The authors^{1), 2)} experimentally examined the flow field in the near-field of ships and clarified the reason of existing discrepancies between wave making resistance theories and experimental results. Non-dispersive waves exist around ships, which considerably contribute to ship resistance. Without sound clarification of these waves, trustworthy development of a ship resistance theory will not be expected.
In this paper, the characteristics of non-dispersive waves around ships are further studied through experiments, and it is verified that these waves satisfy the conditions that shock waves in compressible fluid and nonlinear shallow water waves do. A kind of shock wave exists around ships, and it must be characterized by a nonlinear wave theory. The authors named these non-dispersive waves as free surface shock wave.
New direction of research is pursued taking into account that Kelvin's dispersive waves and free surface shock waves coexist around ships. Some way of analysis and effects of free surface shock waves on dispersive waves are discussed.

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This paper presents a method for optimization of ship hull forms on the basis of wave pattern analysis.
The method is primarily based on the assumption that a linear relation exists between the small difference of prismatic curves and the difference of the amplitude functions of the generated waves.
Firstly wave analysis data are collected of several ship models with variant prismatic curves including the specified ship model. If the difference of prismatic curve, ΔC_pj (ξ), and the difference of amplitude functions, ΔP_j, ΔQ_j, between the specified ship model and the other ship models are known, the modification to be made for a designed ship, ΔC_p (ξ), ΔP, ΔQ, can be expressed by the following linear equations :
ΔC_p (ξ) =∑a_jΔC_pj (ξ) (i)
ΔP+iΔQ=∑a_j (ΔP_j+iΔQ_j) (ii)
As for the coefficients, a_js, as the wave-making resistance coefficient, C_w, of designed ship model is to be derived by making use of ΔP and ΔQ in the equation (ii), the a_js are determined so as to minimize C_w.
The author's method was verified to be successful in the case of being applied to the prismatic-curve series of the ship models with the same hull-form factors. Further study is under way towards extending this method to the case of ship models having different hull-form factors.

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An attempt was made to calculate viscous resistance of ships by applying a higher order boundary layer theory instead of the conventional one. In the higher order theory, the pressure variation across the boundary layer due to the effect of surface curvatures is taken into account.
The calculation method adopted here belongs to the so-called integral method. Coles' wall-wake law is used as the velocity family and an entrainment equation as the auxiliary equation. The velocity at the edge of the boundary layer is calculated considering the displacement effect of the boundary layer.
For several different types of ships, numerical calculations of viscous resistance, which is the sum of viscous pressure resistance and frictional resistance, were made and compared with the towing test results.
As a consequence, good agreement was obtained for fine ships but a large dis-crepancy was found for full ships.
Comparison of the calculated results between high and low Reynolds numbers corresponding to ship and model respectively are also shown.

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This paper is concerned with the calculation method of viscous flow around ship based on the assumption of partially parabolic flow and the K-ε model of turbulence (Spalding 1975, Muraoka 1979). Inlet conditions for the K-ε model of turbulence are improved in comparison with the previous paper (Muraoka 1979). The validity of K-ε model of turbulence is examined through calculating the flow around the axisymmetric bodies and comparing the results with the experiment of Huang et al. (1978). The results give fine agreements with the experiment in not only velocity profile and pressure variation but also turbulent properties when it adopts reasonable conditions at inlet plane. The examination is extended to the flow around ship, and the results are that the agreement of velocity profile between calculation and experiment is better than that in the previous paper and that the turbulent properties seem to represent the phenomena. It can be believed that the 2-equation model of turbulence is more useful tool than any other 0- or 1-equation model in considering the turbulence around ships.

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Two-dimensional transient and quasi-steady separated flows behind a flat plate and a circular cylinder are simulated by inviscid vortex models using a discrete-vortex approximation for free shear layers. The features of the models are discussed through the comparisons of the numerical results with experimental data.
Light is thrown on the time development of wake in transient flow and on a new method for the calculation of vortex shedding from a circular cylinder. The method is developed through the consideration of the treatment of Kutta condition which determines the circumstances of vortex shedding from body surface, on the assumption of the location of the separation point from which free vortices are shed.
The time development of wake not only of a flat plate, but of a circular cylinder in transient flow for short times after their starts can be explained with inviscid vortex models.
The method proposed here is shown to predict, for circular cylinder, the vortex patterns, the drag, the side force and the Strouhal number to a good degree of agreement with the experimental results.

