The energy balance concept was applied to the analysis of crack propagation in a viscoelastic material through the estimation of several kinds of energies, which are derived from a modified relaxation integral law, e.g., the instantaneously released elastic energy, the dissipative energy and/or the residual energy. For this purpose, non-linear relationship between stress and strain due to the intrinsic material properties under large deformation as well as the change of boundary condition during crack extension should be described quantitatively. The experimental results for an epoxy resin used as the tested material showed that the modified linear viscoelastic relaxation integral equation is applicable for the aforementioned analysis up to about 100% straining by use of the logarithmic strain rate instead of the nominal one. Also, it was ascertained experimentally that he average crack can be represented in similar ways by introduction of a correction factor depending on the change of crack length, namely the compliance reduction ratio. Finally, a criterion for the crack propagation in a viscoelastic strip was proposed from a macroscopic view point of the internal energies depending on time.

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This paper is concerned with the numerical analysis of elastoplastic creep deformation of thin shells of revolution under an axisymmetric load with applications to pressure vessels. The mathematical theory of an elasto-plastic creep as it applies to thin shells of revolution undergoing considerably large deformations is developed. The basic differential equations derived for incremental values are numerically solved by a finite difference method, and the solutions are obtained by integration of the incremental values. As a numerical example the problem of elasto-plastic creep deformations of pressure vessels important to practical use is treated. It is shown that in elastoplastic creep deformations of thin shells such as usual pressure vessels the difference between solutions from a linear theory and those from a nonlinear theory becomes large, therefore the nonlinear theory should be employed. The elasto-plastic solutions from the prediction method agree well with experimentally determined values for pressure vessel heads by Findlay and others.

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In the present paper, the author analyzes an elastic contact problem of a half-space under torsion by a flat annular rigid stamp, distribution of the tangential stress on the stamp by an appropriate series, we can reduce the problem to the solution of an infinite system of simultaneous equations. Numerical results are illustrated for the distributions of the displacements and the stresses in the half-space.

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In order to investigate the fundamental features of the transient two-dimensional thermal stress concentrations, a semi-infinite plate with a semi-circular notch in the transient two-dimensional temperature field is analyzed. The temperature and stress distributions are calculated by using the finite-difference method with reference to the polar coordinate system. The value of the thermal stress concentration factor K grows larger with the Biot number B and the Fourier number F, but the influence of variation of the B-value on the K-value becomes rapidly smaller. The results obtained from photothermoelastic experiments by using the through-flowing cooling technique are similar to the analytical solutions. However, both are quantitatively somewhat different from each other. Investigating the cause of this discrepancy, an approximate calculation method of the K-value in a plate with finite depth is also proposed.

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Stresses, shearing force and displacement of the center line of an infinite circular bar are analyzed in the case that an impulsive load is applied normally to its surface. The analysis is based on the fundamental equations of three-dimensional elasticity. Laplace transform and Fourier transform techniques are used in the analysis. The inverse transforms are carried out with the help of stationary phase method. The results obtained by the analysis are compared with approximate theories (elementary theory, Rayleigh's theory and Timoshenko's theory). the applicabilities of the approximate theories are discussed.

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It is the object of this paper to make clear the free flexural vibration characteristics of an elliptical plate with the edge restrained in a manner that prevents transverse edge motion and provides a restoring edge moment proportional to rotational angle of edge. Based on the ordinary thin plate theory, the procedure leading to a frequency equation is given in the case of the normal mode of symmetrical vibration about both axes. The numerical calculations are carried out and the lowest nondimensional frequencies are tabulated for he aspect ratios of the ellipse and the rotational spring stiffnesses of edge restraint in the cases of Poisson's damental ellipse tends to a circle, the frequency equation degenerates to the form for a circular plate.

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The preview control problem of vehicle suspension is discussed. The optimal transfer function of a preview filter is determined under a criterion function which is constructed by the weighted sum of the mean squared value of the vertical acceleration on an arbitrary point of a two-dimensional rigid vehicle body and the relative displacement of rear suspension. In some numerical examples, the rms value of vertical acceleration of the center of gravity of the body is reduced to about one seventh that of a system with passive elements only and to about two fifths that of an optimally controlled system without future value of input under the same constraints on relative displacement of rear suspension. It is possible to design this system to be safe side, even under conditions it was not designed for.

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An aspect of the turbulent far wakes behind symmetrical two-dimensional bodies placed in a uniform shear flow is theoretically described by means of the Oseen type of successive approximation on a uniform flow. The expression for the stream function is determined up to the second approximation both inside and outside the wake region, and the region in which the results of the perturbation analysis are valid is also determined. the theoretical velocity profiles in the wake are well compared with the experiments which were conducted with a circular cylinder proaching stream. It is also found that the profiles of the longitudinal turbulence intensity are almost symmetrical in the downstream neighbourhood of the obstacle, the asymmetry of the profiles increasing as the downstream distance is increased.

