Characteristics of free surface shock waves were experimentally investigated with wedge models whose half-entrance angle is from 5 to 45 degree. Measurements of wave configuration and distribution of velocity components and pressure were undertaken. The wave configuration is ruled by Froude number based on draft, but there exists some scale effect on and behind the wave front, being connected with dissipative property of free surface shock waves. Remarkable features of the structure of free surface shock wave are occurrence of energy deficit at the wave front as a result of ultimate wave steepening, its diffusion in the rear region and partially hydrostatic pressure distribution.

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Two-dimensional separated flows behind a circular cylinder and elliptic cylinders are simulated by the inviscid vortex model.
The fully turbulent separated flow over a circular cylinder is simulated to predict the drag and the pressure distribution on the body surface to a fairly good degree of agreement with experimental results.
The effect of the interaction between the boundary layer and the separated flow on the determination of the separation point is discussed for circular cylinder in laminar flow.
Separated flows behind elliptic cylinders of shiplike forms are described by the inviscid vortex model considering the effect of turbulent boundary layer. The proposed model gives a good simulation of unsteady pattern of separated flow. The effects of separation point and displacement thickness on drag are investigated comparing with viscous pressure resistance analysed from measured data.

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Characteristics of nonlinear stern waves generated by simple 3-D hull forms are studied. They are under the influence of bow waves and local flow due to the 3-D configuration of sterns and consequently their formation and magnitude depend on the particular dimensions of the hull forms. The generation of nonlinear stern waves can be controlled by attenuating the slope of wave profile or suppressing the upward oriented flow at the stern. Both modification of waterlines and attaching stern-end-fins are effective for the weakening of nonlinear stern waves.

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The minimum wave resistance problem based on Michell's thin ship theory has been investigated by means of variational approach so far. In this paper, a kind of the fairing constraint to hull form is introduced into the minimum wave resistance problem, and the optimization technique is applied instead of the variational approach.
Two formulations are shown for the present problem and optimized by means of SUMT (Sequential Unconstrained Minimization Technique) as in the 1st & 2 nd reports. Numerical examples are given under several kinds of design conditions. As the fairing constraint is considered, the minimum wave resistance hull forms without swan necks are obtained.

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This paper presents the full-scale comparative trial results of two different types of propeller, i. e. a conventional propeller and a highly skewed propeller which were fitted on the same existing ship one after another. After analyzing the measured data, it is concluded that in comparison with the conventional propeller, the use of the highly skewed propeller could reduce the 1 st blade frequency component of the pressure fluctuations on the surface of the after body and amplitude of vertical acceleration on the steering deck to 60% and 80% respectively, and also reduce the 1 st blade frequency component of torsional and axial stress at the intermediate shaft to 17%-46%. It is also found that as compared with the propeller exciting forces, the exciting forces induced by the main engine have more influence on the horizontal hull vibrations.

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In the present paper, two aspects of wave energy utilization for ship propulsion or so-called “Wave Devouring Propulsion”^** are clarified.
(1) From a general viewpoint of conversion of the wave energy into the thrust, the possibility of the wave devouring propulsion is proved by considering the property of the ideal thrust generated by incoming waves and that of the drag required to propel a ship.
(2) As a realization of the wave devouring propulsion, the thrust generation by an oscillating hydrofoil advancing in waves is discussed. This problem has already been discussed by wu^{15), 16)} , but the free surface effect is not included in his theory. When the conversion of the wave power into the propulsive power is aimed at through interaction between a wave and a converter, for example, a hydrofoil, it seems to the author that the free surface effect should not be neglected, since the thrust increase due to the wave power absorption and the wave resistance increase are both proportional to the square of the wave amplitude. In the present paper, Wu's theory is improved by including the free surface effect approximately, and some numerical results are given for a non-oscillating hydorfoil advancing in waves or “A Linear Wells Turbine”.

