Stress-constrained topology optimization for compliant mechanism design

This article presents an application of stress-constrained topology optimization to compliant mechanism design. An output displacement maximization formulation is used, together with the SIMP approach and a projection method to ensure convergence to nearly discrete designs. The maximum stress is approximated using a normalized version of the commonly-used p-norm of the effective von Mises stresses. The usual problems associated with topology optimization for compliant mechanism design: one-node and/or intermediate density hinges are alleviated by the stress constraint. However, it is also shown that the stress constraint alone does not ensure mesh-independency.

[1]  Robert F. Cook,et al.  Strength and sharp contact fracture of silicon , 2006 .

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

[3]  Shinji Nishiwaki,et al.  Shape and topology optimization based on the phase field method and sensitivity analysis , 2010, J. Comput. Phys..

[4]  Xianmin Zhang,et al.  A multi-objective method of hinge-free compliant mechanism optimization , 2014 .

[5]  Eduardo Lenz Cardoso,et al.  Design of Compliant Mechanisms with Stress Constraints Using Topology Optimization , 2013 .

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

[7]  James K. Guest,et al.  Eliminating beta-continuation from Heaviside projection and density filter algorithms , 2011 .

[8]  Ole Sigmund,et al.  Topology synthesis of large‐displacement compliant mechanisms , 2001 .

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

[10]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

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

[12]  J. Michael McCarthy,et al.  21st Century Kinematics , 2013 .

[13]  G. I. N. Rozvany,et al.  New optimality criteria methods: Forcing uniqueness of the adjoint strains by corner-rounding at constraint intersections , 1992 .

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

[15]  Gengdong Cheng,et al.  STUDY ON TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS , 1992 .

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

[17]  G. Cheng,et al.  ε-relaxed approach in structural topology optimization , 1997 .

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

[19]  G. K. Ananthasuresh,et al.  TOPOLOGY OPTIMIZATION OF COMPLIANT MECHANISMS WITH STRENGTH CONSIDERATIONS* , 2001 .

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

[21]  Pablo Andrés Muñoz-Rojas,et al.  Optimization of Structures and Components , 2013 .

[22]  Ole Sigmund,et al.  Design of multiphysics actuators using topology optimization - Part I: One-material structures , 2001 .

[23]  Hae Chang Gea,et al.  A strain based topology optimization method for compliant mechanism design , 2014 .

[24]  Ole Sigmund,et al.  New Developments in Handling Stress Constraints in Optimal Material Distributions , 1998 .

[25]  Julián A. Norato,et al.  Stress-based topology optimization for continua , 2010 .

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

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

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

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

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

[31]  U. Kirsch,et al.  On singular topologies in optimum structural design , 1990 .

[32]  O. Sigmund,et al.  Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio , 1996, Proceedings of Ninth International Workshop on Micro Electromechanical Systems.

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

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

[35]  Xianmin Zhang,et al.  A new level set method for topology optimization of distributed compliant mechanisms , 2012 .