Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Geometrically Exact Equations for Beams

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_53-1

Synonyms

Definitions

Beams are structures with one dimension that is much larger than the other two. They may be made from isotropic or anisotropic materials and may be homogeneous or inhomogeneous. They may be prismatic or initially curved and twisted. The term geometrically exact refers to there being no approximations in the geometry of either the reference line or the reference cross section. The geometrically exact equations of motion in their most fundamental form are first-order partial differential equations (PDEs), which may be written with or without displacement or rotational variables. Without these variables, they are referred to as intrinsic equations of motion and may be derived via vectorial or analytical mechanics. To be useful, they must be augmented by kinematical PDEs, often first order, defining generalized strains and generalized velocities in terms of partial...

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Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Guggenheim School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaGeorgia

Section editors and affiliations

  • Dewey Hodges
    • 1
  1. 1.Guggenheim School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA