Keywords: topology optimization, truss structure, automated structural design process, three-dimensional thinning, automated node search, material usage ratio.

An integrated truss design methodology based on homogenization-based topology optimization is proposed. After performing continuum topology optimization to obtain the optimal structural configuration, in the case that the percentage usage of the materials is low, the methodology can automatically proceed to the truss optimization based on the model, and achieve the optimum truss structure meeting the constraints. The three-dimensional continuum topology obtained from the homogenization-based topology optimization will be automatically converted to the truss model by using the unique node and bar detection techniques, and then the truss optimization can be autonomously executed so as to obtain the optimal truss design meeting all constraints.

When converting the optimal configuration, which is the result from the topology optimization, to a truss model the challenge is to identify the nodes and bar members that form a truss from the continuum structure in an automated manner. Using image processing techniques, the method is to thin a two-dimensional topology is well established. One of the most commonly adopted one would be the Zhang-Suen algorithm [1]. As for the thinning of the three-dimensional topology, there are also many scholars involved in recent years. Ma et al. [2] proposed a three-dimensional parallel thinning method, defining thirty eight kinds of model for edge elements. Wang et al. [3,4] proposed a series of strategy adjustments for this model, and presented the Wang and Basu refinement method. In addition, this research incorporates the two-dimensional Zhang-Suen based refinement method. The authors, Lin and Chang, present a revised method which is based on the advantages of the Wang and Basu method [3], to combine the advanced three-dimensional refinement, coupled with the automatic node search and the bar connectivity determination technology, which can successfully convert the structural configuration into the a truss structure, serving as the initial structural model for the subsequent truss optimization.

In general, when the material usage of the optimal topology is low, it is closer to the appearance of discrete truss structures compared to continuum structures. This paper presents an integrated approach to convert the optimal topology of continuum structures into a three-dimensional truss topology based on the unique three-dimensional thinning algorithm and node and bar connectivity detection techniques, and then conduct the truss optimization in a fully automated manner. The proposed method is successfully tested in a number of two- and three-dimensional structural engineering optimization problems.

1

S. Zhang, K.S. Fu, "A Thinning Algorithm for Discrete Binary Images", Proceedings of the International Conference on Computer and Application, 879-886, 1984.

2

C.M. Ma, M. Sonka, "A Fully Parallel 3D Thinning Algorithm and Its Applications", Computer Vision and Image Understanding, 64, 420-433, 1996. doi:10.1006/cviu.1996.0069

3

T. Wang, A. Basu, "An Improved Fully Parallel 3D Thinning Algorithm", Department of Computing Science, University of Alberta, Canada, 2005.

4

T. Wang, A. Basu, "A Note on a Fully Parallel 3D Thinning Algorithm and Its Applications", Pattern Recognition Letters, 28, 501-506, 2007. doi:10.1016/j.patrec.2006.09.004

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