Multiresolution Topology Optimization of Large-Deformation Path-Generation Compliant Mechanisms with Stress Constraints

Topology optimization is a powerful numerical tool in the synthesis of lightweight structures and compliant mechanisms. Compliant mechanisms present challenges for topology optimization, as they typically exhibit large displacements and rotations. Path-generation mechanisms are a class of mechanisms that are designed to follow an exact path. The characteristics of compliant mechanisms therefore exclude the validity of linear finite-element analysis to ensure the proper modeling of deformation and stresses. As stresses can exceed the limit when neglected, stress constraints are needed in the synthesis of compliant mechanisms. Both nonlinear finite-element analysis as well as the consideration of stress constraints significantly increase computational cost of topology optimization. Multiresolution topology optimization, which employs different levels of discretization for the finite-element analysis and the representation of the material distribution, allows an important reduction of computational effort. A multiresolution topology optimization methodology is proposed integrating stress constraints based on nonlinear finite-element analysis for path-generation mechanisms. Two objective formulations are used to motivate and validate this methodology: maximum-displacement mechanisms and path-generation mechanisms. The formulation of the stress constraints and their sensitivities within nonlinear finite-element analysis and multiresolution topology optimization are explained. We introduce two academic benchmark examples to demonstrate the results for each of the objective formulations. To show the practical, large-scale application of this method, results for the compliant mechanism structure of a droop-nose morphing wing concept are shown.

[1]  C. Mattheck,et al.  SKO (soft kill option): the biological way to find an optimum structure topology , 1992 .

[2]  John T. Hwang,et al.  Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models , 2013 .

[3]  D. Tortorelli,et al.  Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity , 1994 .

[4]  Ole Sigmund,et al.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[5]  Fred van Keulen,et al.  A unified aggregation and relaxation approach for stress-constrained topology optimization , 2017 .

[6]  R. Stainko.  An adaptive multilevel approach to the minimal compliance problem in topology optimization , 2005 .

[7]  Renato Vidoni,et al.  Optimal Design for the Passive Control of Vibration Based on Limit Cycles , 2019, Shock and Vibration.

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

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

[10]  D. Tortorelli,et al.  Design sensitivity analysis: Overview and review , 1994 .

[11]  Gyung-Jin Park,et al.  Technical overview of the equivalent static loads method for non-linear static response structural optimization , 2011 .

[12]  Tam H. Nguyen,et al.  Improving multiresolution topology optimization via multiple discretizations , 2012 .

[13]  Fabian Duddeck,et al.  Topology optimization for crashworthiness of thin-walled structures under axial impact using hybrid cellular automata , 2016 .

[14]  Kai A. James,et al.  A stress-based topology optimization method for heterogeneous structures , 2019, Structural and Multidisciplinary Optimization.

[15]  Xianmin Zhang,et al.  A 213-line topology optimization code for geometrically nonlinear structures , 2018, Structural and Multidisciplinary Optimization.

[16]  Ole Sigmund,et al.  Stress-constrained topology optimization for compliant mechanism design , 2015 .

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

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

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

[20]  Daniel A. Tortorelli,et al.  An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms , 2003 .

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

[22]  Jakob S. Jensen,et al.  Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems , 2014 .

[23]  Y. Kim,et al.  Element connectivity parameterization for topology optimization of geometrically nonlinear structures , 2005 .

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

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

[26]  Carlos Eduardo de Souza,et al.  A Study on the Design of Large Displacement Compliant Mechanisms with a Strength Criteria Using Topology Optimization , 2017 .

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

[28]  Ole Sigmund,et al.  Internal contact modeling for finite strain topology optimization , 2020, Computational Mechanics.

[29]  Tam H. Nguyen,et al.  A computational paradigm for multiresolution topology optimization (MTOP) , 2010 .

[30]  H. Kelley.  Method of Gradients , 1962 .

[31]  Rolf Lammering,et al.  Topology synthesis of large‐displacement compliant mechanisms with specific output motion paths , 2012 .

[32]  Mirko Hornung,et al.  Aerodynamic Design of a Morphing Wing Sailplane , 2019, AIAA Aviation 2019 Forum.

[33]  M. Hornung,et al.  Studies of Anisotropic Wing Shell Concepts for a Sailplane with a Morphing Forward Wing Section , 2019, AIAA Aviation 2019 Forum.

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

[35]  Xianmin Zhang,et al.  Design of compliant mechanisms using continuum topology optimization: A review , 2020 .

[36]  A. Michell.  LVIII. The limits of economy of material in frame-structures , 1904 .

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

[38]  J. Petersson,et al.  Large-scale topology optimization in 3D using parallel computing , 2001 .

[39]  Ren-Jye Yang,et al.  Stress-based topology optimization , 1996 .