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NASA NTRS1992

Analytical shape sensitivities and approximations of modal response of generally laminated tapered skew plates

In the present determination of the derivatives of natural frequencies and mode shapes of a generally laminated tapered skew plate, with respect to various shape parameters, springs are used to simulate the essential boundary conditions. The independent shape parameters are plate surface area, aspect ratio, taper ratio, and sweep angle. Eigenvalues and eigenvectors are approximated over the range of the variable using linear, exponential, and pseudoexponential approximation schemes, and are compared with reanalysis-obtained values. Numerical results are presented for symmetrically and unsymmetrically laminated plates.

Singhvi, Sarvesh↗

NASA NTRS1991

Relevance of impacter shape to nonvisible damage and residual tensile strength of a thick graphite/epoxy laminate

A study was made to determine the relevance of impacter shape to nonvisible damage and tensile residual strength of a 36 mm thick graphite/epoxy motor case. The shapes of the impacters were as follows: 12.7 mm and 25.4 mm diameter hemispheres, a sharp corner, and a 6.3 mm diameter bolt-like rod. The investigation revealed that damage initiated when the contact pressure exceeded a critical level. However, the damage was not visible on the surface until an even higher pressure was exceeded. The impact energy to initiate damage or cause visible damage on the surface increased approximately with impacter diameter to the third power. The reduction in strength for nonvisible damage increased with increasing diameter, 9 and 30 percent for the 12.7 mm and 25.4 mm diameter hemispheres, respectively. The corner impacter made visible damage on the surface for even the smallest impact energy. The rod impacter acted like a punch and sliced through the composite. Even so, the critical level of pressure to initiate damage was the same for the rod and hemispherical impacters. Factors of safety for nonvisible damage increased with increasing kinetic energy of impact. The effects of impacter shape on impact force, damage size, damage visibility, and residual tensile strength were predicted quite well assuming Hertzian contact and using maximum stress criteria and a surface crack analysis.

Poe, Clarence C., Jr.↗

NASA NTRS1992

Input shaped control of 3-dimensional maneuvers of flexible spacecraft

This paper deals with the control of three dimensional rotational maneuvers of flexible spacecraft. A spacecraft with a spherical hub and six symmetric appendages is considered here as a model. The appendages are long and flexible leading to low frequency vibration under any control action. To provide a comprehensive treatment of input shaped controllers, both open loop and closed loop controllers are considered. The minimum-time bang-bang and the near-minimum-time controller, used in conjunction with the shaped input technique are studied. In addition, a combination of a Liapunov controller with the shaped input control technique is proposed to take advantage of the simple feedback control strategy and augment it with a technique that can eliminate the vibratory motion of the flexible appendages more efficiently.

Singh, T.↗

NASA NTRS1992

Laboratory study of effects of sonic boom shaping on subjective loudness and acceptability

A laboratory study was conducted to determine the effects of sonic boom signature shaping on subjective loudness and acceptability. The study utilized the sonic boom simulator at the Langley Research Center. A wide range of symmetrical, front-shock-minimized signature shapes were investigated together with a limited number of asymmetrical signatures. Subjective loudness judgments were obtained from 60 test subjects by using an 11-point numerical category scale. Acceptability judgments were obtained using the method of constant stimuli. Results were used to assess the relative predictive ability of several noise metrics, determine the loudness benefits of detailed boom shaping, and derive laboratory sonic boom acceptability criteria. These results indicated that the A-weighted sound exposure level, the Stevens Mark 7 Perceived Level, and the Zwicker Loudness Level metrics all performed well. Significant reductions in loudness were obtained by increasing front-shock rise time and/or decreasing front-shock overpressure of the front-shock minimized signatures. In addition, the asymmetrical signatures were rated to be slightly quieter than the symmetrical front-shock-minimized signatures of equal A-weighted sound exposure level. However, this result was based on a limited number of asymmetric signatures. The comparison of laboratory acceptability results with acceptability data obtained in more realistic situations also indicated good agreement.

Leatherwood, Jack D.↗

NASA NTRS1992

Scattering from arbitrarily shaped microstrip patch antennas

The scattering properties of arbitrarily shaped microstrip patch antennas are examined. The electric field integral equation for a current element on a grounded dielectric slab is developed for a rectangular geometry based on Galerkin's technique with subdomain rooftop basis functions. A shape function is introduced that allows a rectangular grid approximation to the arbitrarily shaped patch. The incident field on the patch is expressed as a function of incidence angle theta(i), phi(i). The resulting system of equations is then solved for the unknown current modes on the patch, and the electromagnetic scattering is calculated for a given angle. Comparisons are made with other calculated results as well as with measurements.

