Conforming polisher for aspheric surface of revolution Patent
Conforming polisher for aspheric surfaces of revolution with inflatable tube
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Conforming polisher for aspheric surfaces of revolution with inflatable tube
Development of near-field method for determining supersonic flow properties about bodies of revolution
Pressure distributions and drag coefficients of 18 constant length and volume slender bodies of revolution at zero incidence for Mach numbers 2.0 to 12.0 - graphs
Wind tunnel apparatus for reproducing coning and spinning motions of bodies of revolution, using six-component strain gage balance for aerodynamic forces
Nonlinear aerodynamic moments for arbitrary motions of bodies of revolution in free flight
Laminar boundary layer on spinning bodies of revolution in oncoming stream, using implicit finite difference technique
Nonlinear dynamic analysis of shells of revolution under symmetric and asymmetric loads, obtaining solutions for shallow cap buckling
Flow field model for steady asymmetric vortex system shed from slender body of revolution in coning motion
Elastic shells of revolution displacement analysis, using incremental variational theory with finite element method
The forebody drag of a supercritical body of revolution was measured in free flight over a Mach number range of 0.85 to 1.05 and a Reynolds number range of 11.5 x 10 to the 6th power to 19.4 x 10 to the 6th power and was compared with wind-tunnel data. The forebody drag coefficient for a Mach number less than 0.96 was 0.111 compared with the wind-tunnel value of 0.103. A gradual increase in the drag occurred in the Langley 8-foot transonic pressure tunnel at a lower Mach number than in the Langley 16-foot transonic tunnel or in the free-flight test. The sharp drag rise occurred near Mach 0.98 in free flight whereas the rise occurred near Mach 0.99 in the Langley 16-foot transonic tunnel. The sharp rise was not as pronounced in the Langley 8-foot transonic pressure tunnel and was probably affected by tunnel-wall-interference effects. The increase occurred more slowly and at a higher Mach number. These results indicate that the drag measurements made in the wind tunnels near Mach 1 were significantly affected by the relative size of the model and the wind tunnel.
A relaxation method is described for the numerical solution of the transonic small disturbance equation for flow about a slender body of revolution. Results for parabolic arc bodies, both with and without an attached sting, are compared with wind-tunnel measurements for a free-stream Mach number range from 0.90 to 1.20. The method is also used to show the effects of wind-tunnel wall interference by including boundary conditions representing porous-wall and open-jet wind-tunnel test sections.
A FORTRAN 4 digital computer program is presented for the initial postbuckling and imperfection sensitivity analysis of bifurcation buckling modes for ring-stiffened orthotropic multilayered shells of revolution. The boundary value problem for the second-order contribution to the buckled state was solved by the forward integration technique using the Runge-Kutta method. The effects of nonlinear prebuckling states and live pressure loadings are included.
A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.
Utilizing element properties, structural stiffness and mass matrices are generated for as many as twenty harmonics and stored on magnetic tape. Matrices generated constitute input data to be used by other stiffness of revolution programs. Variety of boundary and loading conditions can be employed without having to create new mass and stiffness matrices for each case.
A parabolic method for steady transonic flow is extended to bodies of revolution oscillating in a sonic flow field. A Laplace transform technique is employed to derive the dipole solution, and the Adams-Sears iterative technique is used in the stability derivative calculation. A computer program is developed to perform the stability derivative calculation for the slowly oscillating cone and parabolic ogive. Inputs for the program are body geometry thickness ratio, acceleration constant, and pitch axis location. Sample calculations were performed for the parabolic ogive and circular cone and results are compared with those obtained by using other techniques and the available experimental data for circular cones.
A user manual and related program documentation is presented for six compatible computer programs for structural analysis of axisymmetric shell structures. The programs apply to a common structural model but analyze different modes of structural response. In particular, they are: (1) Linear static response under asymmetric loads; (2) Buckling of linear states under asymmetric loads; (3) Nonlinear static response under axisymmetric loads; (4) Buckling nonlinear states under axisymmetric (5) Imperfection sensitivity of buckling modes under axisymmetric loads; and (6) Vibrations about nonlinear states under axisymmetric loads. These programs treat branched shells of revolution with an arbitrary arrangement of a large number of open branches but with at most one closed branch.
The formulation and check out porblems for a computer code DYNAPLAS, which analyzes the large deflection elastic-plastic dynamic response of stiffened shells of revolution, are presented. The formulation for special discretization is by the finite element method with finite differences being used for the evaluation of the pseudo forces due to material and geometric nonlinearities. Time integration is by the Houbolt method. The stiffeners may be due to concentrated or distributed eccentric rings and spring supports at arbitrary angles around the circumference of the elements. Check out porblems include the comparison of solutions from DYNAPLAS with experimental and other computer solutions for rings, conical and cylindrical shells and a curved panel. A hypothetical submarine including stiffeners and missile tube is studied under a combination of hydrostatic and dynamically applied asymmetrical pressure loadings.
The User's manual for the shell theory automated for rotational structures (STARS) 2B and 2V (buckling, vibrations) is presented. Several features of the program are: (1) arbitrary branching of the shell meridians, (2) arbitrary boundary conditions, (3) minimum input requirements to describe a complex, practical shell of revolution structure, and (4) accurate analysis capability using a minimum number of degrees of freedom.