Structural Synthesis for the Worst Case Mitigation Based on the Convex Set of Uncertainty

Abstract

A non-probabilistic methodology is presented for the design to enhance structural integrity against the uncertainty in structural parameters. The uncertainty is represented by a convex set of uncertainty variables, in which the fluctuation of uncertainty variables is bounded within a convex hull given as a hyperellipse without consideration of the probability distribution inside. The worst case is determined in terms of unfavorable index defined so as to indicate the degree of harmfulness for the structural integrity. Use is made of the finite element sensitivity analysis and the Lagrange multiplier method for the search of the nucertainty variables to raise the worst case. The worst unfavorable index thus identified is mitigated less than the tolerance limit in line with the structural synthesis based on the first-order approximation of the worst unfavorable index with respect to design variables. The validity of the proposed formulation is investigated through the numerical example concerning with a three-storied portal frame with three braces.