Design of trusses under uncertain loads using convex models

The optimal design of trusses subjected to loads considered to be uncertain in both magnitude and direction is investigated. A non-probabilistic ellipsoidal convex model is established for considering the uncertainties using three different criteria. The convex model is described as a set of constraints on the upper and lower limits of the load magnitudes and directions. The optimal design of the trusses is performed using two different optimization objectives. The first objective function to be minimized is the structural volume; constraints are imposed on the stresses and buckling loads of the members and on the joint displacements. Another objective function to be minimized is a selected displacement; constraints are implemented on the stresses and buckling loads of the members and on the structural volume. The presented method yields optimal designs that violate stress, displacement, and buckling constraints with less frequency than the assumed worst load condition. This method offers an alternative to formal probabilistic methods.