On the structural optimization for space applications using the min-max technique

Abstract

Optimization plays a very important role in space applications since mass and structural flexibility are critical requirements for space missions, i.e., the structure should be as lightweight and stiff as possible. As a contribution to this area this paper investigates compliance optimization of structures under multiple load cases. The problem can be solved through a multi-criterion optimization where the load cases associated with each and every loading configuration are treated as components of multi-objective function vector. However, numerical evaluation is not an easy task because it sometimes involves a very intensive computational effort. Alternatively, the multi-objective optimization problem can be re-formulated using a min-max strategy that does not require simultaneous consideration of all the load cases as components of multi-objective function vector. Instead, this formulation shows that, for compliance optimization purposes, it is sufficient to consider only those loads, which define the convex hull of the applicable load set, i.e., the selected set of loads which will effectively lead to the optimum design. Through the min-max formulation the number of load cases involved in the design procedure is drastically reduced. The efficiency of the proposed technique is illustrated by one example consisting of a variable thickness beam subjected to uncertain loadings.