Optimum design of structures with discrete variables using approximation concepts

A third order approximation method is developed for structural optimization with both continuous and discrete design variables. Only the diagonal terms of the matrices of the second and third order derivatives are retained. To reduce the cost of computational work involved in the optimization process, the second and third order derivatives are evaluated by employing only the first order derivatives. The information of the previous two design points is used to establish the approximate functions. With the help of this approximation, the continuous optimization is obtained. The results are used as the starting point for the discrete optimization. A new penalty function is introduced for discrete optimum design and the discrete variables are obtained in conjunction with the same function approximation. Examples are given and the numerical results are discussed.