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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

On options for interdisciplinary analysis and design optimization

The interdisciplinary optimization of engineering systems is discussed from the standpoint of the computational alternatives available to the designer. The analysis of such systems typically requires the solution of coupled systems of nonlinear algebraic equations. The solution procedure is necessarily iterative in nature. It is shown that the system can be solved by fixed point iteration, by Newton's method, or by a combination of the two. However, the need for sensitivity analysis may affect the choice of analysis solution method. Similarly, the optimization of the system can be formulated in several ways that are discussed in the paper. It is shown that the effect of the topology of the interaction between disciplines is a key factor in the choice of analysis, sensitivity and optimization methods. Several examples are presented to illustrate the discussion.

Haftka, R. T.↗
NASA NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗
NASA NTRS1992

The sensitivity of a non-isothermal liquid bridge to residual acceleration

An examination is conducted of the steady and unsteady behavior of isothermal and nonisothermal liquid bridge systems under both normal and low-gravity conditions, recasting the full nonlinear equations in terms of a stream-function vorticity formulation in conjunction a nonorthogonal coordinate transformation. For the cases examined, the shape of the bridge is more sensitive to typical spacecraft accelerations than the buoyancy-driven flow. The effect of thermocapillary flow on the surface shape is found to be small, for the range of capillary and Reynolds numbers considered.

Alexander, J. I. D.↗
NASA NTRS1989

Treatment of body forces in boundary element design sensitivity analysis

The inclusion of body forces has received a good deal of attention in boundary element research. The consideration of such forces is essential in the desgin of high performance components such as fan and turbine disks in a gas turbine engine. Due to their critical performance requirements, optimal shapes are often desired for these components. The boundary element method (BEM) offers the possibility of being an efficient method for such iterative analysis as shape optimization. The implicit-differentiation of the boundary integral equations is performed to obtain the sensitivity equations. The body forces are accounted for by either the particular integrals for uniform body forces or by a surface integration for non-uniform body forces. The corresponding sensitivity equations for both these cases are presented. The validity of present formulations is established through a close agreement with exact analytical results.

Saigal, Sunil↗
NASA NTRS1990

Modeling supersonic combustion using a fully-implicit numerical method

A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.

Maccormack, Robert W.↗
NASA NTRS1990

Reduced size first-order subsonic and supersonic aeroelastic modeling

Various aeroelastic, aeroservoelastic, dynamic-response, and sensitivity analyses are based on a time-domain first-order (state-space) formulation of the equations of motion. The formulation of this paper is based on the minimum-state (MS) aerodynamic approximation method, which yields a low number of aerodynamic augmenting states. Modifications of the MS and the physical weighting procedures make the modeling method even more attractive. The flexibility of constraint selection is increased without increasing the approximation problem size; the accuracy of dynamic residualization of high-frequency modes is improved; and the resulting model is less sensitive to parametric changes in subsequent analyses. Applications to subsonic and supersonic cases demonstrate the generality, flexibility, accuracy, and efficiency of the method.

Karpel, Mordechay↗
NASA NTRS1988

Parameter identification and sensitivity analysis for a robotic manipulator arm

The development of a nonlinear dynamic model for large oscillations of a robotic manipulator arm about a single joint is described. Optimization routines are formulated and implemented for the identification of electrical and physical parameters from dynamic data taken from an industrial robot arm. Special attention is given to difficulties caused by the large sensitivity of the model with respect to unknown parameters. Performance of the parameter identification algorithm is improved by choosing a control input that allows actuator emf to be included in an electro-mechanical model of the manipulator system.

