Topological sensitivity to diagonal member flips of two-layered statically determinate trusses under worst loading

The paper deals with the topological sensitivity of free, unsupported, statically determinate plane trusses whose horizontal and vertical members form two horizontal layers of square cells and two or more vertical layers. The topology of a truss is decomposed into a form vector – the placement of cells containing diagonal members – and a binary vector describing the slopes of the diagonals. The construction of complete form and slope spaces is provided for any number of vertical layers. Using exhaustive search, forms with minimum and maximum sensitivity to slope change are found for trusses with 2 × 2 through 2 × 8 layers under worst static load condition, represented by the lowest eigenvalue of the least-squares equilibrium matrix. Typical features of the least and most sensitive forms and associated loads and internal forces are shown. Changes of absolute and relative topological sensitivities with increasing number of vertical layers are discussed.