ON THE USE OF CONSISTENT APPROXIMATIONS FOR THE OPTIMAL-DESIGN OF BEAMS

This paper presents a discretization strategy, based on the concept of consistent approximations, for certain optimal beam design problems, where the beam is modeled using Euler-Bernoulli beam theory. It is sho wn that any accumulation point of the sequence of the stationary point s of the family of resulting approximating problems is a stationary po int of the original, infinite-dimensional problem. The construction of approximating problems requires the development of a relaxation of co nstraints to ensure existence of solutions. The numerical solution of the approximating problems, by means of nonlinear programming algorith ms that are not scale invariant, must be preceded by a change of varia bles to guard against deterioration of performance. The use of such ap proximating problems, in conjunction with a diagonalization strategy, is illustrated by a numerical example.