Optimal cupolas of uniform strength: Spherical M-shells and axisymmetric T-shells

Summary The first part of this paper is concerned with the optimal design of spherical cupolas obeying the von Mises yield condition. Five different load combinations, which all include selfweight, are investigated. The second part of the paper deals with the optimal quadratic meridional shape of cupolas obeying the Tresca yield condition, considering selfweight plus the weight of a non-carrying uniform cover. It is established that at long spans some non-spherical Tresca cupolas are much more economical than spherical ones.

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Optimale Kuppeln gleicher Festigkeit: Kugelschalen und axialsymmetrische Schalen

Übersicht Im ersten Teil dieser Arbeit wird der optimale Entwurf sphärischer Kuppeln behandelt, wobei die von Misessche Fließbewegung zugrunde gelegt wird. Fünf verschiedene Lastkombinationen werden untersucht. Der zweite Teil befaßt sich mit der optimalen quadratischen Form des Meridians von Kuppeln, die der Fließbedingung von Tresca folgen.

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List of Symbols a_k, b_k, c_k, A_k, B_k, C_k coefficients used in series solutions - A, B constants in the nondimensional equation of the meridional curve - normal component of the load per unit area of the middle surface - meridional and circumferential forces per unit width - radial pressure per unit area of the middle surface, - skin weight per unit area of the middle surface, - vertical external load per unit horizontal area, - base radius, - R radius of convergence - s - cupola thickness, - u, w subsidiary functions for quadratic cupolas - vertical component of the load per unit area of middle surface - resultant vertical force on a cupola segment - structural weight of cupola, - combined weight of cupola and skin, - distance from the axis of rotation, - vertical distance from the shell apex, - z auxiliary variable in series solutions - specific weight of structural material of cupola - radius of the middle surface, - uniaxial yield stress - meridional stress, - circumferential stress, - _a, _b, _c, _d, _e subsidiary variables used in evaluating the meridional stress - auxiliary function used in series solutions This paper constitutes the third part of a study of shell optimization which was initiated and planned by the late Prof. W. Prager     

Modelling of the pressure-velocity correlation in turbulence diffusion

Most current computations of trubulent flows with second-moment closure adopt the diffusion models which neglect the effect of pressure-velocity correlation. In the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the second-moment closures. Through the relation between and , established by Lumley, we propose here a new turbulence diffusion model which takes into consideration the pressure effect. Applications of this new model in the computation of shearless turbulence mixing layer and plane and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.     

Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

Plane stress dynamic fields near a propagating crack-tip in a power-law material

Based on the plastic-dynamic equations, the asymptotic behaviour of the near-tip fields for a plane stress tensile crack propagating in a power-law material has been studied in this paper. It is shown that the stress and strain singularities are, respectively, of the order and , whereA is a constant which is related to the size of plastic region,r is the distance to the crack tip,n is the power-law exponent. Projects sponsored by the National Science Foundation.     

Pseudo-molecular dynamics study of grain boundary segregation

The segregation of bismuth atoms on the [101] tilt copper grain boundaries Σ3 ( ) 70.53°, Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° has been studied by pseudo-molecular dynamics using the empiricalN-body potentials. The relationship between bismuth segregation and grain boundary structure has been discussed in detail. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Generalized diagonalization of matrices over quaternion field

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On the dynamic behaviour of an elastically supported beam of infinite length, loaded by a concentrated force

Summary An elastically supported beam of infinite length, initially at rest, carries a variable concentrated force at a prescribed point A. General expressions are given for the deflection and the bending moment at A (6.3 and 6.4). Three special cases are considered; the first one is defined by =0 for and =K=const. for ; the second one by =0 for 0 > > , given function of for 0 ; the third one applies to problems in which, during the period of impact, itself is an unknown. The results given here may be of use in those railway-engineering problems in which a rail can be considered as a beam of infinite length, and in which the supporting ground has the required properties.     

Druckabhängigkeit der Viskosität einiger Polyolefinschmelzen

Zusammenfassung Es wird die Druckabhängigkeit des nicht -Newtonschen Fließverhältens von Polyolefinschmelzen (Hochdruck-, Niederdruck-,Phillips-Polyäthylen und Polypropylen) experimentell untersucht und gefunden, daß der durch Gl. [1] definierte Druckkoeffizient mit zunehmender Deformationsgeschwindigkeit kleiner wird und dabei die (im einzelnen in der Tabelle 1 angeführten) Werte annimmt. Der Druckkoeffizient der Polyolefinschmelzen ist ebenso wie für vieleNewtonsche Flüssigkeiten bis 2000 kp cm^–2 unabhängig vom Druck, er wird mit zunehmender Temperatur kleiner und nimmt mit zunehmender Verzweigung zu. Die Meßergebnisse werden mit Hilfe eines Aufweitungsvolumens interpretiert. Es wird gezeigt, daß eine Deutung des Fließverhaltens von Polyäthylen durch das freie Volumen allein nicht möglich ist.

