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Cosserat-Type Rods

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Generalized Continua from the Theory to Engineering Applications

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 541))

Abstract

In this chapter we discuss a Cosserat-type theory of rods. Cosserat-type rod theories are based on the consideration of a rod base curve as a deformable directed curve, that is a curve with attached deformable or non-deformable (rigid) vectors (directors), or based on the derivation of one-dimensional (1D) rod equations from the three-dimensional (3D) micropolar (Cosserat) continuum equations. In the literature are known theories of rods kinematics of which described by introduction of the translation vector and additionally p deformable directors or one deformable director or three unit orthogonal each other directors. The additional vector fields of directors describe the rotational (in some special cases additional) degrees of freedom of the rod. The aim of the chapter is to present a Cosserat-type theory of rods and to show various applications.

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Authors and Affiliations

  1. Lehrstuhl Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach & Victor A. Eremeyev

  2. Lehrstuhl Nichtlineare Analysis und Modellierung, Fachbereich Mathematik, Universität Duisburg-Essen, Essen, Germany

    Mircea Bîrsan

  3. Department of Mathematics, University “A.I. Cuza” of Iaşi, Iaşi, Romania

    Mircea Bîrsan

  4. South Scientific Center of RASci and South Federal University, Rostov on Don, Russian Federation

    Victor A. Eremeyev

Authors
  1. Holm Altenbach
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  2. Mircea Bîrsan
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  3. Victor A. Eremeyev
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Editors and Affiliations

  1. Otto Von Guericke University, Magdeburg, Germany

    Holm Altenbach

  2. South Federal University and South Scientific Center of Rasci, Rostov on Don, Russian Federation

    Victor A. Eremeyev

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Altenbach, H., Bîrsan, M., Eremeyev, V.A. (2013). Cosserat-Type Rods. In: Altenbach, H., Eremeyev, V.A. (eds) Generalized Continua from the Theory to Engineering Applications. CISM International Centre for Mechanical Sciences, vol 541. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1371-4_4

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