Optimal design of structures 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. 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 truss is performed using as objective the minimization of the structural volume. Constraints are imposed on the stresses and buckling loads of the members and the joint displacements. The present method yields an optimal design which is superior in terms of constraint violations when compared to the optimal design obtained from an assumed worst loading condition.