Layout optimization of structures with distributed self-weight, lumped masses and frictional supports

The well-known ‘ground structure’-based truss layout optimization method has recently been extended to allow accurate modelling of distributed self-weight. By incorporating equally stressed catenaries in the ground structure, non-conservative errors caused by neglecting bending effects within members carrying their own weight are eliminated. However, in cases where the self-weight of a structure has a favourable role in supporting the applied loads, solutions that include convoluted arrangements of overlapping elements may often be generated. To address this, an enhanced layout optimization formulation is proposed that explicitly allows inclusion of favourable unstressed masses, such as counterweights. Frictional supports are also modelled and the cost of abutments and anchorages taken account of in the formulation. The efficacy of the proposed methodology is demonstrated through application to benchmark examples and to the conceptual design of a simplified long-span bridge structure, considering both ground anchored and self-anchored alternatives.