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H2-optimal control with generalized state-space models for use in control-structure optimization

Several advances are provided solving combined control-structure optimization problems. The author has extended solutions from H2 optimal control theory to the use of generalized state space models. The generalized state space models preserve the sparsity inherent in finite element models and hence provide some promise for handling very large problems. Also, expressions for the gradient of the optimal control cost are derived which use the generalized state space models.

Wette, Matt

Update on HCDstruct - A Tool for Hybrid Wing Body Conceptual Design and Structural Optimization

HCDstruct is a Matlab® based software tool to rapidly build a finite element model for structural optimization of hybrid wing body (HWB) aircraft at the conceptual design level. The tool uses outputs from a Flight Optimization System (FLOPS) performance analysis together with a conceptual outer mold line of the vehicle, e.g. created by Vehicle Sketch Pad (VSP), to generate a set of MSC Nastran® bulk data files. These files can readily be used to perform a structural optimization and weight estimation using Nastran’s® Solution 200 multidisciplinary optimization solver. Initially developed at NASA Langley Research Center to perform increased fidelity conceptual level HWB centerbody structural analyses, HCDstruct has grown into a complete HWB structural sizing and weight estimation tool, including a fully flexible aeroelastic loads analysis. Recent upgrades to the tool include the expansion to a full wing tip-to-wing tip model for asymmetric analyses like engine out conditions and dynamic overswings, as well as a fully actuated trailing edge, featuring up to 15 independently actuated control surfaces and twin tails. Several example applications of the HCDstruct tool are presented.

Gern, Frank H.

Combined control-structural optimization

An approach to combined control-structural optimization aimed at enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and is capable of generating families of designs that can be used in early trade studies. Analytical results are obtained for classes of structure/control objectives with LQG and LQR costs. For these, it is demonstrated that global optima can be computed for small values of the homotopy parameter.

Milman, M.

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.

Structural optimization - Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.

Structural optimization: Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.

Structural Optimization for Reliability Using Nonlinear Goal Programming

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

El-Sayed, Mohamed E.

Neural network based decomposition in optimal structural synthesis

The present paper describes potential applications of neural networks in the multilevel decomposition based optimal design of structural systems. The generic structural optimization problem of interest, if handled as a single problem, results in a large dimensionality problem. Decomposition strategies allow for this problem to be represented by a set of smaller, decoupled problems, for which solutions may either be obtained with greater ease or may be obtained in parallel. Neural network models derived through supervised training, are used in two distinct modes in this work. The first uses neural networks to make available efficient analysis models for use in repetitive function evaluations as required by the optimization algorithm. In the second mode, neural networks are used to represent the coupling that exists between the decomposed subproblems. The approach is illustrated by application to the multilevel decomposition-based synthesis of representative truss and frame structures.

Hajela, P.

Structural optimization of large ocean-going structures

Ocean-going vehicles and platforms are among the largest structures in the world and are subjected to relatively harsh conditions of motions and loads. Some of them, such as semi-submersible platforms, are a relatively new type of structure and hence there is no formal, well evolved and established structural design code as there is for more traditional structures. More recently, efforts have also been made to develop a design method of this type for ships and other ocean structures. One of the many advantages of a rationally based design method is versatility; it can be used for structures that have widely differing purposes, measures of merit, shapes and sizes. The purpose is to describe a rationally based design method that has been developed within the field of ocean structures, in order that persons dealing with other types of structure can judge whether and to what extent its various features may be useful for those other types. Also, even though some features may not be applicable they might stimulate some useful ideas.

Hughes, O. F.

Structural optimization with constraints on transients response

An exceptionally elegant method for structural optimization with constraints on the static response presented by Shield and Prager is discussed. Their derivation of the optimality condition was facilitated by a reformulation of the structural elasticity equations in terms of what was then a new variational principle, the principle of stationary mutual potential energy. Their optimality condition relates the design variable to an appropriately defined mutual strain energy. An alternative but related approach, based upon the principle of stationary mutual complementary energy, presented by N. C. Haung, is also discussed. The simplicity of these principles lies in the facts that the energy functionals are stationary at the solution to the field equations and that their stationary value is proportional to the quantity to be optimized.

Reiss, R.

Structural optimization by generalized, multilevel optimization

In the present development history for both a general multilevel optimization capability and a three-level structural optimization, which is taken to be qualitatively equivalent to a multilevel implementation, a structure is partitioned into a number of substructuring levels where each substructure corresponds to a subsystem. The method is illustrated by a portal framework that decomposes into individual beams, each of which is a box that can be further decomposed into stiffened plates. Substructuring therefore spans three different levels. Since further extensions would only add to the intermediate substructuring levels, the three-level case is qualitatively complete.

Sobieszczanski-Sobieski, J.

Application of modern structural optimization to vibration reduction in rotorcraft

This paper explores a number of techniques which are capable of reducing vibration levels in rotorcraft by redistributing the mass and stiffness properties of the structure. First, vibration reduction in the rotor is considered by using formal structural optimization for ensuring optimal frequency placement. Two cases are considered: in the first case aeroelastic constraints are not enforced and the blade is designed for minimum weight; in the second case aeroelastic constraints are enforced and vibration levels are minimized in forward flight. Next, vibration reduction in the fuselage is considered and the various methods available for vibration reduction by local structural modification are reviewed. The feasibility of combining local structural modification with modern structural optimization is discussed and some extensions of previous research are suggested.

Friedmann, P.

Structural Optimization of Conceptual Aerospace Vehicles

Aerospace vehicle structures must be optimized for mass to maximize the mission payload. During the conceptual design phase, structures must be optimized to accurately predict the mass of the design. Analysis methods that are used in sizing members should allow for the selection of a variety of metallic and composite materials and user-defined geometry constraints. Rapid vehicle structural analysis is often necessary to improve the fidelity and the results that are obtained during the preliminary design. Recent experiences are highlighted that utilize the Collier Research Corporation's Hypersizer toolset to optimize structural concepts.

Hrinda, Glenn Andrew

An optimal structure for a 34-meter millimeter-wave center-fed BWG antenna: The Cross-Box concept

An approach to the design of the planned NASA/JPL 34 m elevation-over-azimuth (Az-El) antenna structure at the Venus site (DSS-13) is presented. The antenna structural configuration accommodates a large (2.44 m) beam waveguide (BWG) tube centrally routed through the reflector-alidade structure, an elevation wheel design, and an optimal structural geometry. The design encompasses a cross-box elevation wheel-reflector base substructure that preserves homology while satisfying many constraints, such as structure weight, surface tolerance, stresses, natural frequency, and various functional constraints. The functional requirements are set to ensure that microwave performance at millimeter wavelengths is adequate. The cross-box configuration was modeled, optimized, and found to satisfy all DSN HEF baseline antenna specifications. In addition, the structure design was conceptualized and analyzed with an emphasis on preserving the structure envelope and keeping modifications relative to the HEF antennas to a minimum, thus enabling the transferability of the BWG technology for future retrofitting. Good performance results were obtained.

Chuang, K. L.