THE APPLICATION OF LAGRANGIAN AND UPDATED LAGRANGIAN FORMULATIONS TO PIPE WHIP PROBLEMS

摘要

The problem of pipe-whip is an important problem in the analysis of pipe lines carrying high energy/high pressure fluids. In this paper, a Lagrangian formulation (LF) and an updated Lagrangian formulation (ULF) for the analysis of a general geometric and material nonlinearity problems are outlined. The basic differences between the presented formulations and existing ones in the literature are discussed. Both LF and ULF are then applied to pipe-whip analysis. To simulate the shell effect of the pipe, it is modelled as a three-node isoparametric pipe-beam element. Results are presented for both displacement and velocity time histories. The results are compared with similar ones obtained from the ADINA general purpose finite element program. The effect of various nonlinear terms, in the final equilibrium equations, on the number of increments is then investigated.