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Application of discrete vortex elements for numerical calculations on propeller/duct system is presented. The flexibility and reliability of the computed results by the method is discussed in comparison with the other methods and experiments.
The following items are investigated in this paper :
i) The possibilities of correct modelling on propeller/duct geometry and real physical phenomena ii) The two kinds of interaction model between propeller and duct ; a complete lifting surface (direct interaction model) and an infinite number of blades (indirect interaction model) in place of the propeller toward the duct lifting surface iii) The correlations between measured and calculated circulation, pressure and open water characteristics on propeller/duct systems iv) The influence of relative positions between propeller and duct on duct thrust components and circulation distribution
The advantages of the direct interaction model have been obtained on saving computer time with reasonable accuracy for propeller/duct performance and circulation distribution on a blade. On the other hand, the indirect interaction method has become known to be useful to obtain the good agreement with experiments on pressure distribution on duct surface.

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A practical method for the prediction of cavitation on a propeller operating in a ship wake and hull surface pressure induced by a cavitating propeller is presented.
In this method, the following items are applied :
i) propeller part : the combination of Hanaoka-Koyama's unsteady lifting surface theory and corresponding 2-D wing theory ii) cavitation part : linearized 2-D cavity theory applying the angle of attack and the local cavitation number derived form i)
iii) hull surface pressure part : the application of the method of periodic source in place of cavity volume variation while a propeller blade is turning behind hull, moreover blade loading and blade thickness are included
In order to stand the practical use, correction factors on the cavitation part are adopted from 2-D cavitation test and actual ship observations. The predicted results on blade cavitation and hull surface pressure are compared with measured one, and the advantages of the method are discussed.

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A shallow water theory is newly formulated retaining higher order terms, and a numerical procedure is developed placing emphasis on the application to the diffraction and radiation of waves by a group of floating bodies. In the course of the numerical analysis an irregular frequency phenomenon is observed ; however it is both analytically and numerically proved that the irregularity can be removed by a minor modification to the analysis.
The results have been checked against analytical ones and also against those obtained by three dimensional numerical approaches. The present method appears to be a practical means to solve a multi-body problem, from the viewpoint of computation time as well; some of the results on the diffraction of waves by two and three circular discs are presented.

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The formula for the added resistance of a ship in oblique waves is simplified by the assumption of high frequency of encounter. Numerical computations by the simplified formula are carried out with respect to the Series 60, C_B=0.70 model at various heading angles to the wave. The results of computations are compared with results of experiments by Yamanouchi and Ando, and fairly good agreement between them is observed when the ship is moving against waves. This fact seems to prove the feasibility of the above formula as a practical method of the theoretical prediction of added resistance in oblique waves.

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The hydrodynamic forces of pitch mode on a circular disk as a shallow draft ship in shallow water are investigated. The boundary value problem is formulated by the use of the concept of the surface distributed sources so that integral equation for the source densities are obtained. In the case of long waves, the problem is solved analytically. The numerical solution of the integral equation is found. The added moment of inertia, wave damping factor, wave exciting moment, radiation pressures, wave exciting pressures and motions are calculated. The corresponding experiments are carried out and the results of the numerical calculation are in good agreement with those of the experiments.

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In this work, the experimental value of the hydrodynamic forces acting on two different types of the floating offshore structure were obtained by the excited method by the transient water waves.
Another object of this paper is to check the reliability of the new developed program that calculate the motions and hydrodynamic forces of the offshore structure. Therefore, the comparison between the experimental and calculating values of the wave exciting forces, added masses, damping coefficients and motions in waves are presented.
Consequently, both of the calculating values by the new program and the estimating values from the experimental hydrodynamic coefficients were coincident with the experimental values of motions in waves.

