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NASA NTRS2016

Conceptual Design and Structural Optimization of NASA Environmentally Responsible Aviation (ERA) Hybrid Wing Body Aircraft

Simultaneously achieving the fuel consumption and noise reduction goals set forth by NASA's Environmentally Responsible Aviation (ERA) project requires innovative and unconventional aircraft concepts. In response, advanced hybrid wing body (HWB) aircraft concepts have been proposed and analyzed as a means of meeting these objectives. For the current study, several HWB concepts were analyzed using the Hybrid wing body Conceptual Design and structural optimization (HCDstruct) analysis code. HCDstruct is a medium-fidelity finite element based conceptual design and structural optimization tool developed to fill the critical analysis gap existing between lower order structural sizing approaches and detailed, often finite element based sizing methods for HWB aircraft concepts. Whereas prior versions of the tool used a half-model approach in building the representative finite element model, a full wing-tip-to-wing-tip modeling capability was recently added to HCDstruct, which alleviated the symmetry constraints at the model centerline in place of a free-flying model and allowed for more realistic center body, aft body, and wing loading and trim response. The latest version of HCDstruct was applied to two ERA reference cases, including the Boeing Open Rotor Engine Integration On an HWB (OREIO) concept and the Boeing ERA-0009H1 concept, and results agreed favorably with detailed Boeing design data and related Flight Optimization System (FLOPS) analyses. Following these benchmark cases, HCDstruct was used to size NASA's ERA HWB concepts and to perform a related scaling study.

Quinlan, Jesse R.↗

NASA NTRS1994

JPL-ANTOPT antenna structure optimization program

New antenna path-length error and pointing-error structure optimization codes were recently added to the MSC/NASTRAN structural analysis computer program. Path-length and pointing errors are important measured of structure-related antenna performance. The path-length and pointing errors are treated as scalar displacements for statics loading cases. These scalar displacements can be subject to constraint during the optimization process. Path-length and pointing-error calculations supplement the other optimization and sensitivity capabilities of NASTRAN. The analysis and design functions were implemented as 'DMAP ALTERs' to the Design Optimization (SOL 200) Solution Sequence of MSC-NASTRAN, Version 67.5.

Strain, D. M.↗

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.↗

NASA NTRS1985

Structural optimization by generalized, multilevel decomposition

The developments toward a general multilevel optimization capability and results for a three-level structural optimization are described. The method partitions a structure into a number of substructuring levels where each substructure corresponds to a subsystem in the general case of an engineering system. The method is illustrated by a portal framework that decomposes into individual beams. Each beam is a box that can be further decomposed into stiffened plates. Substructuring for this example spans three different levels: (1) the bottom level of finite elements representing the plates; (2) an intermediate level of beams treated as substructures; and (3) the top level for the assembled structure. The three-level case is now considered to be qualitatively complete.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1966

Structural optimization with probability of failure constraint

Probability of failure constraint concept for optimization of general structural system under simultaneous and alternative load systems - truss example

LOADING↗

NASA NTRS1989

Structural optimization using synthetic functions

An efficient method for solving the structural optimization problem of defining member properties and responses in terms of design variables and calculated direct responses is proposed. The present approach provides the user with a simple means of interfacing design analysis models, as well as imposing constraints on functions which are not otherwise directly available. Results are presented for the examples of a three-bar truss, a 25-bar truss, the matching of calculated responses to measured responses, and the design of a rectangular beam.

Vanderplaats, G. N.↗

NASA NTRS1989

Methods for combined control-structure optimization

This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objective of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to asist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further consideration, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose, and a numerical example is presented.

Milman, M.↗

NASA NTRS1981

A programing system for research and applications in structural optimization

The paper describes a computer programming system designed to be used for methodology research as well as applications in structural optimization. The flexibility necessary for such diverse utilizations is achieved by combining, in a modular manner, a state-of-the-art optimization program, a production level structural analysis program, and user supplied and problem dependent interface programs. Standard utility capabilities existing in modern computer operating systems are used to integrate these programs. This approach results in flexibility of the optimization procedure organization and versatility in the formulation of contraints and design variables. Features shown in numerical examples include: (1) variability of structural layout and overall shape geometry, (2) static strength and stiffness constraints, (3) local buckling failure, and (4) vibration constraints. The paper concludes with a review of the further development trends of this programing system.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1995

Displacement based multilevel structural optimization

Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Striz, Alfred G.↗

NASA NTRS1996

Displacement Based Multilevel Structural Optimization

In the complex environment of true multidisciplinary design optimization (MDO), efficiency is one of the most desirable attributes of any approach. In the present research, a new and highly efficient methodology for the MDO subset of structural optimization is proposed and detailed, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures is performed. In the system level optimization, the design variables are the coefficients of assumed polynomially based global displacement functions, and the load unbalance resulting from the solution of the global stiffness equations is minimized. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. The approach is expected to prove very efficient since the design task is broken down into a large number of small and efficient subtasks, each with a small number of variables, which are amenable to parallel computing.

