Ck. Neto et E. Polak, ON THE USE OF CONSISTENT APPROXIMATIONS FOR THE OPTIMAL-DESIGN OF BEAMS, SIAM journal on control and optimization, 34(6), 1996, pp. 1891-1913
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.