On the numerical solution of nonlinear string problems using the theory of a Cosserat point (Q1083917)

The objective of this paper is to develop an appropriate form of the theory of a Cosserat point [the author, J. Appl. Mech. 52, 368-372 (1985; Zbl 0569.73002)], which can be used to formulate the numerical solution of the three-dimensional motion of a nonlinear elastic string. The string is divided into N material parts, each of which is modelled as a Cosserat point with its own equations of motion and constitutive equations. Then the motion of each Cosserat point is coupled with that of its neighbours and boundary conditions are introduced to obtain a system of ordinary differential equations of time only which describe the motion of the string. Two examples of a rotating string are considered. For each example we show that director inertia (rotary inertia) is significant and that the Cosserat solution converges rapidly to the exact solution developed by \textit{P. Rosenau} and the author [Phys. Rev. A 31, 3480 ff. (1985)].