ON A GAME APPROACH TO OPTIMAL STRUCTURAL DESIGN

A game problem of structural design is formulated as a problem of playing against external circumstances. The compliance plays the role of the pay-off function. Two players - the designer and nature - try to respectively minimize or maximize it, possessing limited resources. Discrete and continual optimization problems are considered. It is proved that the essential game characteristic, the upper game value, is expressed in terms of the minimal eigenvalue of the inverse operator of the system (continual case), or the response matrix (discrete case). For a special case of convex game, this eigenvalue is equal to the value of the game, and the optimal strategies of the designer and nature are uniquely determined.