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Nonlinearity in normal (lateral) force for a slender body with small incidence to flow is discussed by the asymptotic expansion method under the assumptions, 1>>β>>ε>>1/√R_n and (ε/β) ^1/2>>β, where β is an angle of attack, ε a slenderness parameter, and R_n the Reynolds number. The theory is developed utilizing a slender body theory technique. The near field is composed of two vortex layers extending downstream infinitely in cross flow direction. Kirchhoff's dead water theory is applied to the cross flow with the inclusion of three-dimensional effect which increases the velocity between the vortex layers in a lateral section. The first term of the normal force coefficient is derived only from the near field consideration and expressed by lateral drag coefficient of the Kirchhoff's theory. The second term is derived by considering the increase of lateral flow velocity by the effect of vortex layers in the vortex field, which is a flow field existing between the near and far fields and consists of vortex layers of finite extension. The second term of the coefficient is obtained analytically by assuming the form of vortex layers and the strength of vorticity. The obtained results are compared with experimental results.

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As a sequel to Ref 1, comparison between results of theoretical calculation and tank experiment was mainly carried out at the zone where encounter frequency approaches zero in following waves. Vertical shearing force, which was not dealt with previously, is included in this paper. Meanwhile, problem on following long crested irregular waves are also dealt with. The following are outlines of conclusions.
1) Calculated results by the widely used New Strip Method (NSM) or Ordinary Strip Method (OSM) for transfer function of vertical shearing force in following waves were compared to experimental results. This comparison shows bad agreement, worse than that in the case of vertical bending moment. Hence, these methods are regarded to be impracticable in following waves.
2) Transfer function of vertical shearing force by N (A), recommended in the previous paper to be a new practical method for vertical bending moment, shows a considerable difference from experimental results. Therefore, it can not be regarded as having practical precision of prediction on vertical shearing force.
3) In following waves, results of theoretical calculation of vertical wave loads transfer function at F_n=0 express experimental ones the best quantitatively in any ship speed. Hence, this approximate calculation can be recommended as a practical tentative one.
4) It is understood that there is still certain problem in calculation of diffraction forces and Froude Krylov forces in following waves by presently used theoretical methods.
5) By applying transfer function obtained from experiment, characteristics in long crested irregular following waves can be precisely predicted. In other words, despite the singular form of spectra in the encounter phenomena in following waves, the popular method of short term prediction based on the principle of linear superposition is proved with experimental evidence.
6) Encounter mean period, both obtained from estimated encounter spectra and measured directly from encounter time history, appear to be nearly identical. This means that it is possible to predict encounter mean period in long crested waves from encounter spectrum.

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Bodily responses and elastic distortions of full-form ship advancing in short head waves are analyzed analytically for a ballast-loaded large tanker. In order to derive the wave exciting force acting on ship hull, a method for analyzing the diffraction problems of a blunt ship advancing in short head waves are presented. The Unified Dynamic Theory of ship responses in waves developed by Bishop and Price is applied for the analyses of motions and flexural vibrations of ship hull. Because that there are no complete data sets available for actual ship structures, a hypothetical model of a ballast-loaded large tanker is introduced for the numerical analysis. Some discussions are made by using the numerical results.

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The design trend of large industrial carriers brought out a new type of ship hull : high block coefficient and small length-beam ratio. Such hull proportions are liable to make a ship unstable on course. Since then minimum necessary course-stability has been of common interest.
There are two criteria for the minimum necessary course-stability. The first relates to safe navigation normally under manual control. The second point is the propulsive power loss in a seaway under automatic coursekeeping ; the less stable is a ship, the more power loss from this reason assuming the same performance of the autopilot.
The power loss is composed of three parts : elongation of ship path caused by course fluctuation, inertial drag caused by yawing and the drag of activated rudder. We'made theoretical analysis on them, taking account of the on-off (non-linear) performance of the “power unit”, a hydraulic servomechanism to control the steering gear. Also we paid attention to some non-linear elements normally called “weather adjust”, that is to avoid too frequent rudder activity in a seaway.
Next we made numerical calculation of the power loss of a series of assumed ships whose course-stability vary systematically. Realistic sea and wind spectra are employed in this analysis.
The conclusions are :
(1) provided that the rudder gain and the yawrate gain of an auto-pilot is properly adjusted, even a very unstable ship can navigate with very small power loss, unless any low-frequency external disturbance exists ;
(2) but this optimum rudder gain is so small that any frequency disturbance, very probably induced by wind gust, will cause a severe course deviation and then a considerable path elongation ;
(3) from this reason, any spiral loop width (a measure of instability) greater than 15 degrees should not be permitted for fuel economy under automatic course-keeping in a seaway.

