Planar Equilibrium Problems for Elastic Rods
A theory of rods is the characterization of the motion of slender solid bodies by a finite number of equations in which there is but one independent spatial variable. (The theory of strings, formulated in Chap. II, is thus an example of a theory of rods.) In this chapter we formulate and analyze equilibrium problems for the planar deformation of elastic rods. The intrinsically one-dimensional theory that we employ, which may be called the special Cosserat theory of rods, has several virtues: It is exact in the same sense as the theory of strings of Chap. II is exact, namely, it is not based upon ad hoc geometrical approximations or mechanical assumptions. It is much more general than the standard theories used in structural mechanics. Many important concrete problems for the theory admit detailed global analyses, some of which are presented below.
KeywordsConstitutive Equation Phase Portrait Equilibrium Problem Closed Orbit Reference Configuration
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