Generalization of dual structural optimization problems in terms of fractional programming

Abstract

Summary.Duality now plays an important role in the theory of optimum structures but has not been given adequate detailed consideration within this context. The paper makes a limited attempt to satisfy this requirement through a generalization of the associated duality theory by formulating the structural optimization as a fractional program. This provides some new forms for the dual objective function and crystalizes some of the intrinsic problems associated with dual structural programs. Introduction.Duality theory has played an important role in the development of structural optimization theory and the associated computer-based solution algorithms. Normally the problems examined have centered on the minimum-weight design of structures subject to a variety of behavioral constraints which are of practical importance in the fabrication of aerospace structures.Early applications of the theory [1] show that certain formulations may be conveniently described in terms of the standard duality theory of linear programming. Unfortunately, many problems do not fit into this category and recent efforts have been devoted to the use of the more complex nonlinear duality theory. An early and somewhat straightforward application was to check the validity of the popular stress-ratioing method and to providing a corrective strategy when the method converges towards non-optimal solutions [2]. Recently Templeman [3] has attempted a more comprehensive exploitation of the dual problem to provide a rapidly convergent algorithm for the optimum design of general pin-

Solution of structural optimization problems by piecewise linearization

“…However, as stated e.g. by Morris in [1], they can frequently be cast in a form where both the objective function and the constraints are fractions of polynomials in the design variables. Such problems can readily be piecewise linearized, and a global optimum can be found through mixed integer programming.…”