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In the previous paper, the methodology of the evaluation on the design of submersible was proposed based on the optimal control theory. Two sets of control system of longitudinal motion were introduced, which were composed of evaluation index of the optimal control, state equations and output equations. The relationship between the systems structures and 15 design parameters clarified.
In this paper, the relation between the control performance of the longitudinal motion and the design parameters is derived and systematized. The relation is obtained from the numerical analysis of the longitudinal motion due to a series of step change of the sea current using optimal control law. The time constant which characterises late response behavior of the control systems is selected to be O. 1 of the mean interval for the sea current change.
The following results are clarified by means of systematized relationship :
(1) The performance of the control systems is sufficient for the mission of the underwater exploration if the submersible is designed within the proposed design range. Hence, the quality of the control system can be decided by the product of the evaluation index and the weighted factor.
(2) The larger slenderness ratio of the body and geometric aspect ratio are, or the smaller tail fin width, time constant of propulsion apparatus and representative length are, the higher the control performance of surging motion is.
(3) On the design point of standard model, the sensitivity of the control performance of surging motion to the design parameters is higher in the order, (1) representative length (mass), (2) slenderness ratio of the body, (3) time constant of propulsion apparatus, etc.
Moreover, the similar results can be obtained in the case of the motion containing both heaving and pitching motion.
It is concluded that the fundumental design of the control system to the longitudinal motion of the submersible, can be established by the usage of the systematized relationship between the control performance and design parameters.

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This is a theoretical and experimental study of the water wave reflector which is floating and moored.
Solving motions of a moored floating body among waves by the two-dimensional wave theory, we may predict the amplitude of reflected and transmitted wave, so that we may easily find the wave-length at which the incident wave is reflected or transmitted completely. This wave-length depends mainly on the spring constant of its mooring system. Hence, adjusting this restoring force, we may compose a complete reflector or transmitter for an incident wave of arbitrary wave-length.
Then we describe conditions of complete reflection and transmission by making use of phases of wave exciting force and mechanical impedance of mooring system in the complex plane. This description enables us to estimate easily the necessary spring constant at an arbitrary wave-length.
Experiments on a semi-submerged vertical plate and a circular cylinder show good agreements with theoretical prediction.
According to this theory, it becomes possible to design a reflector of long wave over ten times of the breadth of floating body.

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Hydrodynamic forces acting on a vertical circular cylinder moving forward with a constant velocity and making forced oscillations are measured. Wave forces on the moving cylinder in regular waves are also measured. The purpose of this investigation is improving the accuracy in estimation of the motion of an ocean structure in waves, and the reduced velocity and Keulegan-Carpenter number chosen in these experiments are larger than those in exper-iments for the structural vibration induced by the vortex.
The measured force is compared with that with no advance velocity.
The conclusions obtained are as follows;
1) Steady drag coefficient C_DY0 of a cylinder forced to sway, nondimensionalized by foward velocity U and swaying velocity X, does not depend on K_C number but depend slightly on the advance velocity U.
2) Oscillating drag coefficient C_DX1 of the cylinder does not depend on U and decrease with the decrease of K_c number at K_c<30.
3) Steady drag coefficient C_D0 of a cylinder forced to surge does not depend on K_c number but depend slightly on U.
4) Oscillating drag coefficient C_D1 of the cylinder does not depend on U and decrease with the decrease of K_c number at small K_c number.
5) Steady drag coefficient C_DW0 of a cylinder in regular waves decreases with the increase of U.
6) Oscillating drag coefficient C_DW1 is smaller than that with no advance velocity and is slightly smaller than that in steady flow.
7) Inertia coefficient C_M is almost equal to that with no advance velocity