Shively, David G.↗

NASA NTRS1993

The velocity fields of elliptical galaxies: Steps toward a solution of the intrinsic shape problem

One of the few surviving signatures, at low redshift, of the process of galaxy formation should be the distribution of shapes of elliptical galaxies. Yet the problem of inferring this distribution from the observed ellipticals is still unsolved, because insufficient use has been made of kinematic information. The levels of 'sophistication' of the theoretical models and of the observations have up to now been poorly matched. The kinematic data available for most ellipticals consists of only major and minor axis spectra; and Franx et al. (1991) find, using simple geometric models, that the addition of only one kinematic parameter (the ratio of minor axis to major axis rotation velocity) to the photometry is just not enough to finely constrain the intrinsic shape distribution. On the other hand, the more elaborate self-consistent models (e.g., Levison and Richstone 1987, Statler 1987) have made only infrequent and model-dependent predictions of complicated velocity patterns, mostly at small radii, and have not discussed how they change with shape.

Statler, Thomas S.↗

NASA NTRS1992

Implementation of input command shaping to reduce vibration in flexible space structures

Viewgraphs on implementation of input command shaping to reduce vibration in flexible space structures are presented. Goals of the research are to explore theory of input command shaping to find an efficient algorithm for flexible space structures; to characterize Middeck Active Control Experiment (MACE) test article; and to implement input shaper on the MACE structure and interpret results. Background on input shaping, simulation results, experimental results, and future work are included.

Chang, Kenneth W.↗

NASA NTRS1992

Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers

The computational advantages associated with the utilization of preconditined iterative equation solvers are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.

Guru Prasad, K.↗

NASA NTRS1992

X-ray constraints on the shape of the dark matter in five Abell clusters

X-ray observations obtained with the Einstein Observatory are used to constrain the shape of the dark matter in the inner regions of Abell clusters A401, A426, A1656, A2029, and A2199, each of which exhibits highly flattened optical isopleths. The dark matter is modeled as an ellipsoid with a mass density of about r exp -2. The possible shapes of the dark matter is constrained by comparing these model isophotes to the image isophotes. The X-ray isophotes, and therefore the gravitational potentials, have ellipticities of about 0.1-0.2. The dark matter within the central 1 Mpc is found to be substantially rounder for all the clusters. It is concluded that the shape of the galaxy distributions in these clusters traces neither the gravitational potential nor the gravitating matter.

Buote, David A.↗

NASA NTRS1992

Interstellar cloud shapes - A minimum-hypothesis account involving a purely gravitational effect

The effect produced by the anisotropic gravitational field on the shape of a nonspherical, self-gravitating interstellar cloud is examined. The projected axial ratios observed for molecular clouds can be accounted for if clouds are not generally in a state of strict dynamical equilibrium. For clouds having spectral line widths dominated by supersonic turbulent motions, this purely gravitational effect predicts a mean true axial ratio q about 0.3 for both oblate and prolate cloud geometries. Clouds having p less than about 0.3 are likely to be prolate and quite elongated. The observational data on molecular cloud cores, which have essentially thermal line widths, can be fitted equally well to either oblate or prolate spheroids having q between 0.1 and 0.4 with q about 0.2 providing the best match: highly elongated cores are again more likely to be prolate. While other processes certainly operate throughout the Galaxy to influence cloud shape, it appears plausible that at least some clouds may be shaped principally by their anisotropic gravitational field.

Fleck, Robert C., Jr.↗

NASA NTRS1992

Software issues in three dimensional continuum shape optimization employing boundary formulations

The paper addresses the issue of how individual computational techniques for the accurate and economical calculation of information required for large-scale 3D continuum structural shape optimization via boundary element analysis (BEA) formulations can be prudently selected and incorporated in large-scale BEA programs, employing either direct or iterative equation solvers. A series of techniques that allows for the incorporation of economical shape design sensitivity analysis capability with a minimal amount of software development is described. The use of reanalysis is shown to be the key ingredient associated with each of these techniques. It is concluded that, from a software engineering perspective, capabilities that facilitate 3D shape optimization can be implemented in BEA programs with only modest investments in program development.

Kane, James H.↗

NASA NTRS1993

Recent developments in equivalent plate modeling for wing shape optimization

A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first order shear deformation plate theory in combination with numerical analysis based on simple polynomials which define geometry, construction and displacement approximations lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of current equivalent plate wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison to finite element analysis and test results. Analytical derivatives of stiffness, mass and load terms with respect to wing shape lead to analytic sensitivities of displacements, stresses and natural modes with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗

NASA NTRS1993

Hypersonic stagnation line merged layer flow on blunt axisymmetric bodies of arbitrary shape

The problem of hypersonic stagnation line merged-layer flow of variously shaped blunt asisymmetric bodies is here formulated in such a way as to allow analytical calculations for bodies generated by a conic section. The governing equations encompass, apart from the usual parameters, the eccentricity of the conic section that generates the body-of-revolution for the effect of body shape on the solution obtained. The stagnation-point surface pressure increases as the favorable pressure gradient decreases, in the course of a change of body shape from spherical to hyperboloid.