Brewer, D. W.↗
NASA NTRS1995

Multidisciplinary design optimization using multiobjective formulation techniques

This report addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for calculating computational grid sensitivities and aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The developed sensitivity analysis technique are then used within a multidisciplinary optimization procedure for designing aerospace vehicles. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The proceduredeveloped is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the aircraft aerodynamic and structural performance when compared to a reference or baseline configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

Chattopadhyay, Aditi↗
NASA NTRS1993

On hydrologic similarity: A dimensionless flood frequency model using a generalized geomorphologic unit hydrograph and partial area runoff generation

One of the shortcomings of the original theory of the geomorphologic unit hydrograph (GUH) is that it assumes that runoff is generated uniformly from the entire catchment area. It is now recognized that in many catchments much of the runoff during storm events is produced on partial areas which usually form on narrow bands along the stream network. A storm response model that includes runoff generation on partial areas by both Hortonian and Dunne mechanisms was recently developed by the authors. In this paper a methodology for integrating this partial area runoff generation model with the GUH-based runoff routing model is presented; this leads to a generalized GUH. The generalized GUH and the storm response model are then used to estimate physically based flood frequency distributions. In most previous work the initial moisture state of the catchment had been assumed to be constant for all the storms. In this paper we relax this assumption and allow the initial moisture conditions to vary between storms. The resulting flood frequency distributions are cast in a scaled dimensionless framework where issues such as catchment scale and similarity can be conveniently addressed. A number of experiments are performed to study the sensitivity of the flood frequency response to some of the 'similarity' parameters identified in this formulation. The results indicate that one of the most important components of the derived flood frequency model relates to the specification of processes within the runoff generation model; specifically the inclusion of both saturation excess and Horton infiltration excess runoff production mechanisms. The dominance of these mechanisms over different return periods of the flood frequency distribution can significantly affect the distributional shape and confidence limits about the distribution. Comparisons with observed flood distributions seem to indicate that such mixed runoff production mechanisms influence flood distribution shape. The sensitivity analysis also indicated that the incorporation of basin and rainfall storm scale also greatly influences the distributional shape of the flood frequency curve.

Sivapalan, Murugesu↗
NASA NTRS1989

On processing development for fabrication of fiber reinforced composite, part 2

Fiber-reinforced composite laminates are used in many aerospace and automobile applications. The magnitudes and durations of the cure temperature and the cure pressure applied during the curing process have significant consequences for the performance of the finished product. The objective of this study is to exploit the potential of applying the optimization technique to the cure cycle design. Using the compression molding of a filled polyester sheet molding compound (SMC) as an example, a unified Computer Aided Design (CAD) methodology, consisting of three uncoupled modules, (i.e., optimization, analysis and sensitivity calculations), is developed to systematically generate optimal cure cycle designs. Various optimization formulations for the cure cycle design are investigated. The uniformities in the distributions of the temperature and the degree with those resulting from conventional isothermal processing conditions with pre-warmed platens. Recommendations with regards to further research in the computerization of the cure cycle design are also addressed.

Hou, Tan-Hung↗
NASA NTRS1991

Transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis

Structural shape design sensitivity analysis (DSA) is presented for objects subjected to gravity, centrifugal, and general thermal loading. DSA employs implicit differentiation of the governing boundary integral equations. Both a surface integral and a particular integral approach are discussed for computation of these effects in response analysis and sensitivity analysis. It is shown that the particular integral approach is capable of computing the sensitivities of objects subjected to nonharmonic temperature distributions. Attention is also given to several techniques for the modeling of temperature distributions in the DSA process. In particular, an approach that eliminates the need for the incorporation of thermal response analysis and sensitivity analysis is described in the overall shape optimization process. A sharp corner formulation is also presented that can account for the jump in the surface traction components at a sharp corner in an interzone boundary.

Kane, James H.↗
NASA NTRS1997

Atmospheric Effects of Subsonic Aircraft: Interim Assessment Report of the Advanced Subsonic Technology Program

This first interim assessment of the subsonic assessment (SASS) project attempts to summarize concisely the status of our knowledge concerning the impacts of present and future subsonic aircraft fleets. It also highlights the major areas of scientific uncertainty, through review of existing data bases and model-based sensitivity studies. In view of the need for substantial improvements in both model formulations and experimental databases, this interim assessment cannot provide confident numerical predictions of aviation impacts. However, a number of quantitative estimates are presented, which provide some guidance to policy makers.

