Layout optimization of long-span structures subject to self-weight and multiple load-cases

Layout optimization provides a powerful means of identifying materially efficient structures. It has the potential to be particularly valuable when long-span structures are involved, since self-weight represents a significant proportion of the overall loading. However, previously proposed numerical layout optimization methods neglect or make non-conservative approximations in their modelling of self-weight and/or multiple load-cases. Combining these effects presents challenges that are not encountered when they are considered separately. In this paper, three formulations are presented to address this. One formulation makes use of equal stress catenary elements, whilst the other two make use of elements with bending resistance. Strengths and weaknesses of each formulation are discussed. Finally, an approach that combines formulations is proposed to more closely model real-world behaviour and to reduce computational expense. The efficacy of this approach is demonstrated through application to a number of 2D- and 3D-structural design problems.