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The effects of coupled motion with swaying and water depth on the performance of Salters Duck as an energy extractor from ocean waves are studied both experimentally and numerically on the basis of linear theory. Main conclusions are as follows : the optimum load systems under given springs which restrict the translational modes can make the performance as excellent as the case where supports are perfectly rigid, and the extremely shallow water depth reduces its efficiency.

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Multi-mooring system is one of the popular means to position a floating offshore structure on the ocean. On doing basic design of it, we have to make static and dynamic analyses of mooring lines, but of the two the static one is more basic.
Till now there were no useful method to make statical analysis considering sea bed condition, and so we were in trouble with making mooring design of floating structure in the ocean region that have complicated sea bed condition.
Authors tried to express sea bed condition by assuming the sea bed to be made of small straight lines and made statical analysis by using difference equation method. The numerical results were in very good agreement not only with experimental results but also with catenary theory.
Further we made design charts using parameters such as friction between line and sea bed, line scope, slope and roughness of sea bed, weight of sinker, buoyancy of float, line's extension, and analyzed the effects of these parameters have on mooring characteristics.

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This paper considers the ultimate strength of stiffened rectangular plates under compressive and lateral pressure. The approximate analytical method consisted of two parts. The first is elastic large deformation analysis which takes into account the plastification of the stiffener in a simplified way. The second is plastic analysis in which a collapse mechanism is assumed. In the author's first reporto, the plastic analysis was carried out without plastic moment of the stiffener. Thus, the method was too conservative when lateral pressure is predominant. In this report, particular attention is given to the efficiency of plates stiffened on one side and subjected to lateral pressure. For this purpose, plastic analysis is developed from the plastic moment of plate and stiffener considering Faulkner's effective width formula. The analysis and experiments were carried out for various stiffened plates subjected to compression loading or subjected to combination with compression and lateral pressure loading. The following conclusions were obtained :
1) The calculated ultimate strength of stiffened rectangular plates agrees well with the experimental results.
2) The present method provides an effective means of analysing the ultimate strength of stiffened plates under uniform compression and simultaneous lateral pressure.

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In the previous paper the general formulation of curved rigid element models was described for the discrete limit analysis of several standard shells defined by the orthogonal curvilinear coordinates. These elements were derived without the approximation of shapes of curved surfaces. In this paper the triangular flat rigid element model is introduced for the analysis of shell structures of arbitrary shape. This type of element, being also used in the conventional finite element analysis, is of great use in the development of the general-purpose computer program, though it includes the shape approximation.
The physical concept of the flat rigid element model can be obtained by the combined use of those of the plane strain and plate bending elements proposed by Kawai, and the development of the algorithm for the general thin shells was carried out recently by Toi.
In this report the formulation is limited to the elasto-plastic analysis of static problems under the assumption of small deformation. The outline of the method of discrete limit analysis by using the flat rigid element model is described with some numerical examples on the standard problems. The application to the plastic instability and dynamic collapse problems is now under way and will be reported in the further reports.

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So far, the protection of a nuclear powered ship has been evaluated by its own capacity absorbing the collision energy in its destruction. On the other hand, it is recently reported that instead of the energy absorbing type barrier, a resisting type barrier has been developed which absorbs the collision energy mainly in the destruction of the striking bow.
To design such a type of barrier, it is necessary to estimate the load acting on the side structure of the nuclear powered ship. This load is obtained by the following procedure :
(1) Calculate the ultimate strength of a bow construction of the striking ship to get a load-deformation curve.
(2) Carry out a collision simulation analysis to obtain the bow deformation in collision.
(3) Estimate the load corresponding to the bow deformation using the load-deformation curve.
It seems that there is not any established method of calculating the ultimate strength of a bow construction.
So we have studied the ultimate strength of a bow construction of the striking ship.
First, we have made a theoretical calculation by the F. E. M. on a ideal mathematical frame model of bow construction. Then, in order to clarify the behavior of the bow collapse and verify the calculation method, we have carried out collapse experiments using 1/10-scale bow models of tanker and container ship and compared the results of the experiments with those of the theoretical calculation, by which a reasonable agreement of both has been confirmed. Further, we have estimated the collapse loads of bow construction of actual ships and obtained the load-deformation curves. By these studies, it has become possible to determine the load acting on the side structure of the nuclear powered ship and the bow deformation of the striking ship in collisions.

