In this paper, the three-dimensional solutions for the stresses and displacements in a semi-infinite body having a spherical cavity are given for the case of a uniform pressure applied to the plane boundary and to the surface of the cavity. In analysis, the method of Boussinesq's two harmonic stress functions are used. The two stress functions are given by simple expressions of the cylindrical and spherical harmonics. The boundary conditions both on the face of the plane and on the surface of a cavity are satisfied with the aid of Hankel transform and the relations between the two harmonics. Further, numerical calculations are carried out for four different values of the radius of a cavity.

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In this report, four types of slip-line field solutions are presented for the initial plastic yielding of a shallow notched bar bent as in the Charpy test. The slip-line field is statically indeterminate because it is uniquely determined by both of stress and velocity boundary conditions. Then making use of the analogy of Hencky's equation and Geiringer's equation, we studied the method of solution of a statically indeterminate problem when the profile of the base characteristic lines on the hodograph or the normal velocity components along the base slip-line in the physical plane are given. Using this method, slip-line field, constraint factor and maximum tensile stress are calculated. From the coincidence of the field of critical depth calculated by this method with the corresponding field of a deeply notched bar, we conclude that our method is appropriate.

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The three dimensional stress analysis usually is much complicated ; sometimes, however, it is rather easier in an anisotropic elastic body, the solution of which contains one of an isotropic body as a degenerated case. The present paper concerns a stress analysis in a normal-anisotropic body with a circum-ferential crack, uniformly extended or subjected to a couple of concentrated forces. By use of the stress functions formulated by Higuchi, the boundary conditions are expressed in dual integral equations. The solution is obtained and the stress field near the crack tip, the stress-intensity factors and the crack extension stress criteria are presented.

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An experimental method of determining the dynamic stress-strain relation of materials and the results of tests on specimens of annealed copper are reported in this paper. 1) Remarkable stress drops after the dynamic yield stress were observed in the stress-strain curves of copper in a certain range of strain rates. 2) The stress near the impact end of the specimen should be considered as three dimensional. In practice, however, if the ratio of specimen diameter to pulse length is reduced sufficiently, uniaxial stress state should be realized, so that this method can be employed to determine the dynamic characteristic of materials. Furthermore, a constitutive equation of metal was proposed from the standpoint of relaxation phenomenon. But for a more reasonable description of the dynamic plastic behavior of metals it may be necessary to take the strain history into consideration.

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A conception of the equivalent stress and the equivalent strain rate can be used for comparison of the yield surfaces or the stress-strain diagrams of the materials deformed plastically under combined stresses. There is a close relationship between formulating the equivalent strain rate and selecting the type of the equivalent stress. In this paper, when the principal axes of anisotropy coincide with those of stresses, a new conception of the equivalent stress and the equivalent strain rate is suggested for the theory of anisotropic plasticity based on the maximum shear stress hypothesis. Then it is found that lines connecting the tops of strain rate vectors on the sides and corners of the yield surface becomes straight lines respectively, that is, the tops of these strain rate vectors from a polygon when the equivalent strain rate or the change of the amount of deformation is constant. Theoretical results obtained here are concise and this will make it easy to analyze the problems of plastic anisotropy.

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A study is made on the plane stress fields produced in a plate by a moving load, and the general expressions for steady stress fields are obtained. Using those expressions, the stress fields due to a concentrated force moving in a plate or along its edge are calculated. The results are compared with those of the experiments by dynamic photoelasticity method with polyurethan rubber. Comparisions are made for three speed ranges : subsonic, transonic and supersonic. The ptotoelastic fringe patterns coincide fairly well with the calculated isochromatic lines if the load speed does not exceed the propagation velocity of the longitudinal stress waves.

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There is little quantitative knowledge about mechanical behaviors of mechanochemical materials which directly convert the chemical energy into a mechanical one like the muscle. In this paper a formulation of entropy change involved in deformation is presented. The formula developed is different in the coefficient of the logarithmic term from the one currently accepted, in which an uncross linked polymer is assumed to be in an initial state in regard to the deformation of network and the effect of the association of dissolved chains is considered. The latter contains the pressure exerted by undeformed network while the former does not contain it. In the present paper, it is considered that a probability (Ω₂) associated with the uncrosslinked chains is independent of entropy change involved in the deformation after the formation of cross-linkages, because the size and shape of the volume element must change under deformation. An equation of equilibrium swelling was derived from the corrected formula of the elastic entropy change and the osmotic pressure due to effective gegen-ions. The physical meaning of the equation is simple and clear. Theoretical results based on the equation agree well with experimental ones for a particle-like or a film-like material.

