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  • Engineering  (3)
  • Nonhomogeneity  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Torsion of an elastic non-homogeneous layer by two circular discs (1996)
    Springer
    Journal of engineering mathematics 30 (1996), S. 557-572 
    Details
    ISSN: 1573-2703
    Keywords: Torsion ; Nonhomogeneity ; Elastic layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Two circular discs of different radii on the opposite faces of an infinite, non-homogeneous elastic layer, whose rigidity is assumed to vary with two cylindrical coordinates r, z by a power law (% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiabeY7aTjabg2da9iabeY7aTnaaBaaaleaa% cqaHXoqycaGGSaaabeaakiabek7aInaaCaaaleqabaGaeqiXdq3aaW% baaWqabeaacqaHXoqyaaWccaWG6bWaaWbaaWqabeaacqaHYoGyaaaa% aaaa!4CAB!\[\mu = \mu _{\alpha ,} \beta ^{\tau ^\alpha z^\beta } \]), are forced to rotate through two different angles of rotation. The rest of each surface is kept stress free. Using the Hankel integral transform, this problem is shown to lead to two pairs of dual integral equations, the solution of which is governed by two simultaneous Fredholm integral equations of the second kind. The latter may be solved either numerically or by iteration (in the case of sufficiently large values of the layer's thickness compared to the maximum of the radii of the circles and for β=0). The solutions for some particular cases previously investigated are recovered by assigning specific numerical values to physical and geometrical parameters. Expressions for some quantities of physical importance, such as the torques applied on the two surfaces and the stress intensity factors, are obtained for the two surfaces and some numerical values are displayed graphically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00036618
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Torsion of a non-homogeneous infinite elastic cylinder slackened by a circular cut (1996)
    Springer
    Journal of engineering mathematics 30 (1996), S. 547-555 
    Details
    ISSN: 1573-2703
    Keywords: Torsion ; Nonhomogeneity ; Elastic cylinder ; Circular cut
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract We consider the torsional deformation of a non-homogeneous infinite elastic cylinder slackened by an external circular cut. The shear modulus of the material of the cylinder is assumed to vary with the radial coordinate by a power law. It is assumed that the lateral surface of the cylinder as well as the surface of the cut are free of stress. The main object of this study is to establish the effect of the non-homogeneity on the stress intensity factor at the tip of the cut. The problem leads to a pair of dual series relations, the solution of which is governed by a Fredholm integral equation of the second kind with a symmetric kernel. This equation is solved numerically by reducing it to an algebraic system. It is concluded that for any degree of non-homogeneity and for D, the relative depth of the cut, greater than 0.6, the cylinder may be replaced by a half-space. However, as the non-homogeneity increases, D decreases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00036617
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A hodograph-based method for the design of shock-free cascades (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 197-213 
    Details
    ISSN: 0271-2091
    Keywords: Transonic ; Hodograph ; Shock-free ; Cascades ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A hodograph-based method, originally developed by the first author for the design of shock-free aerofoils, has been modified and extended to allow for the design of shock-free compressor blades. In the present procedure, the subsonic and supersonic regions of the flow are decoupled, allowing the solution of either an elliptic or a hyperbolic-type partial differential equation for the stream function. The coupling of both regions of the flow is carried out along the sonic line which adjoins both regions. For the subcritical portion of the flow considered here, the pressure distribution is prescribed in addition to the upstream and downstream flow conditions. For the supercritical portion of the flow, the stream function on the sonic line is given instead of the supercritical pressure distribution which is found as part of the solution. In the special hodograph variables used, the equation for the stream function is solved iteratively using a second-order accurate line relaxation procedure for the subsonic portion of the flow. For the supercritical portion of the flow, a characteristic marching procedure in the hodograph plane is used to solve for the supersonic flow. The results are then mapped back to the physical plane to determine the blade shape and the supercritical pressures. Examples of shock-free compressor blade designs are presented. They show good agreement with the direct computation of the flow past the designed blade.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070302
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Euler solutions for self-generated rotor blade-vortex interactionsPresented as AIAA paper 90-1588 at the AIAA 20th Fluids and Plasma Dynamics Conference, Buffalo, New York, June 1990. (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 427-451 
    Details
    ISSN: 0271-2091
    Keywords: Aerodynamics ; Rotor ; Blade-vortex ; Interactions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite-difference procedure has been developed for the prediction of three-dimensional rotor blade-vortex interactions. The interaction velocity field was obtained through a non-linear superposition of the rotor flow field, computed using the unsteady three-dimensional Euler equations, and the embedded vortex wake flow field, computed using the law of Biot-Savart. In the Euler model, near wake rotational effects were simulated using the surface velocity ‘transpiration’ approach. As a result, a modified surface boundary condition was prescribed and enforced at each time step of the computations to satisfy the tangency boundary condition. For supercritical interactions using an upstream-generated vortex, accuracy of the numerical results were found to rely on the user-specified vortex core radius and vortex strength. For the more general self-generated subcritical interactions, vortex wake trajectories were computed using the lifting-line helicopter/rotor trim code CAMRAD. For these interactions, accuracy of the results were found to rely heavily on the CAMRAD-predicted vortex strength, vortex orientation with respect to the blade, and to a large extent on the user-specified vortex core radius. Results for the one-seventh scale model OLS rotor and for a non-lifting rectangular blade having a NACA0012 section are presented. Comparisons with the experimental windtunnel data are also made.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150405
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    The design of shock-free supercritical airfoils including viscous effects (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 37-45 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical procedure has been developed for the design of shock-free supercritical airfoil sections with an allowance for viscous effects, provided the boundary layer is fully attached over the airfoil. The method described combines, in an interative process, an inviscid hodograph-based inverse-design algorithm (IDA) developed by the author and the inverse-boundary layer algorithm (LTBLCEQL) by Miner, Anderson and Lewis. Here, the subcritical portion of the inviscid solution is obtained by solving the full stream function equation in a computational plane which is a conformal map of the two-sheeted hodograph plane. For the supercritical portion, a characteristics calculation is carried out in the hodograph plane. Viscous effects are then incorporated via the displacement surface concept. A Crank-Nicolson type implicit finite difference scheme is utilized to solve the laminar and turbulent boundary layer equation which are expressed in Levy-Lees variables. A transition model allowing for gradual, rather than instantaneous, transition to turbulent flow is also incorporated. The numerical coupling procedure is applied to the design of two airfoil sections for a range of supercritical Mach numbers.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020107
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