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NASA NTRS1989

Response of moderately thick laminated cross-ply composite shells subjected to random excitation

This study deals with the dynamic response of transverse shear deformable laminated shells subjected to random excitation. The analysis encompasses the following problems: (1) the dynamic response of circular cylindrical shells of finite length excited by an axisymmetric uniform ring loading, stationary in time, and (2) the response of spherical and cylindrical panels subjected to stationary random loadings with uniform spatial distribution. The associated equations governing the structural theory of shells are derived upon discarding the classical Love-Kirchhoff (L-K) assumptions. In this sense, the theory is formulated in the framework of the first-order transverse shear deformation theory (FSDT).

Elishakoff, Isaak↗

NASA NTRS1989

Significance of norms and completeness in variational based methods

By means of a simple structural problem, an important requirement often overlooked in practice on the basis functions used in Rayleigh-Ritz-Galerkin type methods is brought into focus. The problem of the static deformation of a uniformly loaded beam is solved variationally by expanding the beam displacement in a Fourier Cosine series. The potential energy functional is rendered stationary subject to the geometric boundary conditions. It is demonstrated that the variational approach does not converge to the true solution. The object is to resolve this paradox, and in so doing, indicate the practical implications of norms and completeness in an appropriate inner product space.

Storch, Joel A.↗

NASA NTRS1990

Elimination of Gibbs' phenomena from error analysis of finite element results

This paper is one of a series on error analysis and correction of finite element solutions for plates and shells. The error analysis in the earlier papers used half-range double Fourier sine series for numerical harmonic analysis. The half-range formulas are simple to apply, but they can be inaccurate near the ends of the ranges of the independent variables. The Gibbs' phenomenon exhibited by half-range sine series in one independent variable has a two-dimensional analog; a classic example is the Navier solution in a double half-range sine series for the simply supported plate under a uniform load. A simple change of variables is introduced in the paper to improve the accuracy of the double Fourier sine series without adding complexity to the numerical analysis. The change of variables is applied to the problem of approximating a transverse load that is tabulated on a rectangular grid. A solution based on the change of variables is compared with results from the Navier solution for the simply supported plate problem and finite element results for the same problem.

Thurston, Gaylen A.↗

NASA NTRS1991

Hierarchic models for laminated plates

The research conducted in the formulation of hierarchic models for laminated plates is described. The work is an extension of the work done for laminated strips. The use of a single parameter, beta, is investigated that represents the degree to which the equilibrium equations of three dimensional elasticity are satisfied. The powers of beta identify members in the hierarchic sequence. Numerical examples that were analyzed with the proposed sequence of models are included. The results obtained for square plates with uniform loading and homogeneous boundary conditions are very encouraging. Several cross-ply and angle-ply laminates were evaluated and the results compared with those of the fully three dimensional model, computed using MSC/PROBE, and with previously reported work on laminated strips.

Szabo, Barna A.↗

NASA NTRS1991

The use of carboranes as oxidation inhibitors for carbon-carbon composites

Carbon-carbon composites have many beneficial properties for use in aerospace applications, including their high specific strength and modulus at elevated temperatures. However, they share with all carbon based substances a strong tendency to burn when heated in air. In order to exploit their good qualities, it is necessary to slow or prevent their oxidation during use. Molecular inhibiters offer protection with the advantage of being able to form a homogeneous solution with the resin. Since boron oxides are known to provide the desired kind of protection, molecular compounds based on boron seem reasonable candidates to test as inhibitors. Performance tests indicated that carboranes are excellent materials for obtaining high uniform loadings of boron inhibitors in glassy carbon materials and thus reducing their rates of oxidation. Further, there is evidence that the use of substituted derivatives could provide more complete and thorough forms of protection.

Petty, John T.↗

NASA NTRS1993

A photovoltaic catenary-tent array for the Martian surface

To provide electrical power during an exploration mission to Mars, a deployable tent-shaped structure with a flexible photovoltaic (PV) blanket is proposed. The array is designed with a self-deploying mechanism utilizing pressurized gas expansion. The structural design for the array uses a combination of cables, beams, and columns to support and deploy the PV blanket. Under the force of gravity, a cable carrying a uniform load will take the shape of a catenary curve. A catenary-tent collector is self shading which must be taken into account in the solar radiation calculation. The shape and the area of the shadow on the array was calculated and used in the determination of the global irradiance on the array. The PV blanket shape and structure dimensions were optimized to achieve a configuration which maximizes the specific power (W/kg). The optimization was performed for three types of PV blankets (silicon, gallium arsenide over germanium, and amorphous silicon) and two types of structural materials (carbon composite and arimid fiber composite). The results show that the catenary shape of the PV blanket corresponding to zero end angle at the base with respect to the horizontal results in the highest specific power. The tent angle is determined by optimizing the specific mass and the output power for maximum specific power. The combination of carbon fiber structural material and amorphous silicon blanket produces the highest specific power.

