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NASA NTRS1986

The structure of the Uranian atmosphere - Constraints from the geometric albedo spectrum and H2 and CH4 line profiles

Recent high quality spectral observations have allowed the derivation of constraints on the atmospheric structure of Uranus. The present analysis, which is based on the detailed modeling of a broadband geometric albedo spectrum and high resolution observations of the H2 4-0 quadrupole and 6818.9-A CH4 features, yields (1) a family of models which parameterize an upper tropospheric haze layer, (2) a lower, optically infinite cloud at a given pressure level, (3) the cloud-level methane molar fraction, and (4) the mean ortho/para ratio in the visible atmosphere. The single scattering albedo of atmospheric aerosols exhibits a steep darkening between 5890 and 6040 A.

Baines, K. H.↗

NASA NTRS1987

A structure-based model of semantic integrity constraints for relational data bases

Data base management systems (DBMSs) are in widespread use because of the ease and flexibility with which users access large volumes of data. Ensuring data accuracy through integrity constraints is a central aspect of DBMS use. However, many DBMSs still lack adequate integrity support. In additon, a comprehensive theoretical basis for such support the role of a constraint classification system - has yet to be developed. This paper presents a formalism that classifies semantic integrity constraints based on the structure of the relational model. Integrity constraints are characterized by the portion of the data base structure they access, whether one or more relations, attributes, or tuples. Thus, the model is completely general, allowing the arbitrary specification of any constraint. Examples of each type of constraint are illustrated using a small engineering data base, and various implementation issues are discussed.

Rasdorf, William J.↗

NASA NTRS1982

Structural optimization with aeroelastic constraints - A survey of US applications

The paper describes recent developments in the United States in the application of structural optimization techniques to problems of design under aeroelastic constraints. The material is divided into sections on: (1) conventional strength design using aeroelastically calculated loads; (2) aeroelastic tailoring for improved performance; (3) design under flutter and static aeroelastic constraints; and (4) miscellaneous applications. Because of the high cost of applying formal optimization techniques to practical design problems, there have been very few applications of structural optimizations to actual aircraft. The paper is focused on trends that may eventually reverse this situation.

Haftka, R. T.↗

NASA NTRS1987

Control augmented structural synthesis with transient response constraints

An integrated approach to the optimum design of control augmented structural systems is presented in which structural variables and control variables are changed simultaneously during the design process. Constraints are imposed on peak transient dynamic displacements and accelerations, static displacements, natural frequencies, and control system effort. Side constraints imposed on structural member sizes and control system thresholds and actuator output forces insure the generation of physically meaningful designs. Example problems are presented which bring out the benefits of simultaneous treatment of both the structural design variables and the control design variables.

Manning, R. A.↗

NASA NTRS1988

Structural optimization with aeroelastic constraints of rotor blades with straight and swept tips

This paper describes a study in which structural optimization techniques are used to minimize the n/rev vertical hub shears in forward flight, subject to aeroelastic stability constraints and frequency placement constraints. A special technique is used to build a sequence of approximate, inexpensive to solve optimization problems, the solutions of which converge to the solution of the exact, expensive to solve optimization problem. Blade configurations with both straight and swept tips, and single- and double-cell cross sections are analyzed. The results show that the approach used in this study is very efficient, and produces improved designs with a very small number of blade aeroelastic analyses.

Celi, R.↗

NASA NTRS1991

Helicopter vibration reduction using structural optimization with aeroelastic/multidisciplinary constraints - A survey

This paper presents a survey of the state-of-the-art in the field of structural optimization when applied to vibration reduction of helicopters in forward flight with aeroelastic and multidisciplinary constraints. It emphasizes the application of the modern approach where the optimization is formulated as a mathematical programming problem, the objective function consists of the vibration levels at the hub, and behavior constraints are imposed on the blade frequencies and aeroelastic stability margins, as well as on a number of additional ingredients that can have a significant effect on the overall performance and flight mechanics of the helicopter. It is shown that the integrated multidisciplinary optimization of rotorcraft offers the potential for substantial improvements, which can be achieved by careful preliminary design and analysis without requiring additional hardware such as rotor vibration absorbers of isolation systems.

Friedmann, Peretz P.↗

NASA NTRS1994

Line profiles variations from atmospheric eclipses: Constraints on the wind structure in Wolf-Rayet stars

Binary systems in which one of the components has a stellar wind may present a phenomenon known as 'wind' or 'atmospheric eclipse', in which that wind occults the luminous disk of the companion. The enhanced absorption profile, relative to the spectrum at uneclipsed orbital phases, can be be modeled to yield constraints on the spatial structure of the eclipsing wind. A new, very efficient approach to the radiative transfer problem, which makes no requirements with respect to monotonicity of the velocity gradient or size of that gradient, is presented. The technique recovers both the comoving frame calculation and the Sobolev approximation in the appropiate limits. Sample computer simulations of the line profile variations induced by wind eclipses are presented. It is shown that the location of the wind absorption features in frequency is a diagnostic tool for identifying the size of the wind acceleration region. Comparison of the model profile variations with the observed variations in the Wolf-Rayet (W-R)+6 binary system V444 Cyg illustrate how the method can be used to derive information on the structure of the wind of the W-R star constrain the size of the W-R core radius.

