An augmented formulation of distributed compliant mechanism optimization using a level set method

Topology optimization has emerged as one of the key approaches to design compliant mechanisms. However, one of the main difficulties is that the resulted compliant mechanisms often have de facto hinges. For this reason, a simple yet efficient formulation for designing hinge-free compliant mechanisms is developed and examined within a level set–based topology optimization framework. First, the conventional objective function is augmented using an output stiffness. Second, the proposed formulation is solved using a level set method for designing some benchmark problems in the literature. It is shown that the proposed augmented objective function can prevent the de facto hinges in the obtained compliant mechanisms. Finally, some concluding remarks and future work are put forward.

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

[2]  Salam Rahmatalla,et al.  Sparse Monolithic Compliant Mechanisms Using Continuum Structural Topology Optimization , 2004 .

[3]  J. Zolésio,et al.  Introduction to shape optimization : shape sensitivity analysis , 1992 .

[4]  Alex M. Andrew,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition) , 2000 .

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

[6]  Hong Zhou.  Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model , 2010 .

[7]  G. K. Ananthasuresh,et al.  A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms , 2009 .

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

[9]  Kyung K. Choi,et al.  Structural Sensitivity Analysis and Optimization 1: Linear Systems , 2005 .

[10]  Zhang,et al.  Topology Optimization of Compliant Mechanisms with Geometrical Nonlinearities Using the Ground Structure Approach , 2011 .

[11]  Michael Yu Wang,et al.  Compliant Mechanism Optimization: Analysis and Design with Intrinsic Characteristic Stiffness , 2009 .

[12]  S. Ta'asan,et al.  Introduction to shape design and control , 1997 .

[13]  Motiee Mehrnaz,et al.  Development Of a Novel Multi-disciplinary Design Optimization Scheme For Micro Compliant Devices , 2008 .

[14]  İsmail Durgun,et al.  Structural Design Optimization of Vehicle Components Using Cuckoo Search Algorithm , 2012 .

[15]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

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

[17]  Martín A. Pucheta,et al.  Design of bistable compliant mechanisms using precision–position and rigid-body replacement methods , 2010 .

[18]  N. Wang,et al.  Compliant mechanisms design based on pairs of curves , 2012 .

[19]  M. Wang,et al.  COMPLIANT MECHANISMS WITH CHARACTERISTIC STIFFNESS , 2007 .

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

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

[22]  Z. Kang,et al.  A multi-material level set-based topology and shape optimization method , 2015 .

[23]  Nong Zhang,et al.  Level-set topology optimization for multimaterial and multifunctional mechanical metamaterials , 2017 .

[24]  Kazuhiro Saitou,et al.  Topology Synthesis of Multicomponent Structural Assemblies in Continuum Domains , 2011 .

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

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

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

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

[29]  Nianfeng Wang,et al.  Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method , 2013 .

[30]  Michael Yu Wang,et al.  Designing Distributed Compliant Mechanisms With Characteristic Stiffness , 2007 .

[31]  Yi Min Xie,et al.  A further review of ESO type methods for topology optimization , 2010 .

[32]  Takayuki Yamada,et al.  INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING , 2022 .

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

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

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

[36]  Y. Y. Kim,et al.  Hinge-free topology optimization with embedded translation-invariant differentiable wavelet shrinkage , 2004 .

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

[38]  Takayuki Yamada,et al.  A topology optimization method based on the level set method incorporating a fictitious interface energy , 2010 .

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

[40]  Michael Yu Wang.  A Kinetoelastic Formulation of Compliant Mechanism Optimization , 2009 .

[41]  Peter B. Coffin,et al.  Level set topology optimization of cooling and heating devices using a simplified convection model , 2015, Structural and Multidisciplinary Optimization.

[42]  F. Santosa,et al.  A topology-preserving level set method for shape optimization , 2004, math/0405142.