The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focused on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design- oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors'' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

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Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments

The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focussed on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design-oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

/pdf/multidisciplinary-aerospace-design-optimization-survey-of-ghzjxaiur6.pdf

Multidisciplinary aerospace design optimization: Survey of recent developments

This paper presents an analytically robust, globally convergent approach to managing the use of approximation models of various fidelity in optimization. By robust global behavior we mean the mathematical assurance that the iterates produced by the optimization algorithm, started at an arbitrary initial iterate, will converge to a stationary point or local optimizer for the original problem. The approach we present is based on the trust region idea from nonlinear programming and is shown to be provably convergent to a solution of the original high-fidelity problem. The proposed method for managing approximations in engineering optimization suggests ways to decide when the fidelity, and thus the cost, of the approximations might be fruitfully increased or decreased in the course of the optimization iterations. The approach is quite general. We make no assumptions on the structure of the original problem, in particular, no assumptions of convexity and separability, and place only mild requirements on the approximations. The approximations used in the framework can be of any nature appropriate to an application; for instance, they can be represented by analyses, simulations, or simple algebraic models. This paper introduces the approach and outlines the convergence analysis.

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A Trust Region Framework for Managing the Use of Approximation Models in Optimization

This paper reviews the basic approximation concepts used in structural optimization. It also discusses some of the most recent developments in that area since the introduction of approximation concepts in the mid-seventies. The paper distinguishes between local, medium-range and global approximations; it covers function approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It appears also that some new methodologies emerge which could greatly benefit from the introduction of new computer architectures.

Approximation concepts for optimum structural design — a review

An efficient automated minimum weight design procedure is presented which is applicable to sizing structural systems that can be idealized by truss, shear panel, and constant strain triangles. Static stress and displacement constraints under alternative loading conditions are considered. The optimization algorithm is an adaptation of the method of inscribed hyperspheres and high efficiency is achieved by using several approximation concepts including temporary deletion of noncritical constraints, design variable linking, and Taylor series expansions for response variables in terms of design variables. Optimum designs for several planar and space truss examples problems are presented. The results reported support the contention that the innovative use of approximation concepts in structural synthesis can produce significant improvements in efficiency.

Some Approximation Concepts for Structural Synthesis

A new equilvalent plate analysis formulation is described which is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. Multiple trapezoidal segments are used to represent such planforms. A Ritz solution technique is used in conjunction with global displacement functions which encompass all the segments. This Ritz solution procedure is implemented efficiently into a computer program so that it can be used by rigorous optimization algorithms for application in early preliminary design. A direct method to interface this structural analysis procedure with aerodynamic programs for use in aeroelastic calculations is described. This equivalent plate analysis procedure is used to calculate the static deflections and stresses and vibration frequencies and modes of an example wing configuration. The numerical results are compared with results from a finite element model of the same configuration to illustrate typical levels of accuracy and computation times resulting from use of this procedure.

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Equivalent plate analysis of aircraft wing box structures with general planform geometry

This article presents a sensitivity-based linearly varying scale factor used to reconcile results from simple and refined models for analysis of the same structure. The improved accuracy of the linear scale factor compared to a constant scale factor, as well as the commonly used tangent approximation, is demonstrated. A wing-box structure is used as an example, with displacements, stresses, and frequencies correlated. The linear scale factor could permit the use of a simplified model in an optimization procedure during preliminary design to approximate the response given by a refined model over a considerable range of design changes. HE design optimization of an engineering system typi- cally requires hundreds of analyses of that system. The use of approximation s to the objective function and con- straints during portions of the design process is quite com- mon,1 because of the high computational cost of these detailed analyses. Such design approximations can be divided into two classes. First there are local, derivative-based approximations such as the linear approximation based on a Taylor-series expansion about a design point. These approximations are typically based on an accurate model to obtain the system response and its derivatives. Second, there are global ap- proximations that try to capture the behavior of the objective function or constraints over the entire design domain. Such approximations can be based on a response surface which is constructed on the basis of many analyses.2 However, global approximations are often based on a simplified theory, a coarser model, or both.3 Such global approximations are referred to here as simple-model approximations. Local approximations are typically very accurate near the design point where they are generated, but since they are based on an extrapolation procedure their accuracy can deteriorate catastrophically at a distance. Simple-model approximations are intended to cap- ture the physics of the problem at some lower, but acceptable level of accuracy over the entire design domain. Therefore, at a particular design point the simple-model approximations are generally less accurate than local approximations, but on the other hand, they typically do not experience the cata-

Sensitivity-Based Scaling for Approximating Structural Response

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described, allow modeling of wing cross sections having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

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Further Generalization of an Equivalent Plate Representation for Aircraft Structural Analysis

This paper describes an analysis method that generates conceptual-level design data for aircraft wing structures. A key requirement is that this data must be produced in a timely manner so that is can be used effectively by multidisciplinary synthesis codes for performing systems studies. Such a capability is being developed by enhancing an equivalent plate structural analysis computer code to provide a more comprehensive, robust and user-friendly analysis tool. The paper focuses on recent enhancements to the Equivalent Laminated Plate Solution (ELAPS) analysis code that significantly expands the modeling capability and improves the accuracy of results. Modeling additions include use of out-of-plane plate segments for representing winglets and advanced wing concepts such as C-wings along with a new capability for modeling the internal rib and spar structure. The accuracy of calculated results is improved by including transverse shear effects in the formulation and by using multiple sets of assumed displacement functions in the analysis. Typical results are presented to demonstrate these new features. Example configurations include a C-wing transport aircraft, a representative fighter wing and a blended-wing-body transport. These applications are intended to demonstrate and quantify the benefits of using equivalent plate modeling of wing structures during conceptual design.

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Equivalent plate modeling for conceptual design of aircraft wing structures

Results from a continuing effort to develop automated methods for structural design are described. A system of computer programs presently under development called SAVES is intended to automate the preliminary structural design of a complete aerospace vehicle. Each step in the automated design process of the SAVES system of programs is discussed, with emphasis placed on use of automated routines for generation of finite-element models. The versatility of these routines is demonstrated by structural models generated for a space shuttle orbiter, an advanced technology transport,n hydrogen fueled Mach 3 transport. Illustrative numerical results are presented for the Mach 3 transport wing.

Gary L. Giles

Papers

Equivalent plate analysis of aircraft wing box structures with general planform geometry

Sensitivity-Based Scaling for Approximating Structural Response

Further Generalization of an Equivalent Plate Representation for Aircraft Structural Analysis

Equivalent plate modeling for conceptual design of aircraft wing structures

Automated procedures for sizing aerospace vehicle structures /SAVES/