Colozza, Anthony J.↗

NASA NTRS1958

Investigation of Minimum Drag and Maximum Lift-drag Ratios of Several Wing-body Combinations Including a Cambered Triangular Wing at Low Reynolds Numbers and at Supersonic Speeds

Theoretical and experimental data for wing-body combinations with wings of triangular, arrow, and diamond plan form are presented for Mach numbers of 1.62, 1.93, and 2.41 and a Reynolds number range of 1.4 x 10 to the 6th power to 0.7 x 10 to the 6th power. Included are two each of triangular and arrow plan-form wings cambered for approximately uniform load at m = 1.62 and lift coefficients of 0.08 and 0.20. Liquid-film studies of the flow over the various configurations are also presented.

Brown, Clinton E↗

NASA NTRS1951

Investigation of the Effects of Twist and Camber on the Aerodynamic Characteristics of a 50 Degrees 38 Minutes Sweptback Wing of Aspect Ratio 2.98 : Transonic-bump Method

An investigation of two semispan wings swept back 50 degrees 38 minutes was conducted in the Langley high-speed 7- by 10-foot tunnel over a Mach number range of 0.68 to 1.15 by use of the transonic-bump technique. This paper presents the results of the investigation of wing-alone and wing-fuselage configurations of the two wings; one was an untwisted uncambered wing and the other was the same wing but incorporated twist and camber designed to give uniform load at a lift coefficient of 0.25 at a Mach number of 1.10. The semispan wings had their quarter-chord lines swept back 50 degrees 38 minutes, aspect ratios 2.98, taper ratios 0.45, and modified NACA 64A-series airfoil sections tapered in thickness. Lift, pitching moment, drag, and bending moment were obtained for these configurations.

WINGS, COMPLETE - DESIGN VARIABLES↗

NASA NTRS1947

Voltera's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic Airfoil Problems

A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformly loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the triangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application.

Heslet, Max A↗

NASA NTRS1953

Deflection and Stress Analysis of Thin Solid Wings of Arbitrary Plan Form with Particular Reference to Delta Wings

The structural analysis of arbitrary solid cantilever wings by small-deflection thin-plate theory is reduced to the solution of linear ordinary differential equations by the assumption that the chordwise deflections at any spanwise station may be expressed in the form of a power series in which the coefficients are functions of the spanwise coordinate. If the series is limited to the first two and three terms (that is, if linear and parabolic chordwise deflections, respectively, are assumed), the differential equations for the coefficients are solved exactly for uniformly loaded solid delta wings of constant thickness ratio. For cases for which exact solutions to the differential equations cannot be obtained, a numerical procedure is derived. Experimental deflection and stress data for constant-thickness delta-plate specimens of 45 degree and 60 degree sweep are presented and are found to compare favorably with the present theory.

Stein, Manuel↗

NASA NTRS1955

Theoretical study of the tunnel-boundary lift interference due to slotted walls in the presence of the trailing-vortex system of a lifting model

The equations presented in this report give the interference on the trailing-vortex system of a uniformly loaded finite-span wing in a circular tunnel containing partly open and partly closed walls, with special reference to symmetrical arrangements of the open and closed portions. Methods are given for extending the equations to include tunnel shapes other than circular. The rectangular tunnel is used to demonstrate these methods. The equations are also extended to nonuniformly loaded wings.

Matthews, Clarence W↗

NASA NTRS1930

Contribution to the theory of propeller vibrations

This report presents a calculation of the torsional frequencies of revolving bars with allowance for the air forces. Calculation of the flexural or bonding frequencies of revolving straight or tapered bars in terms of the angular velocity of revolution. Calculation on the basis of Rayleigh's principle of variation. There is also a discussion of error estimation and the accuracy of results. The author then provides an application of the theory to screw propellers for airplanes and the discusses the liability of propellers to damage through vibrations due to lack of uniform loading.

Liebers, F↗

NASA NTRS1994

Improved Carbon Anodes For Rechargeable Lithium Cells

Carbon anodes for rechargeable lithium cells improved by choosing binder contents and fabrication conditions to achieve maximum porosity, uniform loading, and maximum reversible lithium capacity. Stacking electrodes under pressure during assembly of cells increases cyclability of lithium. Rechargeable, high-energy-density lithium cells containing improved carbon anodes find use in spacecraft, military, communications, automotive, and other demanding applications.

