Analytical Treatment of Some Extended Problems in Structural Optimization,Part I

ABSTRACT

Optimization problems involving supports of unspecified location as well as variable external actions and reactions of nonzero cost are discussed in the context of both plastic and elastic beams and frames, of non-preassigned, partially preassigned, and preassigned cost distribution, and of strength or deflection constraints.

The static-kinematic optimality criteria for various classes of problems are illustrated with simple examples and the results are checked by an independent method, i.e., by differentiation of the total cost with respect to the unknown variables. It is shown that for certain classes of problems the conditions introduced reduce to existing criteria by Prager and Masur.