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The supposed wave condition has direct effects upon the theoretically estimated extreme value on the long-term distribution of wave induced variable of a ship. So, the accuracy of the estimated value is not reliable in the case when the visually observed wave data are directly applied as the supposed wave condition.
Authers studied on the statistical characters of wave statistics in the North Pacific Ocean by 163 th Research Committee of the Japan Ship Research Association which are the most reliable wave data observed there. It is showed that the frequency distribution of both wave height and period can be described by the log-normal distribution. The theoretical distribution of wave height appears to be valid in range of the cumulative probability up to 0.99999. The method of the correction of the observed wave statistics is indicated. Applying the theoretical distributions, the original wave statistics in the North Pacific is corrected. The wave data introduced by the correction are the most reliable data of the sea zone to be supposed in the theoretical estimation of wave induced valiables.

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In this paper, the whole dynamic response characteristics of taut moored platforms subjected to regular waves are concluded by both experimental and theoretical investigations. Up to this time, a series of tests on the models of vertically taut moored single buoy and vertically or splayed taut moored platform subjected to regular waves have been conducted in wide range of wave frequency and wave height, and their results are discussed as a whole with both linear analysis in frequency domain and non-linear analyses based on numerical time integration method and approximate theory according to peculiarity of each non-linearity. Particularly, the results on super-harmonic resonance, sub-harmonic resonance and critical wave height for slacking are discussed both qualitatively and quantatively. Finally, a basic recommendation is given for actual initial planning or designing taut moored platforms.

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When a difference of specific weights of supplied and purged gas exists in an oil tank of a tanker, the gas flow and gas dispersion during gas purging are varied with discrepant values of each specific weight. In case of the heavy gas being purged by the light gas, the interception of gas purging is especially remarkable by the existence of stagnated flow.
In this paper, two dimensional analyses of flow velocity and gas concentration in tank models by finite element method are carried out to make clear the relations between a difference of specific weights of both gases and efficiency of gas purging. The effects of the location of inlet and the arrangement of inner structures of tank against gas flow and gas dispersion are also clarified due to discrepancy of specific weights of gases.
In case of forming the interface between supplied and purged gases, the criterion of arising this phenomenon and the governing equation of gas concentration in tank as the time proceeds are presented. Comparing the calculated values of gas concentration and the measured values in actual oil tank, good agreements between them are shown.

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It is important from the viewpoint of prevention of the sea disaster to predict the process of oil dispersion on the sea surface flowing out from the tanker which has come into collision or smashed into the rocks. Some theoretical results are available in case of one-dimensional dispersion including the axisymmetric case.
The object of the present investigation is to develop the simulation techniques for the process of two-dimensional oil dispersion under the arbitrary initial and boundary conditions including the effects of wind and tidal flow.
After the introductory remarks in Section 1 some theoretical solutions are derived in Section 2 based on the procedure described in Refs. 1) and 2), where the oil flow and the flow in the water boundary layer is assumed to be turbulent. This analysis is extended to the two-dimensional case in Section 3 by using the finite element method applied to the shallow water equation including the wind and tide effect. Two different approaches are described where inertial terms are considered in one approach and neglected in the other approach. In Section 4 the general procedure for the prediction of two-dimensional oil dispersion is shown with some numerical examples by the combined use of theoretical solutions, experimental results, and the finite element approach. Section 5 contains concluding remarks.

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In this report discussed are the shallow water effects on the ship's hull torudder interaction on the same assumption as in the previous report that the main hull and the rudder can be replaced by rectangular flat plates placed in a line. However, the spanwise distribution of vorticity on the rudder is simplified to be constant in each of equal sections into which the total length of rudder's span is divided for convenience of numerical analysis. In conse-quence of this simplification, the computing time necessary to solve the integral equations which determine the vorticity distribution of the main hull and the rudder could be reduced remarkably.
From the results of numerical calculation, it is concluded that the hydrodynamic force induced on the main hull by deflecting the rudder increases as the water depth decreases. This conclusion is confirmed by quantitative agreement with the results of experiments in shallow water carried out recently by Nonaka and others. On the contrary, the hydrodynamic force of the rudder behind the main hull does not monotonously increase as the water depth decreases, but it may be less than that in infinitely deep water. The conclusion obtained in the previous report that the hydrodynamic force acting on the rudder itself is reduced by the presence of the main hull, however, remains true still in shallow water.
The effectiveness of the rudder as a means to keep a ship on her course and to make a ship turn is evaluated by the amount of the total force generated on the main hull and the rudder. The results of numerical calculation indicate that from the viewpoint just stated above the rudder effectiveness increases with decrement of the water depth. Besides, this conclusion agrees well with the results of experiments conducted previously by one of the authors.

