The present paper describes an application of Hellinger-Reissner's variational principle to the finite element formulation for general shells. The authors derived three types of stiffness matrices, two of which depend on Novozhilov and Mushtari-Vlasov's strain-displacement relations respectively, and the last one is represented for flat elements. Some simple examples for cylindrical shells show that a flat element gives more exact values than curved ones. As applications of above methods, stress concentration problems of cylindrical shells with a circular cutout or curved plates with a central through-wall crack were solved. Finite element solution for the stress distributions along a circular cutout of the cylindrical shell under internal pressure is found to agree with Durelli's experimental value for a photo-elastic model. Solution for the curved plate with a central through-wall crack was compared with Ishida's theoretical value of a rectangular flat plate with a central crack and the curvature effect was found to be significant.

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In the previous paper, an extension of the classical main results in the theory of elastic potential to the case of inhomogeneous materials and a reduction of the fundamental boundary value problems in elastostatics to Fredholm's system of singular integral equations were attembted. In the present paper, with intent to establish the theoretical foundations of the previous results, we constructed the uniqueness and the existence theorems of solutions.

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The elasto-plastic behavior of fiber-glass reinforced plastics (FRP) appears to be caused by the cracks progressing along the interface between different constituents and propagating across the matrix. This paper reports an investigation on the relationship between the value of strain applied in the FRP specimen and the state of micro-fracture by considering the value of elastic index of work-done (E.I.W). For the plastics reinforced by the glass fabrics which has systematic structure, the E.I.W. decreased rapidly at the knee point. After the strain passed the knee, it recovered again, and even a small reduction occurred in a certain region. The large reduction of the E.I.W. at the knee is due to the cracks inside of woof strands, and the later small reduction is due to the cracks inside of warp strands. Specially the transition of E.I.W. by step-wise increasing of strain shows the progress and propagation of cracks in the corresponding parts of FRP.

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Surface crack produced during hydrostatic extrusion of brittle metal was investigated. The effect of die angle, length of die bearing and frictional force on the critical back pressure which prevents cracking was studied. It was found that the surface crack is initially produced in the perpendicular direction to the axis near the exit of deformation zone. Then, under some conditions, the crack propagates in the inclined direction to the axis, which is usually called the "fir-tree crack". It was suggested that the surface crack is produced by the axial tensile stress acting on the surface at the exit, which results from non-uniform deformation of the billet at the exit, elastic repulsive force of the die and frictional force between the die bearing and the billet.

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A method to calculate the static deflection, the bending moment, the reactions at supports, etc. is proposed for continuous beams which have nonlinear supports. The calculation method is a kind of relaxation method. We linearize the system by replacing nonlinear supports with linear springs, and carry out the calculation of static deflection for the line-arized system. By iterating the linear calculations in which the linear spring constants are determined from the previous calculation result, we can obtain the solution which also satisfies the characteristics of nonlinear supports. The characteristics of the following supports are described as the examples of nonlinear ones: (1) a section of stern tube bearings made of lignumvitae, (2) a rigid support with backlash, and (3) a spring of which the end is separable from the beam when unloaded. As an example of numerical calculation, a calculation result for a propeller shaft of a ship is illustrated.

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This paper deals with the reliability of response calculus in random (irregular) vibration in relation to the problem of aseismic theory in mechanical engineering. Some stochastic phenomena in a random vibration of structures in earthquake are dominated by two main factors. One is the uncertainty (randomness) of parameters in the system equations and the other is a disturbance (earthquake ground motion) to the system. Here truncated waves from stationary random inputs and responses subjected to them are studied theoretically and experimentally and in this case, statistical characteristics of the amplification factors considerably fluctuate around the valves obtained by the analyses using stationary random inputs. From these studies, it is found that the reliability analyses of response calculi are very important. Especially for lightly damped systems we should pay full attention to the confidence of the result from response calculation.

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In the two-dimensional retarded cascade, it is well known that axial velocity increase through the blade row unless boundary layer on the sidewall of the wild tunnel is sucked away. Increase of the axial velocity at outlet often causes a drop in the performance of cascade. The first purpose of this paper is to find, among many factors that prescribe the cascade geometry, which factor affects most remarkably the two-dimensionality of flow. The axial velocity ratio, which represents the degree of two-dimensionality, depends mainly on the virtual retardation ratio cosβ₁/cosβ₂ at the center of blade span. Secondly, the performances of a cascade with solid sidewall and with porous sidewall for boundary layer suction are compared. The difference of the performance between both cascades increases as the inlet becomes larger. Furthermore, comparison between the effective operating ranges of both cascade arrangements shows a remarkable difference in the case of high inlet angles.

