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Robust Design of Large-displacement Compliant Mechanisms : Volume 2, Issue 2 (22/08/2011)

By Lazarov, B. S.

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Book Id: WPLBN0003984338
Format Type: PDF Article :
File Size: Pages 8
Reproduction Date: 2015

Title: Robust Design of Large-displacement Compliant Mechanisms : Volume 2, Issue 2 (22/08/2011)  
Author: Lazarov, B. S.
Volume: Vol. 2, Issue 2
Language: English
Subject: Science, Mechanical, Sciences
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Sigmund, O., Schevenels, M., & Lazarov, B. S. (2011). Robust Design of Large-displacement Compliant Mechanisms : Volume 2, Issue 2 (22/08/2011). Retrieved from

Description: Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Nils Koppels Alle, B. 404, 2800 Lyngby, Denmark. The aim of this article is to introduce a new topology optimisation formulation for optimal robust design of Micro Electro Mechanical Systems. Mesh independence in topology optimisation is most often ensured by using filtering techniques, which result in transition grey regions difficult to interpret in practical realisations. This problem has been alleviated recently by projection techniques, but these destroy the mesh independence introduced by the filters and result in single node connected hinges. Such features in the design are undesirable as they are not robust with respect to geometric manufacturing errors (such as under/over etching). They can be avoided by optimising for several design realisations which take into account the possible geometry errors. The design variations are modelled with the help of random variables. The proposed stochastic formulation for the design variations results in nearly black and white mechanism designs, robust with respect to uncertainties in the production process, i.e. without any hinges or small details which can create manufacturing difficulties.

Robust design of large-displacement compliant mechanisms

Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B., and Sigmund, O.: Efficient topology optimization in MATLAB using 88 lines of code, Struct. Multidiscip. O., 43, 1–16, doi:10.1007/s00158-010-0594-7, 2011.; Belytschko, T., Liu, W. K., and Moran, B.: Nonlinear Finite Elements for Continua and Structures, Wiley, 2000.; Bendsøe, M. P. and Sigmund, O.: {T}opology {O}ptimization – {T}heory, {M}ethods and {A}pplications, Springer Verlag, Berlin Heidelberg, 2004.; Beyer, H.-G. and Sendhoff, B.: Robust optimization - A comprehensive survey, Comput. Method. Appl. M., 196, 3190–3218, doi:10.1016/j.cma.2007.03.003, 2007.; Bonet, J. and Wood, R. D.: Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, 1997.; Bourdin, B.: Filters in topology optimization, Int. J. Numer. Meth. Eng., 50, 2143–2158, 2001.; Bruns, T. E. and Tortorelli, D. A.: Topology optimization of non-linear elastic structures and compliant mechanisms, Comput. Method. Appl. M., 190, 3443–3459, 2001.; Guest, J., Prevost, J., and Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions, Int. J. Numer. Meth. Eng., 61, 238–254, 2004.; Krenk, S.: Non-linear Modeling and Analysis of Solids and Structures, Cambridge University Press, 2009.; Lazarov, B. and Sigmund, O.: Filters in topology optimizat ion based on Helmholtz type differential equations, Int. J. Numer. Meth. Eng., 86, 765–781, 2011.; Pedersen, C. B. W., Buhl, T., and Sigmund, O.: Topology synthesis of large-displacement compliant mechanisms, Int. J. Numer. Meth. Eng., 50, 1097–0207, 2001.; Sigmund, O.: On the design of compliant mechanisms using topology optimization, Mech. Struct. Mach., 25, 493–524, 1997.; Sigmund, O.: Morphology-based black and white filters for topology optimization, Struct. Multidiscip. O., 33, 401–424, 2007.; Sigmund, O.: Manufacturing tolerant topology optimization, Acta Mech. Sinica, 25, 227–239, doi:10.1007/s10409-009-0240-z, 2009.; Svanberg, K.: The M}ethod of {M}oving {A}symptotes – {A New Method for Structural Optimization, I. J. Numer. Meth. Eng., 24, 359–373, 1987.; Tsompanakis, Y., Lagaros, N. D., and Papadrakakis, M. (Eds.): Structural Design Optimization Considering Uncertainties, Vol. 1, Structures & Infrastructures Series, Taylor & Francis Group, 2008.; Wang, F., Lazarov, B., and Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization, Struct. Multidiscip. O., 43, 767–784, doi:10.1007/s00158-010-0602-y, 2011.; Xiu, D.: Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, 2010.; Xiu, D. and Hesthaven, J. S.: High-Order Collocation Methods for Differential Equations with Random Inputs, SIAM J. Sci. Comput., 27, 1118–1139, 2005.; Xu, S., Cai, Y., and Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions, Struct. Multidiscip. O., 41, 1615–1488, 2010.


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