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Summary The influence of pressure of the non-Newtonian flow behaviour of polyolefin melts (Low- and High density Polyethylene,Phillips-Polyethylene and Polypropylene) was investigated. The results are: the coefficient of pressure as defined by eq. [1], decreases with increasing shear rate and reaches the values given in table 1 . The pressure coefficient of polyolefin melts does not depend on pressure up to 2000 kp cm^–2. As observed with manyNewtonian fluids, decreases with increasing temperature and increases with the degree of branching. The experimental results are explained by means of a so called volume of expansion. It has been shown that it is impossible to explain the flow behaviour of polyethylene exclusively with the free volume.

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Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe.     

Dimensional analysis of pore scale and field scale immiscible displacement

A basic re-examination of the traditional dimensional analysis of microscopic and macroscopic multiphase flow equations in porous media is presented. We introduce a macroscopic capillary number which differs from the usual microscopic capillary number Ca in that it depends on length scale, type of porous medium and saturation history. The macroscopic capillary number is defined as the ratio between the macroscopic viscous pressure drop and the macroscopic capillary pressure. can be related to the microscopic capillary number Ca and the LeverettJ-function. Previous dimensional analyses contain a tacit assumption which amounts to setting = 1. This fact has impeded quantitative upscaling in the past. Our definition for , however, allows for the first time a consistent comparison between macroscopic flow experiments on different length scales. Illustrative sample calculations are presented which show that the breakpoint in capillary desaturation curves for different porous media appears to occur at 1. The length scale related difference between the macroscopic capillary number for core floods and reservoir floods provides a possible explanation for the systematic difference between residual oil saturations measured in field floods as compared to laboratory experiment.     

A study of stationary crack-tip deformation fields in thin sheets by computer vision

The in-plane deformation fields near a stationary crack tip for thin, single edge-notched (SEN) specimens, made from Plexiglas, 3003 aluminum alloy and 304 stainless steel, have been successfully obtained by using computer vision. Results from the study indicate that (a) in-plane deformations ranging from elastic to fully plastic can be obtained accurately by the method, (b) for U, and , the size of the HRR dominant zone is much smaller than forV and , respectively. Since these results are in agreement with recent analytical work, suggesting that higher order terms will be needed to accurately predict trends in the data, it is clear that the region where the first term in the asymptotic solution is dominant is dependent on the component of the deformation field being studied, (c) the HRR solution can be used to quantity only in regions where theplastic strains strongly dominate the elastic strain components (i.e., when ); forV, the HRR zone appears to extend somewhat beyond this region, (d) the displacement componentU does not have the HRR singularity anywhere within the measurement region for either 3003 aluminum or 304 SS. However, the displacement componentV agrees with the HRR slope up to the plastic-zone boundary in 3003 aluminum ( ) and over most of the region where measurements were obtained ( ) in 304 SS and (e) the effects of end conditions must be included in any finite-element model of typical SEN specimen geometries to accurately calculate theJ integral and the crack-tip fields.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Production of temperature fluctuations in grid turbulence: Wiskind's experiment revisited

Measurements have been made in nearly-isotropic grid turbulence on which is superimposed a linearly-varying transverse temperature distribution. The mean-square temperature fluctuations, , increase indefinitely with streamwise distance, in accordance with theoretical predictions, and consistent with an excess of production over dissipation some 50% greater than values recorded in previous experiments. This high level of production has the effect of reducing the ratio,r, of the time scales of the fluctuating velocity and temperature fields. The results have been used to estimate the coefficient,C, in Monin's return-to-isotropy model for the slow part of the pressure terms in the temperature-flux equations. An empirical expression by Shih and Lumley is consistent with the results of earlier experiments in whichr 1.5, C 3.0, but not with the present data where r 0.5, C 1.6. Monin's model is improved when it incorporates both time scales.List of symbols C coefficient in Monin model, Eq. (5) - M grid mesh length - m exponent in power law for temperature variance, x ^m - n turbulence-energy decay exponent,q ² x ^-n - p production rate of - p pressure - q ² - R microscale Reynolds number - r time-scale ratiot/t - T mean temperature - U mean velocity - mean-square velocity fluctuations (turbulent energy components) - turbulent temperature flux - x, y, z spatial coordinates - temperature gradient dT/dy - thermal diffusivity - dissipation rate ofq ²/2 - dissipation rate of - Taylor microscale (₂=5q₂/) - temperature microscale - _v temperature-flux correlation coefficient, /v - dimensionless distance from the grid,x/M     

A technique for evaluation of three-dimensional behavior in turbulent boundary layers using computer augmented hydrogen bubble-wire flow visualization