Auer, L. H.↗

NASA NTRS1990

Influence of structural and aerodynamic modeling on optimization with flutter constraint

The influences of structural and aerodynamic modeling on multidisciplinary optimization in an aeroelastic environment are not well understood. Therefore, optimizations with flutter and frequency constraints were performed to investigate the effects these modeling factors have on various representative wings. To this end, the Automated Structural Optimization System (ASTROS) was used as a tool to minimize the weight of various fully built-up finite element wing models in subsonic and supersonic flow under given flutter and frequency constraints. First, the performance of the optimization module was tested against results from other codes on a straight and uniform wing widely used for optimization with flutter constraints. Then, fully built-up finite element models of various wings with different aspect ratios were investigated for the influence on the structural optimization for minimum weight of the following modeling factors: finite element selection, structural grid refinement; number of selected modes, retention of breathing modes; selection of reduced frequencies to be used in flutter analysis; aerodynamic panel size and placement; splining of the aerodynamic grid to the structural grid selection of extra points of the structural wing box for splining; and number of constraints to be retained. Knowledge of these influences as well as of the program behavior is important, since optimization can be made more efficient by the selection of reasonable initial models. Also, it was shown previously that modeling has an impact on the results of modal and aeroelastic analyses. Thus, if modeling errors can negatively affect the analyses, a minimum weight optimization can be jeopardized and result in an optimal design that is rather unreliable. In the following, selected results are presented and the influences of some modeling parameters on optimization are pointed out.

Striz, Alfred G.↗

NASA NTRS1989

An improved algorithm for optimum structural design with multiple frequency constraints

An optimality criterion (OC) method for minimum-weight design of structures having multiple constraints on natural frequencies is presented. In this work a new resizing strategy is developed based on relaxation techniques. A computationally adaptive control parameter is used in conjunction with existing OC recursive formulae to promote convergence of optimum structural designs. Some considerations regarding the coupling of the modified Aitken accelerator with the OC method are discussed. Improved and rapidly converged minimum-weight designs are obtained when using an under-relaxed recursive scheme combined with the modified Aitken accelerator.

Mcgee, Oliver G.↗

NASA NTRS1992

Impact of structural optimization with aeroelastic/multidisciplinary constraints on helicopter rotor design

This paper presents a review of the state-of-the-art in the field of structural optimization when applied to vibration reduction of helicopters in forward flight with aeroelastic and multidisciplinary constraints. It emphasizes the application of the modern approach where the optimization is formulated as a mathematical programming problem and the objective function consists of the vibration levels at the hub and behavior constraints are imposed on the blade frequencies, aeroelastic stability margins as well as on a number of additional ingredients which can have a significant effect on the overall performance and flight mechanics of the helicopter. It is shown that the integrated multidisciplinary optimization of rotorcraft offers the potential for substantial improvements which can be achieved by careful preliminary design and analysis without requiring additional hardware such as rotor vibration absorbers or isolation systems.

Friedmann, Peretz P.↗

NASA NTRS1997

Efficient Approximation for Structural Optimization Under Multiple Constraints

The cooperative agreement covered work between August 1995 and August 1997. The focus of the work was efficient approximations of structural response and sensitivity. The effort proceeded in three directions as follows: (1) Development of an approximation extended to efficient sensitivity approximations and demonstrated for structural models for the High Speed Civil Transport; (2) Preliminary development of the adjoint method for calculating sensitivity derivatives; and (3) A review of method for fast exact reanalysis. Attachments of papers which were submitted during this period are included.

Haftka, Raphael T.↗

NASA NTRS1982

Hybrid optimization of truss structures with strength and buckling constraints

An efficient scheme utilizing standard nonlinear programming methodology is presented for the optimal design of elastic, redundant structures with strength and buckling constraints. Numerical examples are given which demonstrate how this method, involving a constraint redefinition, can successfully overcome certain problems typical to such structures. The scheme is applied to the design of a cantilever truss with strength and buckling constraints, in which optimal nonuniform cross section columns are used for all elements critical in buckling. It is found that permitting node movement and adding redundancies can lower the weight of the structure for the prescribed design constraints. In addition, the node excursions in this configuration are shown to be relatively small.

Hajela, P.↗

NASA NTRS1977

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗

NASA NTRS1983

Structural optimization with dynamic behavior constraints

The minimum weight optimum design of damped linearly elastic structural systems subjected to periodic loading with behavior constraints on maximum deflections and side constraints on design variables is addressed. Attention is focused on the two major impediments to an optimal solution: (1) the time parametric nature of the behavior constraints; and (2) the severe nonconvexity of the design space. A solution method based on upper bound approximations for the behavior constraints and an innovative mathematical programming scheme for seeking the optimal frequency subspace is set forth. Numerical results for several test problems illustrate the effectiveness of the method reported.

Mills-Curran, W. C.↗

NASA NTRS1972

Optimization of simple structures with higher mode frequency constraints.

Results of a study of least weight optimization of simple structures with a single natural frequency constraint. Variational techniques were used to derive the necessary equations, and numerical methods were used, where required, to find solutions to the resulting nonlinear, two-point boundary value problems. The numerical results suggest a similarity between the fixed fundamental frequency solution and solutions in which a single frequency other than fundamental is held fixed. Such a similarity is shown to occur under special circumstances, and the knowledge of the fundamental solution in these cases makes it possible to calculate the solution to problems with constraints on frequencies other than the fundamental.

Weisshaar, T. A.↗

NASA NTRSDate not supplied

Some Remaining Challenges in Aerospace Structures

The science behind analyzing and building structures was laid out by legendary scientists such as Euler, Bernoulli, Gauss, Timoshenko and many others. The 20thcentury saw the birth of aviation and space travel, which required more advances in understanding structural behavior. The constraints on aerospace structures relative to weight, durability, performance, and damage tolerance are enormous and in many instances, in competition with each other. Performance requirements driven by other disciplines: aerodynamics, thermal behavior, pressure containment, extreme stability, are now the norm in high performance aerospace structures

Kenneth R Hamm↗

NASA NTRS1994

Thin tailored composite wing for civil tiltrotor

The tiltrotor aircraft is a flight vehicle which combines the efficient low speed (i.e., take-off, landing, and hover) characteristics of a helicopter with the efficient cruise speed of a turboprop airplane. A well-known example of such vehicle is the Bell-Boeing V-22 Osprey. The high cruise speed and range constraints placed on the civil tiltrotor require a relatively thin wing to increase the drag-divergence Mach number which translates into lower compressibility drag. It is required to reduce the wing maximum thickness-to-chord ratio t/c from 23% (i.e., V-22 wing) to 18%. While a reduction in wing thickness results in improved aerodynamic efficiency, it has an adverse effect on the wing structure and it tends to reduce structural stiffness. If ignored, the reduction in wing stiffness leads to susceptibility to aeroelastic and dynamic instabilities which may consequently cause a catastrophic failure. By taking advantage of the directional stiffness characteristics of composite materials the wing structure may be tailored to have the necessary stiffness, at a lower thickness, while keeping the weight low. The goal of this study is to design a wing structure for minimum weight subject to structural, dynamic and aeroelastic constraints. The structural constraints are in terms of strength and buckling allowables. The dynamic constraints are in terms of wing natural frequencies in vertical and horizontal bending and torsion. The aeroelastic constraints are in terms of frequency placement of the wing structure relative to those of the rotor system. The wing-rotor-pylon aeroelastic and dynamic interactions are limited in this design study by holding the cruise speed, rotor-pylon system, and wing geometric attributes fixed. To assure that the wing-rotor stability margins are maintained a more rigorous analysis based on a detailed model of the rotor system will need to ensue following the design study. The skin-stringer-rib type architecture is used for the wing-box structure. The design variables include upper and lower skin ply thicknesses and orientation angles, spar and rib web thicknesses and cap areas, and stringer cross-sectional areas. These design variables will allow the maximum tailoring of the structure to meet the design requirements most efficiently. Initial dynamic analysis has been conducted using MSC/NASTRAN to determine the baseline wing's frequencies and mode shapes. For the design study we intend to use the finite-element based code called WIDOWAC (Wing Design Optimization With Aeroeastic Constraints) that was developed at NASA Langley in early 1970's for airplane wing structural analysis and preliminary design. Currently, the focus is on modification and validation of this code which will be used for the civil tiltrotor design efforts.

Rais-Rohani, Masoud↗

NASA NTRS1989

An approximation function for frequency constrained structural optimization

The purpose is to examine a function for approximating natural frequency constraints during structural optimization. The nonlinearity of frequencies has posed a barrier to constructing approximations for frequency constraints of high enough quality to facilitate efficient solutions. A new function to represent frequency constraints, called the Rayleigh Quotient Approximation (RQA), is presented. Its ability to represent the actual frequency constraint results in stable convergence with effectively no move limits. The objective of the optimization problem is to minimize structural weight subject to some minimum (or maximum) allowable frequency and perhaps subject to other constraints such as stress, displacement, and gage size, as well. A reason for constraining natural frequencies during design might be to avoid potential resonant frequencies due to machinery or actuators on the structure. Another reason might be to satisy requirements of an aircraft or spacecraft's control law. Whatever the structure supports may be sensitive to a frequency band that must be avoided. Any of these situations or others may require the designer to insure the satisfaction of frequency constraints. A further motivation for considering accurate approximations of natural frequencies is that they are fundamental to dynamic response constraints.

Canfield, R. A.↗