6 th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems June 22–25, 2010, Kyoto, Japan A Level Set Based Method for the Optimization of Cast Part Qi XIA 1 , Tielin SHI 1 , Shiyuan LIU 1 and Michael Yu WANG 2 1 Huazhong University of Science and Technology, Wuhan, China 2 The Chinese University of Hong Kong, Shatin, NT, Hong Kong qxia@mail.hust.edu.cn , tlshi@mail.hust.edu.cn, shyliu@mail.hust.edu.cn, yuwang@mae.cuhk.edu.hk Abstract A cast part is formed via casting process in which molten liquid is poured into and solidifies in a cavity enclosed by molds. Then, one obtains the cast part when the molds are removed. An important issue in the casting process is that a cast part should have a proper geometry so that the molds can actually be removed. Accordingly, in the optimization of a cast part one not only needs to optimize the performance of the cast part but also needs to ensure the cast part have a proper geometry. With these goals, a level set based method is proposed for the optimization of cast part. A molding condition and a performance condition on the design velocity are derived for the optimization. Numerical examples are provided. Keywords: structure optimization, level set, cast part, molding constraint 1. Introduction Optimization is an effective tool for obtaining high performance structures. While the performance of a structure can be improved via the optimization, another aspect in the design of a structure – manufacturing – also needs to be carefully treated. Specifically, a structure should be designed in a way that it can be easily manufactured via intended techniques. A cast part considered in this paper is a structure intended to be manufactured via casting process. In the casting process molten liquid is poured into and solidifies in a cavity enclosed by molds, and one obtains the cast part when the molds are removed. An important issue in the casting process is that a cast part should have a proper geometry so that the molds can be removed, or the so-called molding constraint can be satisfied. Therefore, the optimization of a cast part should not only optimize the performance of the cast part but also should ensure the cast part have a proper geometry. Much effort has been made for incorporating the molding constraint of casting process into structure optimization, in particular the topology optimization. TopShape, a program developed at the International Development Center of Adam Opel and based on CAO (Computer Aided Optimization) and SKO (Soft Kill Option), is the first program that success- fully incorporated the molding constraint of casting process into topology optimization [1,2]. Several topology control algorithms (connectivity control, growth direction control, thickness control, et al.) were introduced in the TopShape. Based on the SIMP (Solid Isotropic Microstructure with Penalization) method [3], Zhou et al. proposed a mathematical formulation of the molding constraint that constraints the material densities in the lower positions to be bigger than those in the upper positions [4]. This approach is available in OptiStruct (Altair Engineering, Inc. 2002). Leiva et al. proposed a novel design parametrization that explicitly incorporates growth direction into its design variables for the topology optimization of cast part [5,6] and implemented it in GENESIS [7]. We propose a level set based method [8-10] for the optimization of cast parts by which both the performance of the cast parts and the molding constraint are addressed. 2. A brief introduction to casting process In our present study, we consider the casting process that uses two molds (the two molds are removed in opposite di- rections). As aforementioned, an important issue in the casting process is that a cast part should have a proper geometry so that the molds can be removed, or the so-called molding constraint can be satisfied. Examples of the cases where the molds can be and cannot be removed are given in Fig. 1(a) and Fig. 1(b), respectively. In Fig. 1(b), the lower mold is stuck by a slot called undercut and cannot be removed in the given direction. The direction in which a mold is removed is called the parting direction, and the surface where the two molds contact each other is called the parting surface. We observe that with the casting process described above a cast part should not have any undercut as shown in the Fig. 1(b). Besides, another requirement on a cast part is that the cast part should not have any interior void, i.e., a region completely contained in the interior of a solid, since such interior void cannot be manufactured by casting process. Therefore, we have the following conclusion: with the casting process considered in the present study a cast part is required to have no undercut and no interior void.