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This paper presents a practical method to predict the characteristics of the ship maneuvering motion at the initial design phase. Supposing that the principal particulars of ship hull, propeller and rudder are given at the phase of the ship initial design, an attempt is made to calculate the maneuvering motion utilizing those principal particulars as basic input data. The mathematical model which describes the ship maneuvering motion is based upon the coupled equations of surge, sway, yaw, heel and number of propeller shaft revolution shown in Eq. (1). Computations are made for seven typical merchant ships covering various kinds and sizes of ships shown in Table 1. In order to examine the validity of the calculation method of this paper for wide range of maneuvering motion characteristics, the computed results are compared with the results of the full scale trial for three kinds of typical characteristics, namely turning motion with rudder angle of 35°, 10°-10° zigzag maneuver response and steady turning performance. Both the computed and the full scale trial results are in satisfactory agreement generally for various kinds and sizes of ships, and for wide range of maneuvering motion characteristics, as shown in Figs. 530. It can be concluded that the calculation method proposed in this paper is very useful and powerful for the prediction of the characteristics of the ship maneuvering motion at the initial design phase.

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The performance of a hydrofoil sailing boat, which has dihedral-angled and surface-piercing foils, at high speed is described.
A simple method of performance prediction was devised, which considered two important factors for sailing boats as follows : (i) variation of hydrodynamic drag caused by change of heel and leeway angles ; (ii) limitation of sailing performance due to capsizing.
For the present study one typical sailing hydrofoil configuration was used, i. e. a 5. 08m long catamaran, with a pair of surface-piercing front (main) foils having 40 degree dihedral angles, and one horizontal rear foil, which formed an inverted “T” in combination with the rudder.
The calculations aimed to predict the effect of dihedral angles, width between the foils, and weight of the boat on performance.
The results obtained were as follows : (1) the present method gives good estimated values for the performance of a hydrofoil sailing boat with dihedral-angled and surface-piercing foils ; (2) the sails should be trimmed to produce the maximum thrust force, but the performance of a boat to a beam reach is subject to limitation due to capsizing, and to windward, due to leeway angle ; (3) although the true wind angle varies extensively, the apparent wind angle at high speed varies much less, so that the aerodynamic drag angle of the sail can be regarded approximately constant; (4) the predicted heel angle is between 0 and-6 degrees at high speed (heel to weather-side); (5) the aerodynamic force coefficients of the sail estimated from the seatrial are smaller than the wind tunnel test data ; (6) there are small differences between the predicted and measured immersion of the hydrofoils ; (7) the weight of a boat has an appreciable effect on the light wind performance ; (8) the dihedral angles and width between the foils have a considerable effect of the boat performance. The optimum dihedral angle is between 40 and 45 degrees, and the optimum width between foils is around 1. 21. 6 h_s, h_s beeing the height of C. E., the centre of sail force, above the foil bottom.

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Many researches on water impact pressure have been reported and the following facts are well known :
a) When the impact surface is parallel to the water surface, air is entrapped between the bottom plate and water.
b) On the other hand, when the impact surface is slightly inclined to the water surface, a very sharp pressure sweeps along the plate.
Authors carried out water impact tests using one fifth models of a forward bottom structure of a VLCC (plate thickness was considerably increased). And following results are obtained.
1) When the impact surface is parallel to the water surface, pressure time history becomes very dull by the effect of the entrapped air and the same pressure occurs in large area. Then, equivalent static pressure of each member (bottom plate, longitudinals, bottom transverses, etc) is almost same as to the maximum pressure measured by the pressure gauge.
2) In the case of impact by slightly inclined surface, a very high pressure occurs only in a very narrow band in front part of sweeping pressure, and the effective pressure to the structural response becomes much smaller compared with the peak pressure measured by the pressure gauge. The extent of this reduction in effective pressure depends on the area of structural part under consideration.
3) In the latter case, the effective pressure varies much more slowly than the pressure obtained by a pressure gauge. And it can be said that the effect described in 2) is larger than the so-called dynamic effect.
Those facts should be considered at designing of a structure under impact loads obtained by model tests.