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Mechanical properties of mechanochemical materials have been scarcely investigated. This paper deals with the theoretical and experimental studies on the mechanical behaviors of mechanochemical materials in an equilibrium state. That is, the degree of swelling under external forces and the works developed during the swelling of mechanochemical materials in forms of a particle, a film and particles in a rigid cylinder are treated from the engineering point of view. The expressions of the mechanical works are derived. Several other mechanical characteristics such as the degree of swelling, the restriction of energy conversion due to an external force, the work efficiency and the swelling pressure are also quantitatively explained. Comparison of the present materials with the muscle is made.

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Dynamic characteristics of fluid temperature in a duct is discussed in this paper. For a general case where a duct is imperfectly insulated by a heat insulator having a finite thickness, an exact solution of the frequency response is determined and compared with the experimental results obtained by means of frequency- and step-response methods. The experiment is carried out for the case where heated or cooled air flows in a duct with or without a heat insulator. The comparison shows that the experimental values agree well with the theory for various values of duct length and of air flow rate. The dynamic characteristic of fluid temperature is affected remarkably by the material and thickness of duct wall, but little by those of the heat insulator. Moreover, it is confirmed that the dynamic characteristics becomes worse as the air flow rate is smaller, the duct longer, and the heat capacity per unit lenght of duct larger.

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A series of diffusers for centrifugal turbomachines were derived, which had larger area enlargement than that of the logarithmic spiral. The flow inside them was investigated. A calculation method for boundary layers was given as an extension of the method for diffusers with the shape of logarithmic spiral. Influences of area enlargement, shape, and aerodynamic parameters were discussed. (1) Features of secondary flows and boundary layers are qualitatively equal to those of logarithmic spiral diffusers. Boundary layer development on convex wall is very rapid. (2) Influence of area enlargement is expressed by coefficients g_h and g_L. By the introduction of these coefficients, equations for boundary layer and performance are obtained. (3) For diffusers with large area enlargement, efficiency is generally higher than for the logarithmic spiral ones. The limit of enlargement is given when one keeps the boundary layer at the convex wall outlet just before separation. (4) Influence of inlet momentum thickness upon performance is large in cases of large enlargement, but those of channel depth and Reynolds number are small in these cases.

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Measurement of solid-liquid contact and surface temperature fluctuations is conducted in case of nucleate and transition boiling of water on the horizontal copper surface of 8 mm diameter. From these measurements it is inferred that the mechanism of transition boiling is closely related to the behavior of vapor bubbles. The results obtained from the analysis of surface temperature records are as follows. (1) Transition boiling is distinguished by intermittent solid-liquid contact and the fluctuation of heat flux corresponding to the periodic departure of vapor bubbles from heating surface. (2) Local time rate of solid-liquid contact, which is smallest at the center of heating surface and largest at he circumference, decreases rapidly with the increase of wall superheat. (3) Transition boiling heat transfer can be explained as the coexistence of nucleate boiling heat transfer in the solid-liquid contact part and film boiling heat transfer in the solid-vapor contact part.

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The clamping stiffness of bolted joint is very important because it affects the fatigue stress of the bolt. But, up to now, the estimation of this stiffness has been difficult unless the joint geometry is so simple that the clamping area of the bolted members is clearly defined. However, in this paper, the authors present an analytical method to calculated the stiffnesses for two simplified models of single-bolted joints and multi-bolted joints respectively by using the three-dimensional elastic theory proposed in reference 6. That is, the abutment is assumed as a finite hollow cylinder of inner diameter 2a, outer 2b and thickness 2h which is loaded by the axial pressure on the circular band with width (c-a) around the hole. Numerical results obtained form the abutments of various values of b/a, h/a and c/a are compared with the values calculated by means of well-known F. Rotschers "Effective Cone Method" etc., and respective disagreements are discussed. It is sure that well-known formulas for clamping stiffness of bolted joints do not consider an exact theory of three dimensional elasticity, and generally contain many errors, then careful attention must be paid to actual applications.

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In helical gear design, deflections and moments of rack-shaped cantilever with finite width, must be taken into consideration. This paper contains numerical solutions for deflections and moments of rack-shaped cantilever with finite width. These solutions are obtained with applying calculus of finite differences to the basic differential equation. For a finite rack-shaped cantilever, deflections and moments are closely related to its pressure angle and profile of its section. The numerical solutions showed good agreement with the experimental results of rack shaped cantilever simulating a gear tooth.

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