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Multi-patch Isogeometric Analysis of Planar Compliant Mechanisms

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Mechanism and Machine Science

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

Multi-patch isogeometric analysis (IGA) of planar compliant mechanism, based on the planar Timoshenko beam theory, is presented. IGA is a new computational framework that seamlessly integrates geometric modelling and deformation analysis. The multi-patch technique enables analysis of multi-segmented beam structures with bifurcation points and star junctions. Methods to handle various Dirichlet and Neumann boundary conditions in the framework of IGA are also discussed. Displacement and section force distributions obtained from IGA are compared with the results obtained from finite element analysis (FEA) and analytical solutions. IGA is particularly advantageous in the problems involving geometries with large curvatures, such as curved beams, curved thin plates, etc. Such curved geometries can be used to model various interconnected members in a compliant mechanism. The multi-patch IGA approach discussed in this paper can be used to improve the efficiency of shape optimization process of planar compliant mechanisms, by providing better control over the shape using fewer design variables and by reducing errors arising due to geometric approximation.

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References

  1. Hughes T, Cottrell J, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

    Google Scholar 

  2. Kota S, Ananthasuresh GK (1995) Designing compliant mechanisms. Mech Eng CIME 117(11):93–97

    Google Scholar 

  3. Litewka P, Jerzy R (1997) An efficient curved beam finite element. Int J Numer Methods Eng 40(14):2629–2652

    Google Scholar 

  4. Yang F, Sedaghati R, Esmailzadeh E (2008) Free in-plane vibration of general curved beams using finite element method. J Sound Vib 318(4–5):850–867

    Article  Google Scholar 

  5. Cazzani A, Marcello M, Emilio T (2016) Isogeometric analysis of plane-curved beams. Math Mech Solids 21(5):562–577

    Google Scholar 

  6. Adam C, Bouabdallah S, Zarroug M, Maitournam H (2014) Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams. Comput Methods Appl Mech Eng 279:1–28

    Google Scholar 

  7. Echter R, Bischoff M (2010) Numerical efficiency, locking and unlocking of NURBS finite elements. Comput Methods Appl Mech Eng 199(5–8):374–382

    Article  Google Scholar 

  8. Piegl L, Tiller W (1995) The NURBS book. Springer, London, UK

    Book  Google Scholar 

  9. Lim C, Wan C, Kitipornchai S (1997) Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions. Arch Appl Mech 67:179–190

    Article  Google Scholar 

  10. Hughes TJ, Reali A, Sangalli G (2010) Efficient quadrature for NURBS-based isogeometric analysis. Comput Methods Appl Mech Eng 199:301–313

    Article  MathSciNet  Google Scholar 

  11. Felippa IC (2017) MultiFreedom Constraints II. University of Colorado. http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/

  12. Xu D, Ananthasuresh GK (2003) Freeform skeletal shape optimization of compliant mechanisms. J Mech Design 125(2):253–261

    Google Scholar 

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Correspondence to G. K. Ananthasuresh .

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Bodkhe, S., Ananthasuresh, G.K. (2021). Multi-patch Isogeometric Analysis of Planar Compliant Mechanisms. In: Sen, D., Mohan, S., Ananthasuresh, G. (eds) Mechanism and Machine Science. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4477-4_48

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  • DOI: https://doi.org/10.1007/978-981-15-4477-4_48

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-4476-7

  • Online ISBN: 978-981-15-4477-4

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