Cosserat-Type Rods

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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