The large deformation analysis of flexible pipes subjected to impact loading

摘要

A new method for the dynamic analysis of flexible pipes subjected to impact loading is presented. Impacts and the associated impulsive forces are incorporated into the dynamic formulation using a generalized momentum balance.Each flexible pipe is discretized into a set of geometrically nonlinear Timoshenko beams that account for the condition of pipe whip in which the ruptured pipe undergoes a large angular rotation about a plastic hinge. Nodal coordinates resulting fromthe finite element discretization are employed to define the displacements and slopes of the selected nodes with respect to a pipe reference. The location and orientation of the latter are defined using a set of reference coordinates. Twosources of nonlinearities, namely geometric and inertia nonlinearities, are considered is this formulation. Geometric elastic nonlinearities arise from retaining the quadratic terms in the strain-displacement relationships and accordingly a new geometric stiffness matrix that accounts for the shear sod rotary inertia effects is employed. Inertia nonlinearities, however, are the consequence of the large angular rotations of the pipe and thus the resulting mass matrix is highly nonlinear. In order to account for these nonlinearities, the system stiffness and inertia properties have to be iteratively updated during the dynamic analysis. The present formulation is exemplified using a two dimensional pipe whip model subjected toimpact loading. Numerical experimentations indicate that the inclusion of rotary inertia, shear deformation, and elastic nonlinearities has a significant influence on the dynamics of flexible pipes.