Design of a transversely layered cantilever of minimum mass under specified maximum-deflection constraint

The problem of optimal design of a transversely layered cantilever beam of minimum mass composed of a finite set of elastic homogeneous isotropic materials is considered for the case where a constraint is imposed on the maximum deflection of the beam and information on the loads applied to the beam is incomplete. It is shown that, among these loads, there exists the “worst” point load whose magnitude is equal to the resultant of the forces applied to the beam, for which the deflection is maximal for any material distribution along the beam. The necessary optimality conditions are obtained for the mass-minimization problem of the beam under the “worst” loading, a numerical algorithm is developed for the synthesis of the optimal cantilever, and a numerical example is given.