Topology Optimization using the Level Set and eXtended Finite Element Methods: Theory and Applications
As the capabilities of additive manufactur1 ing techniques increase, topology optimization provides 2 a promising approach to design geometrically sophisti3 cated structures which can be directly manufactured. 4 Traditional topology optimization methods aim at find5 ing the conceptual design but often lack a sufficient res6 olution of the geometry and structural response, needed 7 to directly use the optimized design for manufacturing. 8 To overcome these limitations, this paper studies the 9 viability and characteristics of the eXtended Finite El10 ement Method (XFEM) in combination with the Level11 Set Method (LSM) for topology optimization of three 12 dimensional structural design problems. The LSM de13 scribes the geometry by defining the nodal level set 14 values via explicit functions of the optimization vari15 ables. The structural response is predicted by a gener16 alized version of the XFEM. The LSM XFEM approach 17 is compared against results from a traditional Solid 18 Isotropic Material with Penalization (SIMP) method 19 for two phase "solid void" and "solid solid" problems. 20 The numerical results demonstrate that the LSM XFEM 21 approach can describe crisply the geometry and predict 22 the structural response of complex three dimensional 23 structures with acceptable accuracy even on coarse meshes. 24 However, the LSM XFEM studied here lacks a robust 25 C. H. Villanueva Department of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO 427 UCB, USA e mail: carlos.villanueva@colorado.edu K. Maute Department of Aerospace Engineering, University of Colorado at Boulder, Boulder, CO 427 UCB, USA e mail: maute@colorado.edu and intuitive formulation to control the minimum fea26 ture size, and the optimization results may depend on 27 the initial design. 28