A method for shape and topology optimization of truss-like structure
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RESEARCH PAPER
A method for shape and topology optimization of truss-like structure Qi Xia · Michael Yu Wang · Tielin Shi
Received: 17 February 2012 / Revised: 20 July 2012 / Accepted: 15 August 2012 / Published online: 25 September 2012 c Springer-Verlag 2012
Abstract We present a method for the shape and topology optimization of truss-like structure. First, an initial design of a truss-like structure is constructed by a mesh generator of the finite element method because a truss-like structure can be described by a finite element mesh. Then, the shape and topology of the initial structure is optimized. In order to ensure a truss-like structure can be easily manufactured via intended techniques, we assume the beams have the same size of cross-section, and a method based on the concept of the SIMP method is used for the topology optimization. In addition, in order to prevent intersection of beams and zerolength beams, a geometric constraint based on the signed area of triangle is introduced to the shape optimization. The optimization method is verified by several 2D examples. Influence on compliance of the representative length of beams is investigated. Keywords Truss-like structure · Shape optimization · Topology optimization
1 Introduction A truss-like structure is a structure that has porous trusslike internal morphology. It has low mass, high stiffness, and high strength (Wicks and Hutchinson 2001; Chiras et al. Q. Xia · T. Shi (B) The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China e-mail: [email protected] M. Y. Wang Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
2002; Deshpande et al. 2001; Wallach and Gibson 2001). It is also multi-functional because the porosity facilitates thermal management, energy absorption, mass transportation, etc. A truss-like structure can be manufactured by novel additive manufacturing technologies, such as the investment casting (Chiras et al. 2002), the metal weaving (Sypeck and Wadley 2001), and the layer-based additive manufacturing (Dutta et al. 2001). However, a fundamental issue that remains to be solved is how to design a truss-like structure so that the potential of mass reduction and performance improvements can be fully exploit. Optimization is an effective tool for obtaining efficient structures, and it has been applied in the design of trusslike structures and more generally the cellular material and structures (Takano and Zako 2000; Rodrigues et al. 2002; Wang and Cheng 2005; Zhang and Sun 2006; Liu et al. 2008; Coelho et al. 2008; Su and Liu 2010). Usually, a cell based approach is employed for such design optimization. The admissible space domain for a structure is partitioned into many cells. Then, structure primitives in the cells are optimized. When the structure primitive is periodic in the space domain and its size is far smaller than that of the structure, it is considered as a material micro-structure,
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