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In this paper, described are the results of full-scale measurements and stress analyses on the transverse strength of car carriers, with special reference to the local strength of partial bulkhead constructions above free-board deck of the ships.
The unmanned stress measurements have been carried out on three voyages of ship A and six voyages of ship B, respectively, and the maximum stress amplitude obtained at face plate of a round corner of the partial bulkhead has been 13 kg/mm². A close correlation has been found from the measured data between the stresses in the transverse members and the accerelation in athwartship direction due to ship's motion.
Stress analyses based on the finite element method have been carried out on structural models of the car carriers, and the results have shown that a relatively high stress occurs in the partial bulkhead structures due to racking deformations of the transverse cross section of the ship caused by anti-symmetric load with respect to ship centre line.
A comparison has shown a good coincidence between the measured value of the maximum stress in the transverse members and the theoretically estimated statistical value by the present analysis.

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Fatigue strength of welded tubular joints is one of the most important items in the design of offshore structures. Various design formulas have been proposed both on the stress concentration factors and on the fatigue failure life. However, most of these design curves do not involve any informations on the relationship between the crack initiation life N_c and the failure life N_f, nor on the relationship between the fatigue design curves and the detailed procedure of hot spot stress estimation.
This paper presents a reanalysis of fatigue data of various welded tubular joints obtained in Japan. The relationship between the fatigue crack initiation life N_c and the failure life N_f was examined in wide range of fatigue life. Scatters in fatigue life estimation were also examined in relation with various procedures of hot spot stress estimation : 1) measurement, 2) finite element method, 3) Beale's formulas and 4) Kuang's formulas. Applicability to design is discussed with reference to the confidence limits of fatigue lives N_c and N_f.

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Fatigue crack growth under random loading has been extensively studied since nearly a decade in relation with the design of aircrafts, offshore structures, ship hulls, pressure vessels and so on.
For the sake of simplicity, random loads in service conditions are often simulated by the block programed loads in laboratory fatigue tests. However, very few studies have been performed on the influence of sizes and sequence of load blocks, and on the difference between crack growth behavior under block programed loads and that under real random loads.
The authors previously presented an experimental analysis on fatigue crack growth under block programed loading for simple cases where the stress ratio R= σ_min/σ_max=0.An analytical model was also presented to interprete the features of fatigue crack growth observed in the experiments.
This paper presented an analysis on fatigue crack growth under more generalized block programed loads with varying stress ratio R. An analytical model similar to the previous one was presented to interprete the experimental evidences on crack growth behavior. A good agreement was obtained between experimental results and the calculations by the model. The linear damage law, an application of Palmgren-Miner hypothesis would give a non-conservative estimation for the crack growth life when the mean stress was high and/or the block size was small.

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A project of three years experimental researches on fatigue crack growth from multiple planar surface flaws has been made since 1976, accumulating a lot of data on the changing characteristics of surface fatigue crack shape during growth. On the basis of the data about 99 fatigue cracks, which were obtained from the researches, a statistical analysis was made in order to make a modification of the empirical expressions of surface fatigue crack shape, that were previously proposed by kawahara-Kurihara-Iida.
It was found that the expressions themselves are essentially applicable for the estimation of b/a versus b/t relation, where b, a and t are crack depth, half crack length on surface and plate thickness respectively. Also found is that the constants in the expressions deduced from the present analysis gave a better estimation than the previous ones, within the range of ±20 percent of error percentage in estimation of b/a for over than 90 percent of data. In addition, a simple formula for expression of a fatigue crack shape during growth was newly proposed, showing comparable order of accuracy in estimation.

