Multilevel optimal design of thin-walled continuous beams

Abstract

This paper presents a multilevel approach to the optimal design of continuous thin-walled beams subjected to multiple loading conditions. The structure is assumed to be an assembly of beam elements each of which is completely specified by four independent design variables. The objective is to minimize the volume of the beam subject to behavioral constraints as well as side constraints. The minimization process is carried out in a double scheme where the local minimization of the element design variables is embedded in a global or system minimization. At the system level the design space is spanned over the cross-sectional moments of inertia of the beam elements. The volume associated with a distribution of moments of inertia is obtained by scanning the local design space in a quest for optimal cross-sectional designs. A study of the local design space has enabled the size of the problem at the local level to be reduced to a unidirectional search. The theory is illustrated with examples from the literature, in particular to emphasize the importance of including side constraints on the variables controlling the design of the cross-sections.