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The instability of two pairs of infinitely long parallel vortex sheets for initial disturbances is investigated by a linear analysis in an inviscid incompressible fluid, and it is shown paradoxically that two pairs of parallel vortex sheets can not exist at a gap distance between two pairs less than the distance between vortex sheets of each pair. By calculating the non-linear growth in time of periodic disturbances in the vortex sheets, the essential features of the formation and interaction of two parallel vortex streets are analysed, and it is explained that the initially antisymmetric disturbance is more apt to cause the interaction between two vortex streets in their developing stage than the symmetric one. These theoretical results are compared with the experimental ones which were observed in a flow past two circular cylinders spaced in the direction perpendicular to a uniform flow.

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This report deals with the problem of the optimum blading such as designing the profiles and bladings in turbine cascade to minimize the blade loss for various loading conditions. For this purpose forty cases of cascades, different in blade arrangement and inlet and outlet flow conditions, were examined with the aid of boundary layer theory. The parameters for the optimum blading were the frictional loss coefficient, diffusion factor of the upper surface, pitch-chord ratio and the value of maximum velocity and its location. As a result, some conditions necessary for the optimum blading were made clear, and a new parameter representing the loss coefficient was introduced. Furthermore, the agreement of these results about the optimum pitch-chord ratio with those of conventional methods was fairly good.

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Dimensionless approximate solution for slightly compressible fluid flow are derived from the exact solutions of the fundamental linear equations for unsteady viscous compressible flow, and shown to be reasonable within the region w'≤3c' and c'≥3.375×10⁴(w'=R²w/v, c'=Rc/v ; w, angular frequency ; c, speed of sound ; R, pipe radius ; v, kinematic viscosity). In this region radial velocity and cross-sectional variation of pressure are shown to be negligibly small. Pressure and velocity of air and water flow pulsating through a vertical pipe by means of a piston are measured by the use of a strain-gauge-type pressure transducer and a hot-wire anemometer, respectively. Comparisons of experimental results with approximate solutions show that cross-sectional distribution of oscillating velocities agree closely with the theoretical value within the frequency range 0.02 ≲ f ≲ 12 Hz, independently of Reynolds number, piston amplitude, pipe radius, and fluid, and that oscillating pressure distribution within the pipe and oscillating velocity distribution along the pipe axis also agree well with the theoretical values.

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Fundamental equations for pulsating turbulent flow in a circular tube containing a slightly compressible fluid are derived by describing Reynolds stress in terms of eddy viscosity, for whose distribution five models are introduced. Analytical solutions based on each model are developed for steady flow velocity, oscillating velocity and wave propagation constant. Comparison of these solutions for each model shows that the four-region model proposed by Karman is rather reasonable enough to illustrate the flow behaviours. The distributions of oscillating velocities, wave propagation constant, and oscillating pressures based on the four-region model at low frequencies and small Reynolds numbers are similar to those at high frequencies and small Reynolds numbers are similar to those at high frequencies and large Reynolds numbers. Because of the assumption of time-invariant eddy viscosity profile, the low frequency values of wave propagation constant should not be reliable. The analogy of these turbulent flow solutions with the laminar ones is shown schematically.

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Cross flow fan has various kinds of performance curves according to housing geometry, but quantitative relations between them have not been made clear. In this paper, experiments are carried out systematically with the housings of simplified form at first. However, the following results are valid even for housings of a more generalized form. It is found that the main geometrical parameters of housing, which determine the fan performance are the tip clearance of tongue, the setting angle of its suction side and the size of casing. the delivery angle of impeller and the height of fan outlet have only a secondary effect compared with these main parameters. The tip clearance is important for the stability of performance curve, and the setting angle has a certain optimum value. Various types of performance curves are obtained by changing the size of casing.

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Relations between the shape of performance curve and flow pattern of cross flow fan are investigated. Total pressure distributions along inner periphery of impeller are measured by traversing a three-hole circular yaw probe. Output signals from a hot-wire probe fitted to impeller are photographed to show the relative flow through blades. Movements of the eccentric vortex inside impeller are measured by these methods, and the following results are obtained. When the flow rate decreases, the vortex center moves along the inner periphery of impeller towards the tongue over the flow rate corresponding to the maximum of ψ_t. Substantially different two types of flow patterns appear according as φ is larger than 0.3 or not. That is, when φ>0.3, the shape of tongue is the determining factor to the flow pattern, if casing of ordinary size are used. However, when φ<0.3, both the angle of delivery arc of impeller and the size of casing affect the pattern as well as fan performance.

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The present paper is a theoretical investigation on the MHD entrance region of turbulent flow. In the first place, an approximate solution of the velocity profile for a fully developed turbulent flow between parallel planes is obtained by assuming the solution of the series as the velocity profile. Next a linear combination of the velocity profile for a hydrodynamically developed flow and that for a magnetohydrodynamically developed one is used as the velocity profile in the entrance region and a momentum-integral method is applied. From the comparison between the results of the present analysis and those of Maciulaitis et al., it is found that the present analysis results are applicable only to the region of relatively small Hartmann numbers where the analysis of Maciulaitis et al. can not be applied. In addition, a few examples of the results involving the variation of the frictional shearing stress and the pressure in the entrance region are shown.

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