Nonlinear Wave Equations for Buckle Propagation in an Elastic Pipeline

Abstract

This paper demonstrates the derivation of the equations previously proposed for an 'elastic' buckle propagation in a pipeline subjected to bending under axial tension and hydrostatic side pressure. Formulation is given for a thin cylindrical shell of infinite length in such a way that bending gives rise to a geometrically large but elastic deflection so that a significant cross-sectional deformation takes place. For simplicity, a material behavior of the pipe is assumed by Hooke's law. On the basis of the three-dimensional theory of nonlinear elasticity, the derivation utilizes the asymptotic-expansion method in terms of the thickness-coordinate of the pipe, combined with a Fourier expansion in the circumferential direction and a 'long-wave approximation' in the axial direction. Derived are the nonlinear wave equations which couple the beam-flexural mode with the ring-flexural mode. A further simplification and a physical significance of the equations thus derived are discussed.