The ADS general-purpose optimization program

The mathematical statement of the general nonlinear optimization problem is given as follows: find the vector of design variables, X, that will minimize f(X) subject to G sub J (x) + or - 0 j=1,m H sub K hk(X) = 0 k=1,l X Lower I approx less than X sub I approx. less than X U over I i = 1,N. The vector of design variables, X, includes all those variables which may be changed by the ADS program in order to arrive at the optimum design. The objective function F(X) to be minimized may be weight, cost or some other performance measure. If the objective is to be maximized, this is accomplished by minimizing -F(X). The inequality constraints include limits on stress, deformation, aeroelastic response or controllability, as examples, and may be nonlinear implicit functions of the design variables, X. The equality constraints h sub k(X) represent conditions that must be satisfied precisely for the design to be acceptable. Equality constraints are not fully operational in version 1.0 of the ADS program, although they are available in the Augmented Lagrange Multiplier method. The side constraints given by the last equation are used to directly limit the region of search for the optimum. The ADS program will never consider a design which is not within these limits

Design of structures for optimum geometry

A method is presented for configuration optimization of finite element structures, given a reasonable initial geometry. The objective is to minimize weight or cost. Design variables include geometric as well as member sizing parameters. The number of elements and joints, and the element-joint relationships are prescribed and are not changed during the optimization process. However, the joint locations are changed. The structure is assumed to be linearly elastic and may be statically indeterminate. Multiple loading conditions are allowed. Constraints include limits on stiffness as well as strength. The method is demonstrated with application to truss design, subject to minimum size, strength, buckling, and displacement constraints. Major design improvements are achieved through configurations changes

Numerical Airfoil Optimization Using a Reduced Number of Design Coordinates

A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization

Alternative methods for calculating sensitivity of optimized designs to problem parameters

Optimum sensitivity is defined as the derivative of the optimum design with respect to some problem parameter, P. The problem parameter is usually fixed during optimization, but may be changed later. Thus, optimum sensitivity is used to estimate the effect of changes in loads, materials or constraint bounds on the design without expensive re-optimization. Here, the general topic of optimum sensitivity is discussed, available methods identified, examples given, and the difficulties encountered in calculating this information in nonlinear constrained optimization are identified

TIDY, a complete code for renumbering and editing FORTRAN source programs. User's manual for IBM 360/67

TIDY, a computer code which edits and renumerates FORTRAN decks which have become difficult to read because of many patches and revisions, is described. The old program is reorganized so that statement numbers are added sequentially, and extraneous FORTRAN statements are deleted. General instructions for using TIDY on the IBM 360/67 Tymeshare System, and specific instructions for use on the NASA/AMES IBM 360/67 TSS system are included as well as specific instructions on how to run TIDY in conversational and in batch modes. TIDY may be adopted for use on other computers

Recent developments in multilevel optimization

Recent developments in multilevel optimization are briefly reviewed. The general nature of the multilevel design task, the use of approximations to develop and solve the analysis design task, the structure of the formal multidiscipline optimization problem, a simple cantilevered beam which demonstrates the concepts of multilevel design and the basic mathematical details of the optimization task and the system level are among the topics discussed

Optimized laser turrets for minimum phase distortion

An analysis and computer program which optimizes laser turret geometry to obtain minimum phase distortion is described. Phase distortion due to compressible, inviscid flow over small perturbation laser turrets in subsonic or supersonic flow is calculated. The turret shape is determined by a two dimensional Fourier series; in a similar manner, the flow properties are given by a Fourier series. Phase distortion is calcualted for propagation at serveral combinations of elevation and azimuth angles. A sum is formed from the set of values, and this sum becomes the objective function for an optimization computer program. The shape of the turret is varied to provide minimum phase distortion

Structural optimization--past, present, and future

Presented a Paper 81-0897 at the AIAA 1981 Annual Meeting and Technical Display, Long Beach, Calif., May 12-14, 198

Gear optimization

The use of formal numerical optimization methods for the design of gears is investigated. To achieve this, computer codes were developed for the analysis of spur gears and spiral bevel gears. These codes calculate the life, dynamic load, bending strength, surface durability, gear weight and size, and various geometric parameters. It is necessary to calculate all such important responses because they all represent competing requirements in the design process. The codes developed here were written in subroutine form and coupled to the COPES/ADS general purpose optimization program. This code allows the user to define the optimization problem at the time of program execution. Typical design variables include face width, number of teeth and diametral pitch. The user is free to choose any calculated response as the design objective to minimize or maximize and may impose lower and upper bounds on any calculated responses. Typical examples include life maximization with limits on dynamic load, stress, weight, etc. or minimization of weight subject to limits on life, dynamic load, etc. The research codes were written in modular form for easy expansion and so that they could be combined to create a multiple reduction optimization capability in future

An assessment of airfoil design by numerical optimization

A practical procedure for optimum design of aerodynamic shapes is demonstrated. The proposed procedure uses an optimization program based on the method of feasible directions coupled with an analysis program that uses a relaxation solution of the inviscid, transonic, small-disturbance equations. Results are presented for low-drag, nonlifting transonic airfoils. Extension of the method to lifting airfoils, other speed regimes, and to three dimensions if feasible