Optimal Design for Prestressed Structures Based on Continuous and Discrete Variables

Abstract

The mathematical model of optimal design for prestressed structures is established and a two-level algorithm based on hybrid variables is proposed. At the first level, the prestressed forces are chosen to be the design variables and the optimal design for prestressed forces based on continuous variable is carried out. At the second level, the cross-sectional areas are chosen to be the design variables and the discrete sizing optimization is carried out under fixed prestressed forces, the local constrains are satisfied with one-dimensional search algorithm, the integral constrains are satisfied with the relative difference quotient algorithm, and the efficiency of the relative difference quotient algorithm is greatly improved by introducing the assumption of statically determinant structures. The numerical example shows the correctness and effectiveness of the method.