Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

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

[2]  Seungjae Min,et al.  A note on hinge‐free topology design using the special triangulation of design elements , 2005 .

[3]  Narsingh Deo,et al.  Graph Theory with Applications to Engineering and Computer Science , 1975, Networks.

[4]  Yoon Young Kim,et al.  Multiscale multiresolution genetic algorithm with a golden sectioned population composition , 2008 .

[5]  Branko Grünbaum,et al.  Tilings and patterns : an introduction , 1990 .

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

[7]  T. Belytschko,et al.  Topology optimization with implicit functions and regularization , 2003 .

[8]  Mary Frecker,et al.  Topological synthesis of compliant mechanisms using multi-criteria optimization , 1997 .

[9]  G. K. Ananthasuresh,et al.  Freeform Skeletal Shape Optimization of Compliant Mechanisms , 2001, Adaptive Structures and Material Systems.

[10]  C. S. Jog,et al.  Stability of finite element models for distributed-parameter optimization and topology design , 1996 .

[11]  Eduardo Alberto Fancello,et al.  Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions , 2006 .

[12]  Randy L. Haupt,et al.  Practical Genetic Algorithms , 1998 .

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

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

[15]  Dongwoo Sheen,et al.  Topology optimization using non‐conforming finite elements: three‐dimensional case , 2005 .

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

[17]  Thomas A. Poulsen.  A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization , 2002 .

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

[19]  G. Allaire,et al.  Minimum stress optimal design with the level set method. , 2008 .

[20]  Martin Burger,et al.  Phase-Field Relaxation of Topology Optimization with Local Stress Constraints , 2006, SIAM J. Control. Optim..

[21]  Niels Olhoff,et al.  Topology optimization of continuum structures: A review* , 2001 .

[22]  I. Y. Kim,et al.  Variable chromosome length genetic algorithm for progressive refinement in topology optimization , 2005 .

[23]  G. K. Ananthasuresh,et al.  On an optimal property of compliant topologies , 2000 .

[24]  G. Allaire,et al.  Topology optimization for minimum stress design with the homogenization method , 2004 .

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

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

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

[28]  Kazuhiro Saitou,et al.  Genetic algorithms as an approach to configuration and topology design , 1994, DAC 1993.

[29]  Mark J. Jakiela,et al.  Generation and Classification of Structural Topologies With Genetic Algorithm Speciation , 1997 .

[30]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[31]  M. Bendsøe,et al.  Topology optimization of continuum structures with local stress constraints , 1998 .

[32]  George I. N. Rozvany,et al.  CO-SIMP: extended SIMP algorithm with direct COrner COntact COntrol , 2005 .

[33]  J. T. Pereira,et al.  Topology optimization of continuum structures with material failure constraints , 2004 .

[34]  A. Saxena,et al.  An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms , 2010 .

[35]  O. Sigmund,et al.  Checkerboard patterns in layout optimization , 1995 .

[36]  Hong Zhou,et al.  Shape and Size Synthesis of Compliant Mechanisms Using Wide Curve Theory , 2006 .

[37]  Dongwoo Sheen,et al.  Checkerboard‐free topology optimization using non‐conforming finite elements , 2003 .

[38]  Antonio André Novotny,et al.  Topological optimization of structures subject to Von Mises stress constraints , 2010 .

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

[40]  Anupam Saxena,et al.  A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization , 2008 .

[41]  M. Jakiela,et al.  Genetic algorithm-based structural topology design with compliance and topology simplification considerations , 1996 .