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.

Cosserat-Type Rods

Eremeyev V. A.
2013-01-01

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.
2013
978-3-7091-1370-7
978-3-7091-1371-4
Constitutive Equation
Constitutive Tensor
Entropy Inequality
Pure Traction
Shear Vibration
File in questo prodotto:
File Dimensione Formato  
AltenbachBirsanEremeyev_CISM2013_Chapter_Cosserat-TypeRods.pdf

Solo gestori archivio

Tipologia: versione editoriale
Dimensione 642.09 kB
Formato Adobe PDF
642.09 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/307686
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 50
  • ???jsp.display-item.citation.isi??? 40
social impact