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NASA NTRS1995

An efficiency study of the simultaneous analysis and design of structures

The efficiency of the Simultaneous Analysis and Design (SAND) approach in the minimum weight optimization of structural systems subject to strength and displacement constraints as well as size side constraints is investigated. SAND allows for an optimization to take place in one single operation as opposed to the more traditional and sequential Nested Analysis and Design (NAND) method, where analyses and optimizations alternate. Thus, SAND has the advantage that the stiffness matrix is never factored during the optimization retaining its original sparsity. One of SAND's disadvantages is the increase in the number of design variables and in the associated number of constraint gradient evaluations. If SAND is to be an acceptable player in the optimization field, it is essential to investigate the efficiency of the method and to present a possible cure for any inherent deficiencies.

Striz, Alfred G.↗

NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.

Schuler, James J.↗

NASA NTRS1974

SSME/side loads analysis for flight configuration, revision A

This document describes the dynamic loads analysis accomplished for the Space Shuttle Main Engine (SSME) considering the side load excitation associated with transient flow separation on the engine bell during ground ignition. The results contained herein pertain only to the flight configuration. A Monte Carlo procedure was employed to select the input variables describing the side load excitation and the loads were statistically combined. This revision includes an active thrust vector control system representation and updated orbiter thrust structure stiffness characteristics. No future revisions are planned but may be necessary as system definition and input parameters change.

Holland, W.↗

NASA NTRS1985

An airfoil flutter model suspension system to accommodate large static transonic airloads

A pitch/plunge flutter model suspension system and associated two-dimensional MBB-A3 airfoil models is described. The system is designed for installation in the Langley 6-by-19-inch and 6-by-18-inch transonic blowdown wind tunnels to enable systematic study of the transonic flutter characteristics and static pressure distributions of supercritical airfoils at transonic Mach numbers. A compound spring suspension concept is introduced which simultaneously meets requirements for low plunge-mode stiffness, lightweight suspended model, and large steady lift due to angle of attack without the need for excessive static deflections of the plunge spring. The system features variable pitch and plunge frequencies, changeable airfoil rotation axes, and a self aligning control system to maintain a constant mean position of the model with changing airload.

Reed, W. H., III↗

NASA NTRS1986

Application of the method of lines for solution of the Navier-Stokes equations using nonuniform grid distributions

The method of lines is investigated for the numerical solution of the stream function and velocity form of the Navier-Stokes equations on nonuniform grids. Stiffness characteristics of a linear one-dimensional model equation are examined to establish the feasibility of applying the method to the volicity equation in two dimensions. It is observed that the transformed governing equations in computational domain become stiffer with increasing the number of grid points and the differencing technique affects the stiffness characteristics. The results demonstrate that the method of lines under certain circumstances is highly suitable for the numerical solution of physical problems on domains covered with variable grids.

Tiwari, S. N.↗

NASA NTRS2000

LSENS, The NASA Lewis Kinetics and Sensitivity Analysis Code

A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS (the NASA Lewis kinetics and sensitivity analysis code), are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include: static system; steady, one-dimensional, inviscid flow; incident-shock initiated reaction in a shock tube; and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method (LSODE, the Livermore Solver for Ordinary Differential Equations), which works efficiently for the extremes of very fast and very slow reactions, is used to solve the "stiff" ordinary differential equation systems that arise in chemical kinetics. For static reactions, the code uses the decoupled direct method to calculate sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters. Solution methods for the equilibrium and post-shock conditions and for perfectly stirred reactor problems are either adapted from or based on the procedures built into the NASA code CEA (Chemical Equilibrium and Applications).

Radhakrishnan, K.↗

NASA NTRS1930

Pressure element of constant logarithmic stiffness for temperature compensated altimeter

The usual type of altimeter contains a pressure element, the deflections of which are approximately proportional to pressure changes. An evenly divided altitude scale is secured by using a mechanism between the pressure element and pointer which gives the required motion of the pointer. A temperature-compensated altimeter was constructed at the Bureau of Standards for the Bureau of Aeronautics of the Navy Department which contained a manually operated device for controlling the multiplication of the mechanism to the extent necessary for temperature compensation. The introduction of this device made it difficult to adjust the multiplying mechanism to fit an evenly divided altitude scale. To meet this difficulty a pressure element was designed and constructed which gave deflections which were proportional to altitude; that is, to the logarithm of the pressure. The element consisted of a metal bellows of the sylphon type coupled to an internal helical spring which was designed so as to have a variable number of active coils. This report presents a description of and laboratory data relating to the special pressure element for the altimeter. In addition equations which apply generally to springs and pressure elements of constant logarithmic stiffness are developed, including the deflection and the spacing between the coils in terms of the constants of the helical spring and pressure elements. (author)

