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SUMMARYA new and powerful mathematical programming method is described, which is capable of solving a broad class of structural optimization problems. The method employs mixed directlreciprocal design variables in order to get conservative, first-order approximations to the objective function and to the constraints. By this approach the primary optimization problem is replaced with a sequence of explicit subproblems. Each subproblem being convex and separable, it can be efficiently solved by using a dual formulation. An attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs. Examples of application to real-life aerospace structures are offered to demonstrate the power and generality of the approach presented. BACKGROUNDIt is now widely recognized that many optimal sizing problems can be accurately approximated by a mathematical programming problem having a simple algebraic structure: linear objective function and separable constraints.'T2 This explicit subproblem is generated by linearizing the behaviour constraints with respect to the reciprocals of the design variables. On the other hand, it is often useful, for fabricational reasons, to link the design variables through linear inequality constraints. Therefore at each stage of the iterative optimization process, the approximate subproblem to be dealt with exhibits the following explicit form:In these expressions the x:s denote the design variables, which correspond to the transverse sizes of the structural members (bar cross-sectional areas, membrane thicknesses). The structural weight (I) is a linear objective function, because the weight coefficients wi are prescribed parameters related to the material mass density and to geometrical quantities (bar lengths, membrane areas).

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SUMMARYThis paper is mainly concerned with a new structural optimization method based upon the concept of duality in convex programming. This rigorous formulation permits justification of many intuitive procedures which are used in the classical optimality criteria approaches. Furthermore, the dual algorithms proposed in this paper do not suffer from the drawbacks inherent to the optimality criteria approach. The selection of the set of active constraints does not introduce any difficulty and is achieved correctly in all cases. The subdivision of the design variables in an active and passive group is intrinsically contained in the dual formulation. The efficiency of the dual algorithms is shown with reference to some problems for which the classical methods do not lead to satisfactory results.