Optimal Structure Design by Dynamic Programming

The lower bound theorem of plastic theory offers a direct procedure for structural design: any equilibrium distribution of stress (or force, or bending moment) gives an admissible design if the structure is so proportioned that it is then everywhere at or below yield. A cost can be assigned to each element of the structure, and the total cost is the sum of these costs. The optimal structure is the cheapest of all admissible designs, and is associated with the optimal equilibrium stress distribution. Herein dynamic programming is applied to the problem of locating this optimal stress distribution, and thence the optimal design. An application to the optimal design of a continuous beam is described in detail. It turns out that realistic cost functions can be introduced without difficulty, taking account of nonlinearity, fabrication cost and limited section availability. Extensions of the technique to more complex structures are discussed, and illustrated by the design of a multistory single-bay frame.