Jain, Amolak S.↗

NASA NTRS1993

Shape optimization for aerodynamic efficiency and low observability

Field methods based on the finite-difference approximations of the time-domain Maxwell's equations and the potential-flow equation have been developed to solve the multidisciplinary problem of airfoil shaping for aerodynamic efficiency and low radar cross section (RCS). A parametric study and an optimization study employing the two analysis methods are presented to illustrate their combined capabilities. The parametric study shows that for frontal radar illumination, the RCS of an airfoil is independent of the chordwise location of maximum thickness but depends strongly on the maximum thickness, leading-edge radius, and leadingedge shape. In addition, this study shows that the RCS of an airfoil can be reduced without significant effects on its transonic aerodynamic efficiency by reducing the leading-edge radius and/or modifying the shape of the leading edge. The optimization study involves the minimization of wave drag for a non-lifting, symmetrical airfoil with constraints on the airfoil maximum thickness and monostatic RCS. This optimization study shows that the two analysis methods can be used effectively to design aerodynamically efficient airfoils with certain desired RCS characteristics.

Vinh, Hoang↗

NASA NTRS1993

An iterative multidisciplinary analysis for rotor blade shape determination

A CFD solver called ADPAC-APES is coupled with a NASTRAN structural analysis and a MARC thermal/heat transfer analysis to determine rotor blade shape. Nonlinear blade displacements due to centrifugal loads, aerodynamic pressures, and nonuniform temperature distribution are determined simultaneously. The effect of blade displacements on aerodynamic pressures and temperatures is then analyzed. These calculations are iterated till a steady state is reached across all the disciplines. This iterative procedure is applied to a ducted fan rotor blade and the manufactured shape is determined from a given operating shape. Effect of a part-span shroud on blade deflections is also analyzed.

Mahajan, Aparajit J.↗

NASA NTRS1934

Effect of Combustion-chamber Shape on the Performance of a Prechamber Compression-ignition Engine

The effect on engine performance of variations in the shape of the prechamber, the shape and direction of the connecting passage, the chamber volume using a tangential passage, the injection system, and the direction od the fuel spray in the chamber was investigated using a 5 by 7 inch single-cylinder compression-ignition engine. The results show that the performance of this engine can be considerably improved by selecting the best combination of variables and incorporating them in a single design. The best combination as determined from these tests consisted of a disk-shaped chamber connected to the cylinder by means of a flared tangential passage. The fuel was injected through a single-orifice nozzle directed normal to the air swirl and in the same plane. At an engine speed of 1,500 r.p.m. and with the theoretical fuel quantity for no excess air, the engine developed a brake mean effective pressure of 115 pounds per square inch with a fuel consumption of 0.49 pound per brake horsepower-hour and an explosion pressure of 820 pounds per square inch. A brake mean effective pressure of 100 pounds per square inch with a brake-fuel consumption of 0.44 pound per horsepower-hour at 1,500 r.p.m. was obtained.

Moore, C S↗

NASA NTRS1941

Effect of Body Nose Shape on the Propulsive Efficiency of a Propeller

Report presents the results of an investigation of the propulsive efficiency of three adjustable propellers of 10-foot diameter operated in front of four body nose shapes, varying from streamline nose that continued through the propeller plane in the form of a large spinner to a conventional open-nose radial-engine cowling. One propeller had airfoil sections close to the hub, the second had conventional round blade shanks, and the third differed from the second only in pitch distribution. The blade-angle settings ranged from 20 degrees to 55 degrees at the 0.75 radius. The effect of the body nose shape on propulsive efficiency may be divided into two parts: (1) the change in the body drag due to the propeller slipstream and (2) the change in propeller load distribution due to the change in velocity caused by the body. For the nose shape tested in the report, the first effect is shown to be very small; therefore, the chief emphasis of the report is confined to the second effect.

Stickle, George W↗

NASA NTRS1952

Concerning the flow about ring-shaped cowlings of finite thickness Part I

It is shown how one may obtain, in a simple manner, the forms of ring-shaped bodies from existing tables of functions according to the customary method of superposition of flow due to singularities and parallel flow. A number of examples of the forms and pressure distributions of annular source bodies with and without hub body are given, and the inlet conditions of such ring-shaped cowlings are investigated. Furthermore, the annular bodies of finite length are indicated that correspond to Joukowsky profiles for the two-dimensional case. The examples are to give a basis for the design of cross-sectional forms of ring-shaped cowlings and a survey of the flows to be expected.

FLOW, INCOMPRESSIBLE↗