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The purpose of this study is to examine the ultimate strength of resisting type collision barriers which are installed in nuclear ships. Two kinds of ship side structures containing such barriers were designed by way of experiment as examples. The characteristic of one is that it consists of a grillage of horizontal and vertical webs, and the other's is that more deck plates are set than usual. Four series tests were carried out on these structures as follows, (1) one deck element model tests against a rigid bow model, (2) structural model tests against a rigid bow model, (3) double-hull element model tests against a rigid bow model, (4) structural model tests against two actual bow models.
From the analysis of the test results, the collapse modes were classified into two patterns such as crushing collapse of only the loaded region and bending collapse of the whole structure. The strength in the former collapse could be attributed to the ultimate strength of the members which were carrying a load directly beneath it, where an effective sectional area, which was calculated by the effective width formula, was taken into account. The latter could be explained considering a limit load obtained by the plastic hinge method, where an effective full plastic moment, which was calculated with a sectional area excepting the ineffective parts due to buckling, was taken into account.
Finally, a way to estimate ultimate strength was derived for the above-mentioned two kinds of ship side structures.

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It is very important to predict the collapse strength of externally pressurized spherical shell which have imperfections such as welding deformation and residual stresses.
Many experimental studies on this problem have been made by M. Krenzke et al., but few theoretical researches have been reported.
To exactly obtain a numerical solution of the collapse pressure of the spherical shell, it is necessary to consider the strain hardening in the elasto-plastic analysis of the axisymmetric shell.
This paper introduces a newly developed method by which the elasto-plastic behavior of the axisymmetric shell can be exactly expressed by using the membrane forces and bending moments, and moreover investigates effects of the imperfections on the collapse pressure of the spherical shell.
Main conclusions obtained from this study are as follows ;
(1) The usefullness and accuracy of the new method are confirmed by comparison with the experimental results.
(2) The more plastically the spherical shell collapses, the smaller the effects of the imperfections on the collapse pressure becomes.
(3) In the case that a penetrator or a partial sphere is welded circumferentially to the spherical shell, according as the diameter of the penetrator or partial sphere increases, the collapse pressure of the spherical shell will increase if both have same value imperfection by welding.
(4) If the spherical shell has the residual stress, its collapse pressure will reduce.

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The after body of RORO ship or car ferry is characterized as follows; the frame line under water plane is very fine in order to improve the performance of propulsion, but the frame line upper water plane is very fat so as to take the broader deck area. Therefore the sectional form near the water plane becomes flat, and the angle between the water plane and the transverse section of ship is smaller than the other ship. These ship may suffer from the wave impact pressure on the stern flare. For this reason, the experimental and analytical studies on the stern flare impact pressure were carried out, and following results were obtained.
(1) The fairly good agreement was found between the impact pressure coefficients obtained from the experiment in regular waves with those by Wagner's method. The magnitude of the coefficient was about 1020.
(2) The maximum impact pressure which was predicted in irregular head waves from 3 to 11 Beaufort wind scale was about 2030 t/m² for actual ship. This magnitude is smaller than the bow flare impact pressure, but the probability of occurrence of impact pressure is large. So it seems to be probable that the noise and fatigue due to transient vibration induced by the impact force becomes a problem.

