ICMAMS 2018 First International Conference on Mechanics of Advanced Materials and Structures Turin, 17-20 June 2018 www.icmams.com
A GEOMETRY-BASED METHOD FOR 3D TOPOLOGY OPTIMIZATION G. Costa1, M. Montemurro1,* and J. Pailhès1 1 *
CNRS UMR 5295, I2M, Arts et Métiers ParisTech, Esplanade d’Arts et Métiers, 33405 Talence, France Corresponding author:
[email protected]
This work focuses on an innovative Topology Optimization (TO) strategy to design 3D structures in the framework of the Solid Isotropic Material with Penalization (SIMP) method. The computation domain, wherein the structure is embedded, is described through Finite Elements (FE) and a fictitious density function, defined at the centroids of the mesh elements. Lower and upper bounds of the pseudo-density identify the “void” and “solid” phases, respectively. A penalization of meaningless intermediate densities is employed to provide a well-defined void-material design. Although the standard SIMP method constitutes the basis of TO commercial software (e.g., Altair-OptiStruct), it presents some drawbacks: firstly, the final design is not CAD-compatible; thus, a time-consuming CAD reconstruction phase is necessary. Secondly, the number of design variables, being equal to the number of the underlying elements, could be significant for 3D problems. Finally, suitable filtering techniques must be considered in order to avoid physically meaningless checker-board configurations. The proposed strategy aims at overcoming these issues: the fictitious density field of the SIMP method is described by means of a 4D NURBS hypersurface, i.e., a geometric CADcompatible entity. Therefore, the topology description is now unrelated to the mesh and the NURBS hypersurface constitutes a well-defined geometric parametrization of the computation domain. In this background, the 4D NURBS can be exploited for both the formulation of optimization constraints and the CAD reconstruction phase. The new design variables are the NURBS control points coordinates and weights. Through the proposed approach, the number of design variables can be reduced and a filter zone is implicitly provided thanks to the local support property of the NURBS basis functions. An example of compliance minimization with an equality volume constraint is proposed and a qualitative comparison between the NURBS-based and the standard SIMP method is shown.
Figure 1 Clamped beam example: reference domain
Figure 2 NURBS-based SIMP solution
Figure 3 Altair OptiStruct solution
