On the optimal layout of multi-purpose trusses

Abstract This paper provides a solution to the problem of minimum mass design of multi-purpose trusses for which the design variables are not only the areas of the bars but also the positions of the joints. Displacement constraints and non-constant stress constraints (stability) are taken into account. With multiple loading systems, the optimal structure is normally statically indeterminate and generally not even ·fully stressed”. The solution is obtained by successive iterations, using a gradient method with move-limits. For each iteration only the critical forces and displacements are considered and trusses with up to 40 joints have been optimized. Analytical expressions are derived for the necessary gradients, i.e. for the partial derivatives of the displacements and forces with respect to the bar areas and joint coordinates.