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It is often said that experimental performances of a two-dimensional retarded cascade are not reproducible. In this paper, the technique of cascade testing to obtain the relaible data is presented. Using this method, it is possible to control the inlet and exit flow conditions, so that all the blades of a cascade are operating under the same flow conditions and the axial velocity ratios are equal to unity. Then, the allowable value of axial velocity ratios, which is necessary to ensure the two-dimensional flows, are evaluated. As the inlet angle increases, it becomes more difficult to get the two-dimensionality of flow, and the critical value of axial velocity into approaches unity. Some correcting methods for the cascade performances are discussed when the axial velocity ratio is not kept under the critical value. As the result, some cascade performances at extremely high inlet angle are obtained and their reliability is confirmed by a rotating by cascade test.

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The purpose of this paper is to arrange the analytical method presented in 2nd paper so as to be applicable to "the neighbouring part to the separation point", which is defined to be an extended area of a completely turbulent boundary layer to the separation point, from the experimental results on cases with various strong adverse pressure gradients and the injection. Then, cases with stronger adverse pressure gradients and various inlet main flow velocities have been experimented. From these experiments the following results are obtained for the neighbouring part to the separation point; (1) The character of One-Parameter Family is not applicable to the velocity distribution. (2) The shearing stress at the wall decreases suddenly to zero at the separation point, but the friction work does not show any apparent change. (3) The general fundamental equations of motion, momentum and energy are satisfied except in the nearest part to the separation point. Based on the above experimental results, the analytical method has been derived for determining the momentum thickness θ and the shape factor H(=δ^*/θ.δ^*: displacement thickness) in the neighbouring part to the separation point. It is confirmed that the analytical and the experimental values show very good agreement with each other. Further, a new method of detecting the separation point is presented.

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This paper is intended to theoretically describe the effects of buoyancy due to density difference on a laminar developing flow in the entrance region of a horizontal parallel-plate channel with a constant temperature. The analysis is performed within the framework of the boundary layer theory, and the governing equations are numerically solved by a finite-difference method for a Prandtl number of 0.72. The main items obtainable from the present analysis are: (1) The effects of buoyancy on the velocity and temperature distributions in the entrance region are clarified in detail. (2) The additional pressure drop in the entrance region is increased by a few percent due to buoyancy. (3) The entrance length defined as the axial distance where the velocity at the mid-section of the channel attains 99% of its fully developed value is not affected by buoyancy. (4) The analytical distributions of local and mean heat transfer rates at the channel walls indicate that an omission of the effects of buoyancy will result in an overestimate of overall heat transfer between the channel walls and the fluid by a few percent.

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Fluids moving radial through a rotating channel receive the effect of Coriolis force, and it generates a secondary flow which modifies the distributions of the primary flow velocity. Investigations on this problem are absolutely necessary for the improvements of fluid machines, but the available data are very few because of the difficulties of the experimental works. This paper concerns the hydraulic losses and velocity distributions in a U-shaped rotating channel with a circular section. The losses are found to increase with the rotational speeds when the flow velocity of water is kept constant. The losses are expressed as the ratio of the rotational speeds to the flow velocity. Physical meaning of this ratio on the losses is clarified by the measurements of velocity distributions. When the water moving in the axial direction of the rotating channel is turned in the radial direction, as in the impeller of a fluid machine, the primary flow velocity loses its uniformity and the uneven distribution of velocity causes a peculiar flow changing sinuously along the channel. The detailed nature of this flow is also discussed.

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An analysis is made of the effects of buoyancy forces in a laminar forced-convection flow on a vertical flat plate by using the perturbation method. The solutions are obtained up to the 3rd order approximation; accordingly, the range of applicability of the solution by the analysis is expanded. It is proved that solutions of the 1st report are applicable to a wider region of ξ for the fluids of P_r ≥1 in the case of friction factor and of all Prandtl numbers as to heat transfer, by comparing with the results of this paper. Furthermore, the friction factor and heat transfer coefficient are calculated, and it is shown that a linear relation exists between values. Also it is proved that the solution of energy equation Θ′(ξ, 0) can be presented by a similar formula, Θ′(ξ, 0) = -(0.664+0.48ξ)P_r^1/3, (0≤ξ≤0.3), which is formulated in a purely forced-convection heat transfer problem.

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The heat transfer coefficient from a disk with any prescribed surface temperature change rotating in a uniform stream may be predicted by means of superposition of a step function factor. The validity of an approximate solution for a step function factor obtained in 4th report has been verified in the case of P_r =S_c =2.5 from the mass transfer analogy by a naphthalene sublimation. In order to make clear the end effects produced by a finite diameter of a disk, the local variations in the mass transfer were measured. The end effect in a rotating disk immersed in a stream is considerable, since a flow separation arises in the circumference of a disk. The fact that the mean mass transfer coefficient in Sogin's experiment gives about 20% higher values than the analytical solution may be explained by using the present empirical relation on the local effect.

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