Topology and Sizing Optimization for Frame Structures with a Two-Level Approximation Method

Abstract

This paper discusses the integrated topology and sizing optimization of frame structures where beam elements are used in the structural analysis model. Based on the ground structure approach, discrete variables (0, 1) representing the absence or presence of beam members and continuous sizing variables for beam cross sections are involved in the problem. A two-level multipoint approximation strategy is introduced to address this mixed-variable problem. A first-level approximate problem is first constructed using the branched multipoint approximate function involving both discrete and continuous variables. For solving this problem, discrete variables are optimized through a genetic algorithm, and when calculating the fitness in the genetic algorithm, a second-level approximate problem solved by the dual method is established to optimize the cross sections for the retained beam members. Temporal deletion techniques are used for displacement and stress constraints. Meanwhile, by considering local vibration modes in frequency-constrained problems, material density is assigned with an extremely small value for the removed beams to avoid these local modes. Thence, the singularities encountered in stress, displacement, and frequency constraints are overcome. Typical examples and a satellite application are given to verify the feasibility and efficiency of this method in handling the integrated topology and sizing optimization for frame structures.