Friedl, Randall R.↗
NASA NTRS2009

Regime-based TRMM and GV Microphysical Studies at MSFC and UAH

Differences in rain rate between TMI and PR vary systematically with PR Z-profile statistics, whose frequency of occurrence is modified to create seasonal biases in the sub-tropical Southeastern U.S. (and almost certainly elsewhere). Tropical (non-tropical) DSDs in N. Alabama exhibit larger (smaller) D(sub 0), and larger (smaller) N(sub 0) and mu. The formulation process for empirical retrievals of DSD using dual-pol radar is sensitive to D(sub max) assumptions used in the scattering model stage. 4. DSD retrievals from Parsivel disdrometers compare favorably to those of the 2DVD unless rain rates exceed 25 mm/hr and D(sub m) exceeds 2 mm (at which point the Parsivels overestimate D(sub m) and rain rate).

Petersen, Walter A.↗
NASA NTRS1987

Optimization of shallow arches against instability using sensitivity derivatives

The author discusses the problem of optimization of shallow frame structures which involve a coupling of axial and bending responses. A shallow arch of a given shape and of given weight is optimized such that its limit point load is maximized. The cross-sectional area, A(x) and the moment of inertia, I(x) of the arch obey the relationship I(x) = rho A(x) sup n, n = 1,2,3 and rho is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a corotational formulation. The optimization is carried out using a second-order projected Lagrangian algorithm and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentation. Results are presented for an arch of a specified rise to span ratio under two different loadings and the limitations of the approach for the intermediate rise arches are addressed.

Kamat, Manohar P.↗
NASA NTRS1973

Sensitivity of rotor blade vibration characteristics to torsional oscillations.

A theoretical investigation of dynamic response characteristics of helicopter rotor blades in forward flight was carried out with special emphasis on the torsional degrees-of-freedom. The finite element method was applied in the formulation of the coupled equations of motion for flapwise bending and torsion for blades with non-collinear elastic, mass and aerodynamic axes. The sensitivity of blade vibration characteristics with respect to structural, geometric and aerodynamic properties as well as flight conditions was evaluated. Numerical results for sample blades were plotted to show the variation of the coupling between bending and torsional components of the response.

Bratanow, T.↗
NASA NTRS1994

Controllability of Free-piston Stirling Engine/linear Alternator Driving a Dynamic Load

This paper presents the dynamic behavior of a Free-Piston Stirling Engine/linear alternator (FPSE/LA) driving a single-phase fractional horse-power induction motor. The controllability and dynamic stability of the system are discussed by means of sensitivity effects of variations in system parameters, engine controller, operating conditions, and mechanical loading on the induction motor. The approach used expands on a combined mechanical and thermodynamic formulation employed in a previous paper. The application of state-space technique and frequency domain analysis enhances understanding of the dynamic interactions. Engine-alternator parametric sensitivity studies, similar to those of the previous paper, are summarized. Detailed discussions are provided for parametric variations which relate to the engine controller and system operating conditions. The results suggest that the controllability of a FPSE-based power system is enhanced by proper operating conditions and built-in controls.

Kankam, M. David↗
NASA NTRS1985

A calculation of the Rosseland mean opacity of dust grains in primordial solar system nebulae

The Rosseland mean opacity owing to grains was calculated as a function of temperature and density for nebulae having solar elemental abundances. The values of the mean opacity were evaluated with a generalized formulation allowing for anisotropic scattering. The values of the mean opacity do not depend sensitively on the choice of the particle size distribution function, provided that there are few particles having sizes in excess of several tens of microns. The results indicate that thermal convection in primordial nebulae occurs over broader ranges of altitudes at low temperatures than at high temperatures, and for size distributions for which extensive aggregation has not yet occurred.

Pollack, J. B.↗
NASA NTRS1993

Numerical parametric studies of spray combustion instability

A coupled numerical algorithm has been developed for studies of combustion instabilities in spray-driven liquid rocket engines. The model couples gas and liquid phase physics using the method of fractional steps. Also introduced is a novel, efficient methodology for accounting for spray formation through direct solution of liquid phase equations. Preliminary parametric studies show marked sensitivity of spray penetration and geometry to droplet diameter, considerations of liquid core, and acoustic interactions. Less sensitivity was shown to the combustion model type although more rigorous (multi-step) formulations may be needed for the differences to become apparent.

Pindera, M. Z.↗