Optimum design of structures with discrete variables using higher order approximation

Abstract

Some higher order function approximations are introduced during the optimization process with continuous and discrete design variables. Second and third order approximations are presented by employing only the diagonal terms of the matrices of the higher order derivatives. To reduce the computational cost, these derivatives are estimated by using the first order derivatives available from the previous design points. A hybrid form of the second and third order approximations is also presented for function approximation. It is observed that the hybrid form is more effective. To achieve the optimal discrete variables, a new penalty function is introduced. First the continuous optimization is carried out by means of penalty functions and then the results are used as the starting point for discrete optimization. In both the continuous and discrete optimization, the idea of various function approximations is employed to decrease the computation time required by the design process. Examples are solved and the effects of different proposed approximate techniques are discussed.