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This paper presented fatigue strength criterion for ship structural members subjected to still water bending loads and wave bending loads under service conditions.
Assuming exponential distribution for long term distribution of wave bending stress during 20 years (10⁸ stress cycle), and using ordinary S-N_c curves (N_c : crack initiation life) of notched specimens of mild steel and the modified Miner rulue for fatigue crack initiation, the following equations were proposed for the fatigue strength criterion.
S_a+0.15S_m=14.4 (kg/mm²)
for longitudinal strength members
Where, S_a : nominal stress amplitude (kg/mm²)
(wave bending stress at a probability level of Q=10^-8)
S_m : nominal mean stress (kg/mm²)
S_a+0.3S_m=23.6 (kg/mm²)
for transverse strength members
Where, S_a : true stress amplitude considered stress concentration at a probability of Q=10^-8
S_m : true mean stress considered stress concentration
Applying the above formulae to structural members of several ships, reasonable results were obtained.

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In this paper, phenomenon of fatigue crack propagation is considered as continuous fatigue crack initiation at crack tip. It is assumed that fatigue crack initiation life is used up when damage caused by cyclic strain near crack tip is accumulated and magnitude of the damage is reached to a certain critical value at ΔN strain cycles and size of the crack length Δa is average grain size of material.
Using the above assumptions and proposed cumulative damage law, crack propagation rate da/dN under fully reversed loading is expressed by the following equation.
da/dN=Δa/ΔN=d/ε_f-2ε₀Δε^α_p
where Δε_p : cyclic plastic strain range at a point situated Δa apart from crack-tip
ε_f : monotonic true fracture strain
ε₀ : maximum strain at 1 st cycle
d : average grain size
α : exponent in equation Δε^α_p·N_c=constant
The above equation can be transformed in to the following form.
da/dN=d/ε_f-2ε₀ [ΔK/E√2πd {(ΔK/2σ_Y'√2πd-1) ^Z- (ΔK/2σ_Y'√2πd-1) ^-Z}] ^α
where ΔK : range of stress intensity factor
E : Young's modulus
Z : (1-n) / (1+n)
n : exponent in equation of cyclic stress-strain curve with strain hardening effect
σ_Y' : yield stress in the cyclic stress-strain curve
Further, the above equation may be expressed by the well known power low formula approximately in the range where ΔK is 50 kg·mm^-3/2500 kgmm^-3/2.
da/dN=C (ΔK) ^m
C=d/ε_f {1/E√2πd (1/2σ_Y'√2πd) ^Z} ^α
m= (1+Z) αkg·mm^-3/2
There is the following relation between coefficients C and m.
logC=A·m+B
A=1/1+Z·log1/E√2πd (1/2σ_Y'√2πd) ^Z
B=log (d/ε_f)
Crack propagation rates calculated by these equations agree with experimental ones of mild steel quite well, and then these equation may be used for estimation of crack propagation life with good accuracy.

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In order to obtain the design concept on crack arrestor against shear crack propagation, which is known to propagate with velocity of 200 m/s or so in highly pressurized gas pipelines, the phenomenon of fracture arrest was studied experimentally and analytically using the spring-loaded DCB testing.
The simulated mechanical crack arrestor was of heavy thickness type, which was introduced to the dull grooved DCB specimen. With this type of specimen of different size arrestors on several steels, the behavior of shear crack propagation and/or arrest around the arrestor was examined by measuring dynamically a crack tip position, load depression and ductile crack opening displacement.
The results of experiments were analyzed succesfully by simulated calculation of crack advancing based on the Dugdale model. Further, using the fracture propagating resistance value obtained from the spring-loaded DCB testing without arrestor, the change of ductile crack opening displacement when the crack approaches to an arrestor was also calculated for the prediction analysis purpose and compared with the experimental data obtained.
The main results obtained are as follows.
(1) The change of ductile crack opening displacement near arrestor, calculated from approximated method with fracture propagating resistance value, coincides well the experimental data and enables us to evaluate quantitatively the effects of arrestor.
(2) The increase of arrestor thickness is more effective to the fracture arrest than the increase of arrestor length.
(3) It was found also that fracture was arrested when ductile crack opening displacement at the arrestor front decreased to the level less than that at unstable onset of shear fracture propagation.