Huang, Chen-Kuo↗

NASA NTRS1993

A photovoltaic catenary-tent array for the Martian surface

To provide electrical power during an exploration mission to Mars, a deployable tent-shaped structure with a flexible photovoltaic (PV) blanket is proposed. The array is designed with a self-deploying mechanism utilizing pressurized gas expansion. The structural design for the array uses a combination of cables, beams, and columns to support and deploy the PV blanket. Under the force of gravity a cable carrying a uniform load will take the shape of a catenary curve. A catenary-tent collector is self shadowing which must be taken into account in the solar radiation calculation. The shape and the area of the shadow on the array was calculated and used in the determination of the global radiation on the array. The PV blanket shape and structure dimension were optimized to achieve a configuration which maximizes the specific power (W/kg). The optimization was performed for four types of PV blankets (Si, GaAs/Ge, GaAs CLEFT, and amorphous Si) and four types of structure materials (Carbon composite, Aramid Fiber composite, Aluminum, and Magnesium). The results show that the catenary shape of the PV blanket, which produces the highest specific power, corresponds to zero end angle at the base with respect to the horizontal. The tent angle is determined by the combined effect of the array structure specific mass and the PV blanket output power. The combination of carbon composite structural material and GaAs CLEFT solar cells produce the highest specific power. The study was carried out for two sites on Mars corresponding to the Viking Lander locations. The designs were also compared for summer, winter, and yearly operation.

Crutchik, M.↗

NASA NTRS1994

System concept definition of the Grumman superconducting Electromagnetic Suspension (EMS) Maglev design

Grumman, under contract to the Army Corps of Engineers, completed a System Concept Definition (SCD) study to design a high-speed 134 m/s (300 m.p.h.) magnetically levitated (Maglev) transportation system. The primary development goals were to design a Maglev that is safe, reliable, environmentally acceptable, and low-cost. The cost issue was a predominant one, since previous studies have shown that an economically viable Maglev system (one that is attractive to investors for future models of passenger and/or freight transportation) requires a cost that is about $12.4 M/km ($20 Million per mile). The design is based on the electromagnetic suspension (EMS) system using superconducting iron-core magnets mounted along both sides of the vehicle. The EMS system has several advantages compared to the electrodynamic suspension (EDS) Maglev systems such as low stray magnetic fields in the passenger cabin and the surrounding areas, uniform load distribution along the full length of the vehicle, and small pole pitch for smoother propulsion and ride comfort. It is also levitated at all speeds and incorporates a wrap-around design of safer operation. The Grumman design has all the advantages of an EMS system identified above, while eliminating (or significantly improving) drawbacks associated with normal magnet powered EMS systems. Improvements include larger gap clearance, lighter weight, lower number of control servos, and higher off line switching speeds. The design also incorporates vehicle tilt (plus or minus 9 deg) for higher coordinated turn and turn out speed capability.

Proise, M.↗

NASA NTRS1994

Transverse shear stresses and their sensitivity coefficients in multilayered composite panels

A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

NASA NTRS2003

Probabilistic Evaluation of Advanced Ceramic Matrix Composite Structures

The objective of this report is to summarize the deterministic and probabilistic structural evaluation results of two structures made with advanced ceramic composites (CMC): internally pressurized tube and uniformly loaded flange. The deterministic structural evaluation includes stress, displacement, and buckling analyses. It is carried out using the finite element code MHOST, developed for the 3-D inelastic analysis of structures that are made with advanced materials. The probabilistic evaluation is performed using the integrated probabilistic assessment of composite structures computer code IPACS. The affects of uncertainties in primitive variables related to the material, fabrication process, and loadings on the material property and structural response behavior are quantified. The primitive variables considered are: thermo-mechanical properties of fiber and matrix, fiber and void volume ratios, use temperature, and pressure. The probabilistic structural analysis and probabilistic strength results are used by IPACS to perform reliability and risk evaluation of the two structures. The results will show that the sensitivity information obtained for the two composite structures from the computational simulation can be used to alter the design process to meet desired service requirements. In addition to detailed probabilistic analysis of the two structures, the following were performed specifically on the CMC tube: (1) predicted the failure load and the buckling load, (2) performed coupled non-deterministic multi-disciplinary structural analysis, and (3) demonstrated that probabilistic sensitivities can be used to select a reduced set of design variables for optimization.

Abumeri, Galib H.↗

NASA NTRS1994

Gear tooth topological modification

The topology of parallel axis gears, such as spur and helical gears is modified to produce quieter and more smoothly operating gear sets with more uniform load distribution. A finite element analysis of the gear in its operating mode is made to produce a plot of radial and tangential deflections of the pinion and gear tooth surfaces which will occur when the gears are loaded during operation. The resultant plot is then inverted to produce a plot, or set of coordinates, which will define the path of travel of the gear tooth grinding wheel, which path is a mirror image of the plot of the finite element analysis. The resulting gears, when subjected to operating loads, will thus be deflected tangentially and radially to their optimum operating, or theoretical true involute, positions so as to produce quieter, smoother, and more evenly loaded gear trains.

Kish, Jules G.↗