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

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

ADS: A FORTRAN program for automated design synthesis, version 1.00

A new general-purpose optimization program for engineering design is described. ADS-1 (Automated Design Synthesis - Version 1) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels, being strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired. The program is demonstrated with a simple structural design example

Approximation concepts for numerical airfoil optimization

An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems

COMMAND: A FORTRAN program for simplified composite analysis and design

A FORTRAN program is presented for preliminary analysis and design of multilayered composite panels subjected to inplane loads. All plys are of the same material. The composite is assumed symmetric about the midplane, but need not be balanced. Failure criterion includes limit ply strains and lower bounds on composite inplane stiffnesses. Multiple load conditions are considered. The required input data is defined and examples are provided to aid the use in making the program operational. Average panel design times are two seconds on an IBM 360/67 computer. Results are compared with published literature. A complete FORTRAN listing of program COMAND is provided. In addition, the optimization program CONMIN is required for design

ADS: A FORTRAN program for automated design synthesis: Version 1.10

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis - Version 1.10) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels: strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples, and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired