Constraints of distance from boundary to skeleton: For the control of length scale in level set based structural topology optimization

[1]  H. Blum Biological shape and visual science (part I) , 1973 .

[2]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

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

[4]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .

[5]  G. Allaire,et al.  Optimal design for minimum weight and compliance in plane stress using extremal microstructures , 1993 .

[6]  C. S. Jog,et al.  A new approach to variable-topology shape design using a constraint on perimeter , 1996 .

[7]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

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

[9]  G. Allaire,et al.  Shape optimization by the homogenization method , 1997 .

[10]  N. Olhoff,et al.  Topology optimization of three-dimensional structures using optimum microstructures , 1998 .

[11]  J. Petersson,et al.  Slope constrained topology optimization , 1998 .

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

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

[14]  J. Petersson Some convergence results in perimeter-controlled topology optimization , 1999 .

[15]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[16]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[17]  J. Sethian,et al.  Structural Boundary Design via Level Set and Immersed Interface Methods , 2000 .

[18]  S. Osher,et al.  Level Set Methods for Optimization Problems Involving Geometry and Constraints I. Frequencies of a T , 2001 .

[19]  J. Sethian Evolution, implementation, and application of level set and fast marching methods for advancing fronts , 2001 .

[20]  M. Zhou,et al.  Checkerboard and minimum member size control in topology optimization , 2001 .

[21]  B. Bourdin Filters in topology optimization , 2001 .

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

[23]  G. Rozvany Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics , 2001 .

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

[25]  G. Allaire,et al.  A level-set method for shape optimization , 2002 .

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

[27]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[28]  Han Ding,et al.  Nonlinear diffusions in topology optimization , 2004 .

[29]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

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

[31]  Michael Yu Wang,et al.  PDE-Driven Level Sets, Shape Sensitivity and Curvature Flow for Structural Topology Optimization , 2004 .

[32]  Shengyin Wang,et al.  Bilateral filtering for structural topology optimization , 2005 .

[33]  K. Abdel-Malek,et al.  Compliant mechanism design using multi-objective topology optimization scheme of continuum structures , 2005 .

[34]  O. Sigmund,et al.  Topology optimization using a mixed formulation: An alternative way to solve pressure load problems , 2007 .

[35]  M. Wang,et al.  Topology optimization of thermoelastic structures using level set method , 2008 .

[36]  Aykut Erdem,et al.  Disconnected Skeleton: Shape at Its Absolute Scale , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

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

[39]  Horea T. Ilies,et al.  Distance functions and skeletal representations of rigid and non-rigid planar shapes , 2009, Comput. Aided Des..

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

[41]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[42]  T. Shi,et al.  A level set solution to the stress-based structural shape and topology optimization , 2012 .

[43]  W. Gao,et al.  Topology optimization of structures using meshless density variable approximants , 2013 .

[44]  T. Shi,et al.  A move limit strategy for level set based structural optimization , 2013 .

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

[46]  Nianfeng Wang,et al.  Topology optimization of hinge-free compliant mechanisms using level set methods , 2014 .

[47]  G. Michailidis Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method , 2014 .

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

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

[50]  T. Shi,et al.  A level set method for shape and topology optimization of both structure and support of continuum structures , 2014 .

[51]  T. Shi,et al.  Topology optimization with pressure load through a level set method , 2015 .

[52]  Xu Guo,et al.  Explicit layout control in optimal design of structural systems with multiple embedding components , 2015 .

[53]  G. Allaire,et al.  Thickness control in structural optimization via a level set method , 2016, Structural and Multidisciplinary Optimization.