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Nonlinear Dynamic Modeling of Nano and Macroscale Systems

Using Finite Elements and an Intrinsic Beam Formulation

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Nonlinear Approaches in Engineering Applications

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Abstract

This chapter presents a nonlinear finite element approach for modeling nano and macroscale beam-like materials and structures. The work is based on a series of three articles published by the author and his co-workers from 2007 to 2010 (Leamy 2007; Leamy and Lee 2009; Leamy 2010). The chapter begins by describing a finite element procedure for discretizing a set of nonlinear, intrinsic beam equations. These equations are notable for their use of curvature and strain, vice rotational and displacement, field variables. Included in the finite element development is a discussion of zero energy modes and their remediation. Attention then turns to application of the approach in studying dynamics of systems at the nanoscale (e.g., carbon nanotubes) through to the macroscale (e.g., helical springs).

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Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

Authors
  1. Michael J. Leamy
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Correspondence to Michael J. Leamy .

Editor information

Editors and Affiliations

  1. , Industrial Systems Engineering, University of Regina, Wascana Parkway, Regina, S4S 0A2, Saskatchewan, Canada

    Liming Dai

  2. School of Aerospace, Mechanical, and Man, RMIT University, Bandoora Campus, Building 251.03.42, Melbourne, 3083, Victoria, Australia

    Reza N. Jazar

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Leamy, M.J. (2012). Nonlinear Dynamic Modeling of Nano and Macroscale Systems. In: Dai, L., Jazar, R. (eds) Nonlinear Approaches in Engineering Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1469-8_6

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  • DOI: https://doi.org/10.1007/978-1-4614-1469-8_6

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-1468-1

  • Online ISBN: 978-1-4614-1469-8

  • eBook Packages: EngineeringEngineering (R0)

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