Brombacher, W G↗

NASA NTRS1977

Dynamic tooth loads and stressing for high contact ratio spur gears

A time history, closed form solution is presented for a dynamic model of spur gear systems for all practical contact ratios. The analysis determines the dynamic response of the gear system and the associated tooth loads and stressing. The dynamic model assumes the two gears act as a rigid inertia and the teeth act as a variable spring of a dynamic system excited by the meshing action of the teeth. Included in the analysis are the effects of the nonlinearity of the tooth pair stiffness during mesh, the tooth errors, and the tooth profile modifications. Besides reviewing the features, solution, and program of this analysis, preliminary results from applying the analysis are presented, which show that tooth profile modification, system inertia and damping, and system critical speeds can affect the dynamic gear tooth loads and stressing significantly.

Cornell, R. W.↗

NASA NTRS1985

A 4-node Bilinear Isoparametric Element in Rockwell NASTRAN

The development and evaluation of the Rockwell NASTRAN four node quadrilateral (QUAD4) element is presented. The element derivation utilizes bilinear isoparametric techniques both for membrane and bending characteristics. The QUAD4 element coordinate system, membrane properties, lumped mass matrix, and treatment of warping are based upon the COSMIC/NASTRAN QDMEMI element while the bending characteristics are based on a paper by T. J. R. Hughes. The effects of warping on the bending stiffness, consistent mass, and geometric stiffness are based upon a paper by R. H. MacNeal. Numerical integration is accomplished by Gaussian quadrature on a 2 x 2 grid. Practical user support features include variable element thickness, thermal analysis and layered composite material definitions.

Liao, C.↗

NASA NTRS2000

Equivalent Skin Analysis of Wing Structures Using Neural Networks

An efficient method of modeling trapezoidal built-up wing structures is developed by coupling. in an indirect way, an Equivalent Plate Analysis (EPA) with Neural Networks (NN). Being assumed to behave like a Mindlin-plate, the wing is solved using the Ritz method with Legendre polynomials employed as the trial functions. This analysis method can be made more efficient by avoiding most of the computational effort spent on calculating contributions to the stiffness and mass matrices from each spar and rib. This is accomplished by replacing the wing inner-structure with an "equivalent" material that combines to the skin and whose properties are simulated by neural networks. The constitutive matrix, which relates the stress vector to the strain vector, and the density of the equivalent material are obtained by enforcing mass and stiffness matrix equities with rec,ard to the EPA in a least-square sense. Neural networks for the material properties are trained in terms of the design variables of the wing structure. Examples show that the present method, which can be called an Equivalent Skin Analysis (ESA) of the wing structure, is more efficient than the EPA and still fairly good results can be obtained. The present ESA is very promising to be used at the early stages of wing structure design.

Liu, Youhua↗

NASA NTRS1991

Matrix cracking in composite laminates with resin-rich interlaminar layers

Fracture mechanics analysis and test data for a toughened composite material that has a resin-rich interlaminar layer (RIL) were used to investigate in situ strength. Exposure to a range of environmental conditions was considered. A parametric analysis study was performed to judge the effects of laminate and material variables. A finite thickness effect, indicating an interaction between ply group thickness and effective flaw size, was found dominant. The magnitude of the effect was directly related to RIL stiffness. In situ strength was found to decrease with decreasing RIL stiffness. This work indicates the need to use a fracture mechanics model of actual lamina microstructure and heterogeneous properties to predict in situ strength in materials with RIL.

Ilcewicz, Larry B.↗

NASA NTRS1993

Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.

Jawerth, Bjoern↗

NASA NTRS2006

Dynamic Analysis of Large In-Space Deployable Membrane Antennas

This paper presents a vibration analysis of an eight-meter diameter membrane reflectarray antenna, which is composed of a thin membrane and a deployable frame. This analysis process has two main steps. In the first step, a two-variable-parameter (2-VP) membrane model is developed to determine the in-plane stress distribution of the membrane due to pre-tensioning, which eventually yields the differential stiffness of the membrane. In the second step, the obtained differential stiffness is incorporated in a dynamic equation governing the transverse vibration of the membrane-frame assembly. This dynamic equation is then solved by a semi-analytical method, called the Distributed Transfer Function Method (DTFM), which produces the natural frequencies and mode shapes of the antenna. The combination of the 2-VP model and the DTFM provides an accurate prediction of the in-plane stress distribution and modes of vibration for the antenna.

vibrations↗

NASA NTRS1972

An evaluation of string theory for the prediction of dynamic tire properties using scale model aircraft tires

The string theory was evaluated for predicting lateral tire dynamic properties as obtained from scaled model tests. The experimental data and string theory predictions are in generally good agreement using lateral stiffness and relaxation length values obtained from the static or slowly rolling tire. The results indicate that lateral forces and self-aligning torques are linearly proportional to tire lateral stiffness and to the amplitude of either steer or lateral displacement. In addition, the results show that the ratio of input excitation frequency to road speed is the proper independent variable by which frequency should be measured.