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A deep-water jack-up oil rig must be designed successfully for the worst expected environmental condition. A wave-induced dynamic response analysis is one of the most important problems to assess the structural safety of oil rigs from the view point of fatigue strength.
In the previous papers, the authors presented an analytical method of natural vibration of oil rigs and experimental data by full-scale measurement.
This paper deals with the coupled effect of the global vibration, simple formula of the lowest natural frequency and wave-induced dynamic response analysis.
Main conclusions are as follows :
(1) Coupled vibration of sway mode and torsional mode for the global vibration of jack-up oil rig is discussed. Natural frequency of oil rig is not affected very much in the case of the symmetrical structure such as a rig with 4 legs, but shows ±5 per cent higher value in the case of the cantilever type oil rig with 3 legs.
(2) For a jack-up oil rig with 3 legs, simple formula for estimating the lowest natural frequency of sway mode and torsional mode are derived. Calculated natural frequencies by these formula is found to be in satisfactory agreement with those obtained from full-scale measurement or from FEM analysis.
(3) By taking account of the results of authors' investigation, calculation technique of wave-induced dynamic response is shown. Moreover, some examples of dynamic response spectrums for newly designed three deep water oil rigs were calculated using ISSC wave power spectral density.

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For establishing a method of evalulating quantitatively the brittle fracture strength in structural stress concentrated regions, a series of researches are being conducted. In the researches so far carried out, a study intended for “through the thickness flaws” has been progressed, mainly with mild steels.
In actual structures, however, various kinds of steel plates are used, and in many cases, the “part-through the thickness flaws” are the object of evaluation.
In this research, a study similar to the one explained in the previous report was carried out about 80 kgf/mm² high strength steel which differs largely, in plastic deformation characteristics, as compared with the mild steel, and furthermore, consideration is made on a strength evaluation method for the surface notch, as a typical example of the “part-through the thickness flaws”.

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In the previous papers, the authors proposed the β-value as the constraint coefficient due to the plate thickness.
The purposes of this paper to find analytically the relation between the β-value and thickness B and to evaluate the J_c-value and critical COD, φ_0c for any thickness specimen by using the β-B relation, respectively.
Stress distributions in the thickness direction are estimated, using the results of calculation by the three dimensional elastic FEM and the Prantl's experimental data, to make a analysis of the relation between β and B.
From this study, following conclusions are obtained :
1) The β-values evaluated by this analysis display good agreement with the experimental results shown in the previous paper.
2) It is expected that the J_c-value and φ_0c for any thickness specimen are able to be calculated by formulas proposed this paper considering the thickness effects on the fracture toughness by using a known J_c-value and φ_0c for a standard thickness specimen.

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Recently, Crack Tip Opening Angle (CTOA) was proposed by C. F. Shih et al to describe the instability criterion of ductile crack propagation during plane strain (fiat crack) condilions, and was derived by J. R. Rice analytically by means of the slip line field theory and the incremental theory of plasticity. CTOA appears to be applicable in (some or most) cases, but does not accurately describe the plane stress growing crack (slant crack).
Unstable ductile crack propagation of the plane stress crack is widely studied for the safe design of highly pressurized gas pipelines. The impact absorption energy of the Charpy test is well correlated to the fracture arresting properties of the structures, but the mechanics of the fracture are not yet well established.
In this paper, CTOA of the plane stress growing crack is derived from the plane stress plasticity of perfectly plastic materials by Sokolovsky's approach. Our proposed modification of CTOA expressed as follows :
CTOA= (α/σ₀) (dJ/dl) +β (σ₀/E) ln (eR/r)
where, β=1.40 under the plane stress conditions.
CTOA in the Dugdale model is also defined and compared with the results of lat, oratory test. The results show that α=0.5, and β=1.27 for plane stress crack growth. These analyses give similar results to those obtained by Rice et al for CTOA under plane strain conditions, that is, α=0.65 from the experimental results and β=5.08 from the slip line theory.
The CTOA obtained for plane stress ductile crack growth is applied to the wide plate tensile crack growth test. The results of the present analysis coincide well with those of the plane stress finite element method (FEM) computed by T. Kanazawa et al. The phenomena of plane stress ductile crack propagation are also explained by the CTOA criterion under plane stress conditions.