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In this paper, the load carrying capacities of circular cylindrical shells subjected to hydrostatic pressure were investigated when the shells failed in axisymmetrical collapsing. Twenty six models with one bay and two rings having large sectional area were used for this investigation, but fourteen models result in shell buckling. Those models were fabricated with machine tools on a mandrel having outside diameter 110mm and had the following geometric characteristics (See Table 1).
Inner diameter =110 mm,
Thicknesses=1.0, 1. 2, 1. 4, 1. 5mm
Distances between surfaces of rings= 22. 560. 0 mm
Sectional dimensions of ring =15mm×15mm
Deflection detector shown in Fig. 5 was used to record the deflection patterns at the mid-length prior to the collapsing. The circumferential and axial strains of the shells were measured with electrical strain gages.
On the other hand, the behaviors of the shells for axisymmetrical deformation were analized by finite element method.
The following conclusions were obtained.
(1) Average deflections of the shells prior to the collapsing given by ∫^2πr₀wds/2πr roughly agree with those calculated by the finite element method in most cases.
(2) Correlation of the experimentally obtained axisymmetrical collapsing loads with the calculated results by finite element method showed good agreement.

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The equivalent thickness of deflected panels under compression and bending moment are estimated by the energy method. The effective flexural rigidity of columns with rather small slenderness ratio are estimated by using Johnson's and Euler's formula. Using these equivalent thickness and effective flexural rigidity, the collapse load of corner girders and struts are calculated by elastic finite element method. The collapse load and collapse mechanism are compared with experimental results. This method will be usefull at the initial design stage for the simplicity.

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A method of semi-automatic finite element generation has been previously proposed for elastic-plastic analysis of plate bending problems [1]. This procedure is applied to collapse problems of stiffened plates used in ship structure in the present paper.
Plastic analysis can be performed on the concept of plastic hinge lines, which may appear along the interelement boundary. In this case, result obtained are largely influenced by the mesh patterns. The proposed method of mesh re-subdivision during nonlinear calculation overcomes the above difficulty and it shows satisfactory results even if the original mesh pattern is inadequate for the plastic hinge line analysis.
The stiffened plate under consideration is crossly reinforced by a set of regularly arranged stiffeners which are supported by girders. For convenience sake, the effect of stiffeners are dealt with by introducing an orthotropic plate with stiffness determined corresponding the original one. On the other hand, the girders are treated as beams.

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This paper is intended to show the validity of the simplified formulation based on Reissner's variational principle. A slight modification concerned with the integrations of energy terms is required in order to assure that an element passes the patch test. At the same time this leads to the separation of constant and higher order stress contributions from the element stiffness. In this way, the matrices to be dealt become smaller and the computational effort decreases.
The elements such as plane stress, 3-dimensional solid and plate bending are derived from this mixed formulation under the consideration of the equivalence with the displacement method elements. These elements have the shapes of four-node quadrilateral and eight-node hexahedral in the cases of two and three dimensions respectively. As the plate bending element is based on Mindlin's theory, both thin and thick plates are involved.
In these elements, our primary effort was directed to the economy and moreover to the reliability (i. e. passing the patch test, no having zero energy mode except the rigid body modes and no having any types of locking mechanism) in the plate bending element especially.
Numerical results for several problems indicate that the present elements are efficient and accurate.

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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.
On the first report, the authors studied the instability of perforated plate under shearing force by means of FEM analysis and experimentation to determine the effects of stiffening on the buckling strength. The study dealt with the simply supported plate having oval form perforation and reinforced with stiffener, spigot-plate or doubling.
On this paper, we deal with the girder models coincident with ship structures. The object of this study mainly accounts for the buckling strength of doubling plate, because in the first report, some discrepancy was found between the results of experiment and FEM analysis.
The conclusion drawn are as follows ;
1) As far as this study, the order of shear buckling strength are as follows.
Insert >Spigot-plate>Stiffener≈Doubling
2) In general, stiffener may be selected for the most plactical method for reinforcement and the design strength of reinforced plate with stiffener can be estimated from the plastic collapse strength of the web with perforation.
3) In the case of doubling reinforcement, the eccentricity of the reinforced part takes adverce effect on the buckling strength considerably.