Clark, S. K.↗

NASA NTRS1991

Transfer function modeling of damping mechanisms in viscoelastic plates

This work formulates a method for the modeling of material damping characteristics in plates. The Sophie German equation of classical plate theory is modified to incorporate hysteresis effects represented by complex stiffness using the transfer function approach proposed by Golla and Hughes, (1985). However, this procedure is not limited to this representation. The governing characteristic equation is decoupled through separation of variables, yielding a solution similar to that of undamped classical plate theory, allowing solution of the steady state as well as the transient response problem.

Slater, J. C.↗

NASA NTRS1993

A conventional point of view on active magnetic bearings

Active magnetic bearings used in rotating machinery should be designed as locally controlled, independent devices similar to other types of bearings. The functions of control electronics and power amplifiers can be simply and explicitly related to general bearing properties such as load capacity, stiffness, and damping. The dynamics of a rotor and its supporting active magnetic bearings are analyzed in a modified conventional method with an extended state vector containing the bearing state variables.

Chen, H. Ming↗

NASA NTRS1995

Neural Network Burst Pressure Prediction in Graphite/Epoxy Pressure Vessels from Acoustic Emission Amplitude Data

Acoustic emission (AE) data were taken during hydroproof for three sets of ASTM standard 5.75 inch diameter filament wound graphite/epoxy bottles. All three sets of bottles had the same design and were wound from the same graphite fiber; the only difference was in the epoxies used. Two of the epoxies had similar mechanical properties, and because the acoustic properties of materials are a function of their stiffnesses, it was thought that the AE data from the two sets might also be similar; however, this was not the case. Therefore, the three resin types were categorized using dummy variables, which allowed the prediction of burst pressures all three sets of bottles using a single neural network. Three bottles from each set were used to train the network. The resin category, the AE amplitude distribution data taken up to 25 % of the expected burst pressure, and the actual burst pressures were used as inputs. Architecturally, the network consisted of a forty-three neuron input layer (a single categorical variable defining the resin type plus forty-two continuous variables for the AE amplitude frequencies), a fifteen neuron hidden layer for mapping, and a single output neuron for burst pressure prediction. The network trained on all three bottle sets was able to predict burst pressures in the remaining bottles with a worst case error of + 6.59%, slightly greater than the desired goal of + 5%. This larger than desired error was due to poor resolution in the amplitude data for the third bottle set. When the third set of bottles was eliminated from consideration, only four hidden layer neurons were necessary to generate a worst case prediction error of - 3.43%, well within the desired goal.

Hill, Eric v. K.↗

NASA NTRSDate not supplied

Rollable Corrugated Tubular Booms

A promising candidate for a new class of deployable composite boom is the COrrugated ROllable TUbular Boom (COROTUB), which is to be employed on future large space structures by the National Aeronautics and Space Administration (NASA). The COROTUB’s two corrugated thin shells form a closed section, which yields high bending and torsional stiffness, allowing for high dimensional stability. The corrugation geometry that dictates the boom cross-section shape was completely defined by closed-form analytical equations given a set of key design parameters. Parametric studies of two geometric variables were used to evaluate which parameters most influence the cross-section’s area moment of inertia and torsional constant. The number of corrugations, flattened height of the boom, and concave and convex corrugation radii were varied to study the complete boom design space. Deeper corrugations increased the local buckling (crimpling) loads of the thin-shell boom but reduced the area moment of inertia and therefore the global buckling load of the beam-column member, and thus a fine balance was sought. Finite element analyses of pure bending and compression load cases for short, 1.22-m-long fully-deployed booms ofeither the same size (flattened height) or similar inertia properties, were first carried out to efficiently study this design trade-off in detail.A second computational study evaluated the boom transition shape and the structural response of a 6-m-long partially-deployed boom, where the effects of partially bracing the root of the boom were also assessed. It was found that bracing length could greatly affect the strength and stiffness of this boom.Bracing type (as in the discrete number of clamps at the root) had no effect on stiffness, but particularly impacted strength for loading cases and boundary conditions that promoted the onset of local web buckling at the root. The corrugated designs were also found to improve, by as much as 20%, the boom bending and axial strength and boom transition length from flat to deployed when compared to a state-of-the-art boom alternative of the same size, for short bracing distances, such as those that would be required by small satellite applications. In addition, they showed a comparable structural response for longer bracing supports.

Booms↗