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Bending fatigue tests were performed using plates with transverse (grooves, fillets and protuberances) and through-thickness geometrical discontinuity (holes and grooves) in addition to plain plates. Shape change in fatigue crack growing from surface and corner flaws was investigated and the equation for expression of crack shape was proposed. The conclusions are summarized as follows :
(1) Shape change in part-through fatigue crack growing in a plate with geometrical discontinuity was classified into equilibrated and non-equilibrated growth in the same way as shape change in fatigue surface crack growing in plain plate.
(2) The equation for expression of the fatigue crack shape for the equilibrated growth was induced by simplification of the stress-field where fatigue crack grew ; for plain plate,
b/a=1-b/t,
for transverse geometrical discontinuity plate,
b/a=1- (b/t) ^1/K_t,
and, for through-thickness geometrical discontinuity plate,
b/a= 1/ {∑k i=1 C_i (1+a/ρ) ^{-2 (i-1)} + (2-1/K_t) a/t} (b/t<0.5) 1/K_t/ {∑k i=1 C_i (1+a/ρ) ^{-2 (i-1)} +1/K_t·a/t} (b/t≥0.5)
(3) The equation for expression of the fatigue crack shape for the non-equilibrated growth was induced by considering the relation between the initial flaw shape and the equilibrated growth crack shape ;
for plain plate,
b/a= b/t/ {(b/t/1-b/t) ^m+ (a*/t) ^m} ^1/m (a₀>>b₀) 1/ {1- (b*/t/b/t) ⁿ} ^1/n (a₀<<b₀)
for transverse geometrical discontinuity plate,
b/a= b/t/ [{(b/t/1-b/t) ^1/K_t} + (a*/t) ^m] ^1/m(a₀>>b₀) 1/ {1- (b*/t/b/t) ⁿ} ^1/n- (b/t) ^1/K_t (a₀<<b₀)
and, for through-thickness geometrical discontinuity plate,
b/a= 1/ {∑k i=1 C_i (1+a/ρ) ^{-2 (i-1)} / {1- (a*/t/a/t) ^m} ^1/m+ (2-1/K_t) a/t (b/t<0.5) 1/K_t/ ∑k i=1 C_i (1+a/ρ) ^{-2 (i-1)} / {1- (a*/t/a/t) ^m} ^1/m+1/K_t·a/t} (b/t≥0.5) (a₀>>b₀)
and
b/a= [1/ {∑k i=1 C_i (1+a/ρ) ^{-2 (i-1)} + (2-1/K_t) a/t} ⁿ+ (b*/t/a/t) ⁿ] ^1/n (b/t<0.5) [1/Kⁿ_t/ {∑k i=1 C_i (1+a/ρ) ^{-2 (i-1)} +1/K_t·a/t} ⁿ+ (b*/t/a/t) ⁿ] ^1/n (b/t≥0.5) (a₀<<b₀)

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The rational ship hull design calls for consideration for structural safety as well as for economics. This boils down to the question of how best to optimize the allowance for potential hull structural failures, and for that purpose employing the demand-capability concept, or reliability concept, is a sensible approach to take. In fact, several papers have been written on the application of the reliability concept in evaluating the required ship hull structural strength.
Regarding the detailed ship hull structural design, the author performed, for clarification of the logic of fatigue failure, the Fault Tree Analysis to determine structural strength requirements.
And the author confirmed that the method of stress or fatigue analysis written in this paper could be successfully applied in explaining failures or potential failures of other structural members of similar structures.
In addition, the author designed, using assumed stress conditions, frame end structures. In this, structural stress concentration factor of plural number of frame end structures, results of actual hull structural failure analysis, and the scatter in theoretical and experimental data on the crack initiation and propagation in frame ends were used to select the detailed frame end profiles which could offer adequate reliability required in view of predicted crack initiation and propagation lives.
The research performed by the author therefore is intended to demonstrate that the reliability concept could successfully be applied in fatigue design of actual hull members, as well as to show in what manner to perform the fatigue design.

