Compliance minimization of structures under uncertain loadings

Abstract

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 a multi-objective function vector. Alternatively, the multi-objective optimization problem can be re-formulated using a minimax strategy that does not require simultaneous consideration of all the load cases as components of a multi-objective function vector. Instead, it is shown that, for compliance optimization purposes, it is sufficient to consider only those loads which define the convex hull of the applicable load set, thereby drastically reducing the number of load cases involved in the design procedure. The efficiency of the technique proposed is illustrated through two examples consisting of variable thickness beams and plates subjected to uncertain loadings.

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