Structural topology optimization considering connectivity constraint

Topology optimization has been regarded as a powerful design approach for determining optimal topology of a structure to obtain desired functional performances within a defined design domain. Considering manufacturing process constraints in topology optimization becomes increasingly important due to its potential practical applications. In this paper, we propose a novel topology optimization model with manufacturing process related connectivity constraints. A generalized method, named as virtual scalar field method (VSFM), is developed for describing and enforcing desired connectivity constraint. As an illustrative example, the connectivity constraint can be converted to an equivalent maximum temperature constraint when temperature is chosen as the scalar field. The temperature constraint is then easily integrated and implemented in routine topology optimization. The simply-connected constraint, which excludes interior closed cavities and is representative of many advanced manufacturing techniques, e.g. additive manufacturing (AM) or casting, is used as an example to demonstrate the key ideas and the efficiency of the VSF method. Some numerical examples, which consider the connectivity constraint in topology optimization, are presented to show the validity of this method.

[1]  S. Myers,et al.  Connections between differential geometry and topology. I. Simply connected surfaces , 1935 .

[2]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[3]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[4]  Ming-Chuan Leu,et al.  Progress in Additive Manufacturing and Rapid Prototyping , 1998 .

[5]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[6]  I Zein,et al.  Mechanical properties and cell cultural response of polycaprolactone scaffolds designed and fabricated via fused deposition modeling. , 2001, Journal of biomedical materials research.

[7]  Thomas A. Poulsen.  A new scheme for imposing a minimum length scale in topology optimization , 2003 .

[8]  Jirí Matousek,et al.  Separating an object from its cast , 2002, Comput. Aided Des..

[9]  I. Zein,et al.  Fused deposition modeling of novel scaffold architectures for tissue engineering applications. , 2002, Biomaterials.

[10]  M. Zhou,et al.  PROGRESS IN TOPOLOGY OPTIMIZATION WITH MANUFACTURING CONSTRAINTS , 2002 .

[11]  James K. Guest,et al.  Achieving minimum length scale in topology optimization using nodal design variables and projection functions , 2004 .

[12]  L. Froyen,et al.  Binding Mechanisms in Selective Laser Sintering and Selective Laser Melting , 2004 .

[13]  Lothar Harzheim,et al.  A review of optimization of cast parts using topology optimization , 2005 .

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

[15]  Niels Leergaard Pedersen,et al.  Analytical optimal designs for long and short statically determinate beam structures , 2009 .

[16]  Michael Yu Wang,et al.  Shape feature control in structural topology optimization , 2008, Comput. Aided Des..

[17]  M. Wang,et al.  A new level set method for systematic design of hinge-free compliant mechanisms , 2008 .

[18]  F. Navarrina,et al.  Topology optimization of continuum structures with local and global stress constraints , 2009 .

[19]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

[20]  James K. Guest,et al.  Topology optimization with multiple phase projection , 2009 .

[21]  Ole Sigmund,et al.  Manufacturing tolerant topology optimization , 2009 .

[22]  David W. Rosen,et al.  Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing , 2009 .

[23]  James K. Guest,et al.  Imposing maximum length scale in topology optimization , 2009 .

[24]  Stephen Reay,et al.  Tools for Sustainable Product Design: Additive Manufacturing , 2010 .

[25]  Qi Xia,et al.  A level set based method for the optimization of cast part , 2010 .

[26]  O. Sigmund,et al.  Robust topology optimization accounting for spatially varying manufacturing errors , 2011 .

[27]  Ole Sigmund,et al.  On projection methods, convergence and robust formulations in topology optimization , 2011, Structural and Multidisciplinary Optimization.

[28]  Casper Schousboe Andreasen,et al.  An explicit parameterization for casting constraints in gradient driven topology optimization , 2011 .

[29]  Yonghua Chen,et al.  Manufacturable mechanical part design with constrained topology optimization , 2012 .

[30]  L. Murr,et al.  Metal Fabrication by Additive Manufacturing Using Laser and Electron Beam Melting Technologies , 2012 .

[31]  R. Poprawe,et al.  Laser additive manufacturing of metallic components: materials, processes and mechanisms , 2012 .

[32]  Z. Kang,et al.  An enhanced aggregation method for topology optimization with local stress constraints , 2013 .

[33]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[34]  Robert J. Strong,et al.  A review of melt extrusion additive manufacturing processes: I. Process design and modeling , 2014 .

[35]  Xu Guo,et al.  Explicit feature control in structural topology optimization via level set method , 2014 .

[36]  Xu Guo,et al.  An explicit length scale control approach in SIMP-based topology optimization , 2014 .

[37]  Martin Leary,et al.  Optimal topology for additive manufacture: A method for enabling additive manufacture of support-free optimal structures , 2014 .

[38]  Albert C. To,et al.  Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation , 2015 .

[39]  G. Cheng,et al.  An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures , 2015 .

[40]  Liang Gao,et al.  A level set method for topological shape optimization of 3D structures with extrusion constraints , 2015 .

[41]  Rui Hu,et al.  H-DGTP—a Heaviside-function based directional growth topology parameterization for design optimization of stiffener layout and height of thin-walled structures , 2015 .

[42]  T. Shi,et al.  Constraints of distance from boundary to skeleton: For the control of length scale in level set based structural topology optimization , 2015 .

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

[44]  Glaucio H. Paulino,et al.  Bridging topology optimization and additive manufacturing , 2015, Structural and Multidisciplinary Optimization.