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When an operated period of a structure is close to or over the original design life, it is necessary to reassess the regular inspection program applied to secure the structural integrity. Because, the program is effective only to detect damages in the structural details which occur within the design life. Therefore, another inspection program, that is, a supplemental inspection program which is intended to detect significant damages occurring after the design life with high detection capability, is required for the sake of continuing safe operation of ageing structure.
As to aircraft structures, FAA and ICAO have recently imposed to develop a supplemental inspection document of older aircrafts on manufacturers. In response to the requirements, the Boeing company has released the supplemental inspection documents for Model 707/720 and 727.
The purposes of the present study are ; 1) to define deterministic and probabilistic factors which are necessary in a reliability analysis on the effects of supplemental inspection, 2) to examine results obtained by the Boeing method, and 3) to propose a method to estimate possible extension of service life resulting from a supplemental inspection.
A numerical example of typical aircraft structural significant detail, which is a wing spanwise skin splice consisting of skin and stringer, is given in order to evaluate the validity of the present study.

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In the previous reports, it has been shown that transverse forces acting on tack welds and deformation behavior of groove during butt-welding varied with sizes of welded plates and welding conditions significantly. The purpose of this report is to clarify effects of plate width, length of weld, tack weld pitch and welding condition on the maximum tensile force acting on a finishing end tack weld and to propose a suitable method to predict the maximum tensile force which is a primary factor of end cracking of butt-welding joints.
A series of numerical calculations is performed based on unsteady heat conduction analysis and uncoupled elasto-plastic thermal stress analysis by use of the finite element method. Effect of mesh subdivision on accuracy of calculated results is carefully examined. It is suggested that use of a small time increment and a mesh size proportionate to weld heat input is necessary to acquire satisfactory results.
An approximate formula to estimate the maximum tensile force acting on a finishing end tack weld is proposed. It is shown that the estimated values are fairly in good agreements with the calculated and/or measured values obtained hitherto, and that if we consider the optimum average width of fused zone for a welded joint with a given size, the maximum tensile force is specified only by welding speeds and becomes maximum for a specific welding speed.

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In designing ship equipment, we encounter many problems concerning heat convection which depends upon turbulent flow of gas, such as the distribution of cold air in reefer hold of refrigerating cargo ship and the atmosphere in cabin during air-conditioning. Most of these problems have been treated so far by the practical way along with the empirical trial and error. However, according to enlarge the scale of air-conditioning system and refrigerating system, rigorous analyses to estimate the quantity of heat transfer and the distribution of air temperature are required for strict energy saving.
In this paper, the eddy viscosity coefficient of turbulent flow is obtained by use of so-called two equation models¹⁾ which are the transport equations on the kinetic energy of turbulence and the turbulence energy dissipation rate. The equation of convectional heat diffusion is solved subsequently using the obtained coefficient. Finite element method is applied through the above-mentioned procedure to solve the equations in this report.
Practical applications of the analyses of the atmosphere in reefer holds of refrigerating cargo ship, in which heat sensitive cargoes are stored, are carried out to estimate the variations of the distribution of flow velocity, eddy diffusion coefficient and air temperature.
The relations between the variation of air temperature as time proceeds and the decisive factors governing thermal diffusion, i. e. type of duct system, number of inlets and thickness of heat insulation, are clarified by the results of analyses.

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Many authors have investigated dynamic characteristics of the oil film in journal bearings theoretically. These characteristics can be expressed in terms of stiffness and damping coefficients on the basis of the linearized theory, and have been applied for practical problems, although they do not necessarily agree with experimental results.
The present authors verify the validity of the linearized theory by examining the oil film condition in journal bearings theoretically and experimentally. Conclusions are as follows : Considerable pressure change is caused by the squeeze and strip effects on the unloaded side of the steady-state oil film, and gives significant influences on the stiffness and damping coefficients.

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