher mode vibration of ship structure which is the complicated coupled vibration of the substructures and the main hull girder. The isolated calculation of individual local structure, such as superstructure, double bottom in engine room etc can be combined to yield the final results coupled with main hull vibration. By the present method, it is easy to distinguish what is the main part of coupled vibration. This is very useful from the point of view of the structural design. The calculation and the experiment should be compared in order to confirm the validity of the method in the future works.

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This report deals with a method for the natural vibration analysis of high speed semi-submergeble catamaran which is made up of two cylindrical lower hulls, struts and upper deck.
The exact evaluation of added mass of water is inevitable to estimate the natural frequencies for such a structure, because vibration modes are fully three dimensional and are much different from the ordinary ship hull vibration modes.
Therefore the authors present here a method to compose a three dimensional added mass matrix by use of J factor, which is well known as a three dimensional correction factor.
The exciting tests of the experimental model were carried out, and the measured results showed a fairy good agreement with the calculated values obtained by the proposed method.

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Fracture behaviors in the plate with crack in the vicinity of hole such as opening hole and fastener hole in the structure are different from those in the plate with only a crack, due to interaction between crack and hole. To obtain basic data for safety assessment on plate like that, it is necessary to clarify the effect of interaction on brittle fracture behaviors such as fracture strength and critical COD.
Experimental investigation has been carried out on fracture behaviors in the plates with various F_Ia values under uniform tension, where, F_Ia=K_Ia/σ√πc, K_Ia, σ and c are stress intensity factor at the crack tip in the vicinity of circular hole, remote tensile stress and semi-crack length respectively.
Main results obtained are as follows :
(1) The brittle fracture stresses of the plates with large F_Ia values (F_Ia>1.3), that is, in the case of high interaction of crack and hole, are not so much lower than those of the plate with only a crack, while those of the plates with small F_Ia values (F_Ia≤1.3) are roughly equal to those of the plate with only a crack.
(2) The critical COD values in the plates with large F_Ia values are larger than those in the plates with small F_Ia, values or crack only, while those in small F_Ia, values are roughly equal to those in crack only.
(3) The bi-axialities of stresses in crack tip zone in large F_Ia, values are smaller than those in small F_Ia values or crack only, while there is no significant difference between those in small F_Ia values and those in crack only.
(4) The phenomena described in (2) can be explained by the phenomena described in (3).

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The conventional COD bend tests are frequently used for the purpose of obtaining a critical COD (δ_c). But it is well known that δ_c shows various values depending on notch acuities. Accordingly, COD bend test specimens have usually a fatigue notch. However the industrial material tests are desired to be simple. In this sense, it is desirable that COD bend test specimens have only machined notch.
In this paper, the transformation equations of a mouth COD (V_total) for a machined notch to δ_c for a fatigue notch are proposed by considering the machined notch root displacement. These transformation equations are expressed as follows :
δ= O.45 (W-a) /0.45W+0.55a+Z [(V_total-V_e) -V'] … (V_total-V_e≥2V')
O.45 (W-a) /0.45W+0.55a+Z [(V_total-V_e) ₂/4V'] … (V_total-V_e<2V')
V_e= 0.8d^0.3 … (V_total≥4V')
{0.8d^0.3-0.74d^0.45 (1-V_total/4V')} V_total… (V_total<4V')
where
V'=γσ_YW (1-v²) /E : limit elastic clip gauge COD defined by Wells,
W : specimen width, a : crack depth,
Z : distance from free surface to positions setting a clip gauge,
d : initial notch root width (d≤0.4mm)
The above proposed equations are obtained from results of F. E. M. analysis, and it was confirmed that the relation between δ by the above equations and the plastic zone size is not different in the case of various notch acuities of the specimens. These equations are engineeringly satisfactory in the range of d≤0.4 mm for various materials.

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Reversed bending fatigue tests were carried out in low and high cycle fatigue range on fillet welded joint specimens, which were welded by using 25.4 mm thick ship structure steel of the tensile strength of 47kg/mm². The influencing factors investigated are leg length, throat depth, flank angle, profile of fillet weld and undercut. The specimen was loaded under the condition of constant amplitude of bending deflection of the intercostal plate in low cycle fatigue range, and under the condition of constant amplitude of load applied to the through plate.
The main conclusions obtained are as follows :
(1) The critical throat depth which is defined as the transition value classifying toe land root failure was found to be a function of the fatigue failure life N_f or the nominal stress amplitude S_a. The critical throat depth a_CR is given by the following empirical expressions.
a_CR/T=0.236logS_a+0.00078θ-0.110
a_CR/T=0.468-0.0632logN_f+0.0012θ
where T and θ are plate thickness and flank angle, respectively.
(2) The strain range measured at a point 4mm apart from a toe of fillet weld ε_R (4) is available for the prediction of the fatigue life in case of toe failure. The expression obtained for the prediction of 1% failure probability is
ε_R (4) =6.405 × 10^-4+5.655 × 10^-2N_c^-0.4772
The X curve in AWS Code D 1.1-72 may provide an unsafety prediction of fatigue life, especially in low cycle fatigue range, by comparing with the above expression.
(3) The undercut may act as a reducing factor of approximately 10 to 25 percent for bending fatigue strength.

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The author reported in his previous paper that almost continuous stop and go process of small crack extension was observed on the notched specimen with structural steel during unloading stage of the compression load which had been applied to a certain value at-196°C.
In the present paper these cracking phenomena were investigated theoretically. The state of the plastic zone spread and that of the crack initiation from the initial crack were expressed using the Dugdale model. This equation determines the crack extension length as a function of the applied stress by adopting the ω⁺ (plastic zone length under tension yield stress) concept as a fracture initiation criterion. Through the judgement of the stability of the state that is expressed by this equation, the relation between precompression stress and the final fracture stress was obtained. For the convenience of the practical use, approximate equations of the analytically derived equation for a crack in an infinite plate were proposed. These theoretically derived relations were compared with those obtained through experiments and showed a fair agreement with each other.

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