A system is described which allows the recreation of the three-dimensional motion and deformation of a single hydrogen bubble time-line in time and space. By digitally interfacing dualview video sequences of a bubble time-line with a computer-aided display system, the Lagrangian motion of the bubble-line can be displayed in any viewing perspective desired. The u and v velocity history of the bubble-line can be rapidly established and displayed for any spanwise location on the recreated pattern. The application of the system to the study of turbulent boundary layer structure in the near-wall region is demonstrated.List of Symbols Reynolds number based on momentum thickness u /v - t⁺ nondimensional time - u shear velocity - u local streamwise velocity, x-direction - u ⁺ nondimensional streamwise velocity - v local normal velocity, -direction - x ⁺ nondimensional coordinate in streamwise direction - ⁺ nondimensional coordinate normal to wall - ₊ ^wire wire nondimensional location of hydrogen bubble-wire normal to wall - z ⁺ nondimensional spanwise coordinate - momentum thickness - v kinematic viscosity - _W wall shear stress     

Molecular dynamics study of deformation and fracture of Bi-segregated copper bicrystals

The microprocesses of deformation and fracture of Bi-segregated copper bicrystals Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° have been simulated by molecular dynamics in order to study the relationship between the grain boundary embrittlement (GBE) and grain boundary (GB) structure. It is shown that GBE is related to the segregated concentration and distribution of Bi atoms, while Bi segregation is related to the GB structure. Due to their different structures, the bicrystals Σ33, Σ11 and Σ9 show an increasing propensity for Bi segregated concentration. So under the action of external force, Σ33, Σ11 and Σ9 show transgranular ductile, intergranular tearing and intergranular brittle fracture modes, respectively. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Theoretical mean wave resistance of precursor solition generation in two-layer flow

A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton generation in two-layer flow over a localized topography at near-resonance in this paper. The pseudo mean wave resistance of the precursor soliton generation of two-layer flow is determined in terms of the AfKdV equation. From the theoretical results it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m ₁, wherem ₁ is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total mean energy are invariant constants, i.e. : (−1/2):1:1, in which and are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing, wavetrain at the resonant points respectively, and <D> are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the theoretical mean wave resistance flow over the semicircular topography is carried out in terms of the theoretical results of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical calculation. The project supported by the Foundation of The State Education Commission “The Dynamics of Upper Ocean” and the Grants of The Physical Oceanography Laboratory of Ocean University of Qingdao     

About a condition for blow up of solutions of cauchy problem for a wave equation

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The flow regime in the turbulent near wake of a hemisphere

The work presented is a wind tunnel study of the near wake region behind a hemisphere immersed in three different turbulent boundary layers. In particular, the effect of different boundary layer profiles on the generation and distribution of near wake vorticity and on the mean recirculation region is examined. Visualization of the flow around a hemisphere has been undertaken, using models in a water channel, in order to obtain qualitative information concerning the wake structure.List of symbols C _p pressure coefficient, - D diameter of hemisphere - n vortex shedding frequency - p pressure on model surface - p ₀ static pressure - Re Reynolds number, - St Strouhal number, - U, V, W local mean velocity components - mean freestream velocity inX direction - U ^* shear velocity, - u, v, w velocity fluctuations inX, Y andZ directions - X Cartesian coordinate in longitudinal direction - Y Cartesian coordinate in lateral direction - Z Cartesian coordinate in direction perpendicular to the wall - it* boundary layer displacement thickness, - diameter of model surface roughness - elevation angleI - O boundary layer momentum thickness, - _w wall shearing stress - dynamic viscosity of fluid - density of fluid - streamfunction - _x longitudinal component of vorticity, - _y lateral component of vorticity, - _z vertical component of vorticity, This paper was presented at the Ninth symposium on turbulence, University of Missouri-Rolla, October 1–3, 1984     

The extended Jordan's lemma and the relation between laplace transform and fourier transform

I.IntroductionItiswell4n0wnthatthecontourintergrationofcomp1exvariableftinctioncanmakealotintegrationveryconvenient.Jordan'slemmahasaveryimportantstatusintheonec0mplexvariableintegration,anditisveryusefulforavarityofintegration.Withthetheoryoffunctionsofo…     

Zur Berechnung von Rotationsschalen mit gemischten Variationsprinzipien und Ringelementen für eine beliebige statische Belastung

Übersicht Ausgehend von gemischten Variationsprinzipien, welche die lineare Biegethcorie von Rotationsschalen beschreiben, wird ein gemischtes, finites Ringelement entwickelt. An Hand von zwei Beispielen werden die mit dieser finiten Methode gewonnenen Ergebnisse mit Vergleichsergebnissen dargestellt.

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Summary A finite element formulation of a ring type for shells of revolution, utilizing mixed variational formulations and a linear distribution of the unknows ( ) as well as for the geometrical quantities ( ), across the element, is proposed. The results of the test problems agree satisfactorily with other methods of solution.

     

An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

On the operator of symmetric differentiation on a compact Riemannian manifold with boundary

We state a particular case of one of the theorems which we shall prove. Let Ω be a bounded open set in ℝ ⁿ with smooth boundary and let σ=(σ _ij )be a symmetric second-order tensor with components σ _ij εH ^k(Ω) for some (positive or negative) integer k; H ^k are Sobolev spaces on Ω. Then we have for some u _i εH ^k +1(Ω),i=1,...,n, if and only if (if k<0, the integral is in fact a duality) for any symmetric tensor (ω with components and such that ). Some applications in the theory of elasticity are also given.