A new method of discrete optimization for cross-section selection of truss structures

Abstract

The main goal of this article is to develop a new method of discrete optimization for cross-section selection of truss structures. First, it introduces a parameterized description of discrete cross-section areas in an admissible list, which is an ordered list of manufacturing available cross-section areas (i.e. the ‘available list’ of cross-section areas) and constructs a discrete optimization model for truss structures. Secondly, the generalized shape function-based parameterization (GSFP) method is proposed to transform discrete variables obtained previously into continuous ones, thus transforming the discrete optimization problem into a continuous optimization problem which can be readily solved with gradient-based methods. Thirdly, by comparing the influences of different admissible lists formed with elements of the same available list, on the convergences of the optimization process, an ordering rule is proposed to determine the order of elements in the admissible list. Lastly, the proposed method is applied to several benchmark design examples, generating results with similar or improved accuracy compared to those from heuristic methods, showing significantly improved computational efficiency. The method is shown to be accurate and efficient, which would prove especially beneficial to large-scale problems.

Keywords:

• discrete optimization design
• truss structures
• discrete variables
• topology optimization
• multi-material topology optimization
• GSFP