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The effect of pad plates at intersection of hull structural members has been discussed qualitatively for some time, now but has not yet been elucidated quantitatively.
Recently, pad plates have often been used as reinforcement when large derrick posts are installed or as a remedy when cracks have occurred at corners of superstructures or at the top and bottom of hold frames on ships in service.
The purpose of this study is to find the effect of pad plate's dimensions on strength, thereby contributing to the determination of the appropriate pad plate dimensions.
An outline of the study is as follows.
(1) Fatigue Tests
Standard S-N diagrams were obtained to estimate the fatigue strength required to design pad plates for various combinations of parameters such as the thickness, width, root gap of pad plates and the kind of load.
(2) Analysis
Stress analysis and K value (stress magnification factor) analysis of the fatigue test results were made by the finite element method and the beam theory, and an analysis method for fatigue strength of pad plates was established.

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An experimental study has been performed in order to confirm the validity of the modal synthesis technique derived in the previous paper (1st report). The coupled vibration of the vertical vibration of main hull girder and the longitudinal vibration of superstructure located on aftership has been tested using the aluminum model ship of seven meter length, and the results are compared with theoretical calculation by the modal synthesis technique mentioned above. Results of the calculation show good agreement with those of the experiment.

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In order to overcome difficulties encountered in the present FEM nonlinear analysis, one of the authors Kawai has proposed a family of new discrete elements which are called the Rigid Body Spring Models (abbreviated RBSM). Through basic studies of these elements they are proved to be very useful in limit analysis of structures or solids in general but it was also found that convergency of elastic solution may not be guaranteed.
For improvement of the RBSM models, another new element is proposed by one of the authors Watanabe using the principle of the hybrid complementary energy, and a family of such hybrid stress models are developed for the bending problem of beams, in-plane as well as bending problems of plates. It should be mentioned that the effects of shear deformation can be easily taken into account in bending analysis beam and plate problems.
In the Mechanism Method, so-called plastic hinges, plastic hinge lines or slip lines must be assumed for calculation of limit loads. They are lines of displacement discontinuity. In the present method these problems can be treated as the contact problems. It is shown by numerical examples that they are in good agreement with exact solutions of plastic analysis and effect of element deformation can be taken into account in the analysis.

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Basing on the experimental evidence, one of the authors has proposed new discrete models which consist of rigid elements connected by two types of spring system distributed over the inter-element boundaries.
In this paper it is shown that these models can be derived from direct discretization of the law of momentum conservation and results of the collapse analysis of plate bending problems are given. After verification of the proposed method by analyses of several simple problems, results of computer simulation on the bending collapse of ice plates are reported.
It is concluded from the results of simulation obtained that crack patterns as well as collapse loads are fairly in good agreement with experimental results, and it is hoped to establish a practical method of estimating the collapse load of ice plates by using these simple models in near future.

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New beam bending element was proposed in Ref. 1) including the effect of shearing deformation, which was composed of two rigid bars connected by two different types of springs. In case of uniform division this discrete element derived by physical consideration is equivalent to the beam element in the conventional finite element method, which was introduced in Ref. 2) by employing linear displacement and rotation functions in conjunction with one-point integration based on the penalty method. Almost the same situation holds for the conical frustum element used for the discrete analysis of axisymmetric shell structures.
These discrete elements give accurate linear elastic solutions in spite of their simplicity and they can be effectively used in the limit load analysis because they can construct the plastic collapse mechanisms.
In this paper the application of these discrete elements is treated to the nonlinear dynamic analysis of frames and axisymmetric shell structures. As numerical examples nonlinear behavior is analyzed of plane and space frames, circular plates, circular cylindrical shells, and spherical shells loaded impulsively. The obtained results are compared with theoretical solutions, other numerical ones, and experimental results in order to justify the validity of the present method.

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