Towards adaptive topology optimization

A new approach to adaptive topology optimization.A higher resolution in the description of the optimal shape.The approach proposed requires revisiting density and sensitivity filtering.Applied to the optimization of 3D parts and structures. This paper presents a new fully-automated adaptation strategy for structural topology optimization (TO) methods. In this work, TO is based on the SIMP method on unstructured tetrahedral meshes. The SIMP density gradient is used to locate solid-void interface and h-adaptation is applied for a better definition of this interface and, at the same time, de-refinement is performed to coarsen the mesh in fully solid and void regions. Since the mesh is no longer uniform after such an adaptation, classical filtering techniques have to be revisited to ensure mesh-independency and checkerboard-free designs. Using this adaptive scheme improves the objective function minimization and leads to a higher resolution in the description of the optimal shape boundary (solid-void interface) at a lower computational cost. This paper combines a 3D implementation of the SIMP method for unstructured tetrahedral meshes with an original mesh adaptation strategy. The approach is validated on several examples to illustrate its effectiveness.

[1]  Les A. Piegl,et al.  A Knowledge-Guided Approach to Line NURBS Curve Intersection , 2014 .

[2]  Jiawei Xiang,et al.  Structural Topology Optimization Based on the Level SetMethod Using COMSOL , 2014 .

[3]  Adedeji Aremu,et al.  A Hybrid Algorithm for Topology Optimization of Additive Manufactured Structures , 2011 .

[4]  Shutian Liu,et al.  Topology optimization of beam cross-section considering warping deformation , 2008 .

[5]  Jean-Christophe Cuillière,et al.  Automatic mesh generation and transformation for topology optimization methods , 2013, Comput. Aided Des..

[6]  Ramana V. Grandhi,et al.  A survey of structural and multidisciplinary continuum topology optimization: post 2000 , 2014 .

[7]  Feifei Li,et al.  Adaptive mesh method for topology optimization of fluid flow , 2015, Appl. Math. Lett..

[8]  C.-Y. Lin,et al.  A two-stage approach for structural topology optimization , 1999 .

[9]  Ashraf El-Hamalawi,et al.  Mesh Generation – Application to Finite Elements , 2001 .

[10]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[11]  J. Korvink,et al.  Adaptive moving mesh level set method for structure topology optimization , 2008 .

[12]  Kuo-Young Cheng,et al.  A direction-oriented sharpness dependent filter for 3D polygon meshes , 2008, Comput. Graph..

[13]  M. Bruggi,et al.  A fully adaptive topology optimization algorithm with goal-oriented error control , 2011 .

[14]  N. Kikuchi,et al.  A homogenization method for shape and topology optimization , 1991 .

[15]  T. E. Bruns,et al.  A reevaluation of the SIMP method with filtering and an alternative formulation for solid–void topology optimization , 2005 .

[16]  M. Zhou,et al.  Recent Developments in the Commercial Implementation of Topology Optimization , 2006 .

[17]  Glaucio H. Paulino,et al.  Dynamic Adaptive Mesh Refinement for Topology Optimization , 2010, ArXiv.

[18]  Yi Min Xie,et al.  Evolutionary structural optimisation (ESO) using a bidirectional algorithm , 1998 .

[19]  Z. Kang,et al.  An adaptive refinement approach for topology optimization based on separated density field description , 2013 .

[20]  Ekkehard Ramm,et al.  ADAPTIVE TOPOLOGY AND SHAPE OPTIMIZATION , 1998 .

[21]  Yoon Young Kim,et al.  Integrated topology and shape optimization software for compliant MEMS mechanism design , 2008, Adv. Eng. Softw..

[22]  Marcelo Krajnc Alves,et al.  Layout optimization with h‐adaptivity of structures , 2003 .

[23]  Martin P. Bendsøe,et al.  Optimization of Structural Topology, Shape, And Material , 1995 .

[24]  R. Stainko.  An adaptive multilevel approach to the minimal compliance problem in topology optimization , 2005 .

[25]  Zhan Kang,et al.  Adaptive topology optimization with independent error control for separated displacement and density fields , 2014 .

[26]  Eric de Sturler,et al.  Topology optimization with adaptive mesh refinement , 2008 .

[27]  Maurizio Muzzupappa,et al.  Integrated Computer-Aided Innovation: The PROSIT approach , 2009, Comput. Ind..

[28]  Zhan Kang,et al.  A topology optimization method for geometrically nonlinear structures with meshless analysis and independent density field interpolation , 2014 .

[29]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[30]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[31]  Jean-Christophe Cuillière,et al.  Integration of CAD, FEA and Topology Optimization through a Unified Topological Model , 2014 .

[32]  Raphael Fleury,et al.  Topology Optimization-Practical Aspects for Industrial Applications , 2011 .

[33]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[34]  Mei Yulin,et al.  A level set method for structural topology optimization and its applications , 2004 .

[35]  Yi Min Xie,et al.  A simple and compact Python code for complex 3D topology optimization , 2015, Adv. Eng. Softw..

[36]  Grégoire Allaire,et al.  The homogenization method for topology and shape optimization. Single and multiple loads case , 1996 .

[37]  A. Clausen.  Topology Optimization for Additive Manufacturing , 2016 .

[38]  E. Ramm,et al.  Adaptive topology optimization , 1995 .

[39]  G. Allaire,et al.  THE HOMOGENIZATION METHOD FOR TOPOLOGY AND SHAPE OPTIMIZATION , 1997 .

[40]  J. Remacle,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[41]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[42]  Jiawei Xiang,et al.  Structural Topology Optimization Based on the Level Set Method Using COMSOL , 2014 .

[43]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[44]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[45]  Jean-Christophe Cuillière,et al.  Towards the Integration of Topology Optimization into the CAD Process , 2014 .