A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.

Optimization of multi-constrained structures based on optimality criteria

This paper presents an approach to the determination of structural member sizes to provide minimum weight under a number of load conditions consistent with specified limitations on stress and displacement. The procedure amalgamates the disciplines of matrix displacement analysis and operations research into a scheme suitable for automatic digital computation.

A Procedure for Automated Minimum Weight Structural Design: Part I: Theoretical Basis

Optimal composite structures by deflection-variable programming

The fully-stressed design (FSD) appears to be the most widely used approach for sizing of flight structures under strength and minimum-gage constraints Almost all of the experience with FSD has been with structures primarily under mechanical loading as opposed to thermal loading In this method the structural sizes are iterated with the step size, depending on the ratio of the total stress to the allowable stress In this paper, the thermal fully-stressed design (TFSD) procedure developed for problems involving substantial thermal stress is extended to biaxial stress members using a Von Mises failure criterion The TFSD resizing procedure for uniaxial stress is restated and the new procedure for biaxial stress members is developed Results are presented for an application of the two procedures to size a simplified wing structure

Resizing procedure for structures under combined mechanical and thermal loading

This paper describes optimum design techniques for structures where high temperatures are important design considerations. An improved variant of fully stressed design (FSD), denoted thermal fully stressed design (TFSD), is described which converges significantly faster than FSD for problems where thermal stresses are comparable in magnitude to mechanical stresses. Also, an optimali ty criterion is described for sizing structures subjected to temperature constraints. Simultaneous requirements on strength and temperatures are handled by two different techniques: 1) state-of-the-art mathematical programming method and 2) the optimality criterion technique for temperature constraints combined with FSD for strength constraints. Finally, a method is described to optimize the insulation and ply thickness of an insulated composite panel with a time-varying temperature applied to the outer surface of the insulation and a general set of in-plane loads applied to the panel. Temperature and strength constraints are satisfied at a specified number of times. Only a small number of such discrete times are necessary for adequate results for an example contained herein.

Optimum Design of Structures at Elevated Temperatures

: This report presents the development, application, and evaluation of an automated approach to minimum weight structural design. A computer program based on this approach is described, examples are given of the design of truss, frame, and stiffened plate structures, and projections are made of the efforts required in application of the procedure to major airframe components. An approach to the inclusion of instability effects in the design process is developed. Specific recommendations for future developmental work and applications are presented. (Author)

R. H. Gallagher

Papers

Development of a procedure for automated synthesis of minimum weight structures.