Sobieszezanski-Sobieski, J.↗

NASA NTRS1993

Singularity in structural optimization

The conditions under which global and local singularities may arise in structural optimization are examined. Examples of these singularities are presented, and a framework is given within which the singularities can be recognized. It is shown, in particular, that singularities can be identified through the analysis of stress-displacement relations together with compatibility conditions or the displacement-stress relations derived by the integrated force method of structural analysis. Methods of eliminating the effects of singularities are suggested and illustrated numerically.

Patnaik, S. N.↗

NASA NTRS1988

Structural optimization of rotor blades with integrated dynamics and aerodynamics

The problem of structural optimization of helicopter rotor blades with integrated dynamic and aerodynamic design considerations is addressed. Results of recent optimization work on rotor blades for minimum weight with constraints on multiple coupled natural flap-lag frequencies, blade autorotational inertia and centrifugal stress has been reviewed. A strategy has been defined for the ongoing activities in the integrated dynamic/aerodynamic optimization of rotor blades. As a first step, the integrated dynamic/airload optimization problem has been formulated. To calculate system sensitivity derivatives necessary for the optimization recently developed, Global Sensitivity Equations (GSE) are being investigated. A need for multiple objective functions for the integrated optimization problem has been demonstrated and various techniques for solving the multiple objective function optimization are being investigated. The method called the Global Criteria Approach has been applied to a test problem with the blade in vacuum and the blade weight and the centrifugal stress as the multiple objectives. The results indicate that the method is quite effective in solving optimization problems with conflicting objective functions.

Chattopadhyay, Aditi↗

NASA NTRS1989

Structural optimization of rotor blades with integrated dynamics and aerodynamics

Chattopadhyay, Aditi↗

NASA NTRS1990

Improved first order approximation method for structural optimization

This paper examines various first order approximation methods commonly used in structural optimization. It considers several attempts at improving the approximation by using previous analytical results and introduces an adaptation of a first order approximation method using an exponent adjusted to better fit the constraints and reduce the overall number of iterations needed to attain the optimum.

Fadel, Georges M.↗

NASA NTRS1990

Two point exponential approximation method for structural optimization

Fadel, G. M.↗

NASA NTRS1996

Documentation for a Structural Optimization Procedure Developed Using the Engineering Analysis Language (EAL)

This report describes a structural optimization procedure developed for use with the Engineering Analysis Language (EAL) finite element analysis system. The procedure is written primarily in the EAL command language. Three external processors which are written in FORTRAN generate equivalent stiffnesses and evaluate stress and local buckling constraints for the sections. Several built-up structural sections were coded into the design procedures. These structural sections were selected for use in aircraft design, but are suitable for other applications. Sensitivity calculations use the semi-analytic method, and an extensive effort has been made to increase the execution speed and reduce the storage requirements. There is also an approximate sensitivity update method included which can significantly reduce computational time. The optimization is performed by an implementation of the MINOS V5.4 linear programming routine in a sequential liner programming procedure.

Martin, Carl J., Jr.↗

NASA NTRS1976

Alloy and structural optimization of a directionally solidified lamellar eutectic alloy

Mechanical property characterization tests of a directionally solidified Ni-20 percent Cb-2.5 percent Al-6 percent Cr cellular eutectic turbine blade alloy demonstrated excellent long time creep stability and indicated intermediate temperature transverse tensile ductility and shear strength to be somewhat low for turbine blade applications. Alloy and structural optimization significantly improves these off-axis properties with no loss of longitudinal creep strength or stability. The optimized alloy-structure combination is a carbon modified Ni-20.1 percent Cb-2.5 percent Al-6.0 percent Cr-0.06 percent C composition processed under conditions producing plane front solidification and a fully-lamellar microstructure. With current processing technology, this alloy exhibits a creep-rupture advantage of 39 C over the best available nickel base superalloy, directionally solidified MAR M200+ Hf. While improved by about 20 percent, shear strength of the optimized alloy remains well below typical superalloy values.

Sheffler, K. D.↗

NASA NTRS1990

A homotopy approach for combined control-structure optimization - Constructive analysis and numerical examples

This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objectives of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to assist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further considerations, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose. Analytical and numerical examples are also presented.

Scheid, R. E.↗