摘要
A method is presented for solving the three-dimensional axisymmet- ric field equations for a perfectly plastic material which obeys the von-Mises yield criterion and the Levy-Mises flow law. The method is used for the particular case in which a small axisymmetric perturbed flow is superposed on a uniform flow without flow reversal taking place. The method then leads to solving a fourth order differen- tial equation for the velocity potential. The special case of a thick cylindrical shell under compressive flow is examined. The solution so obtained, being derived from the three dimensional theory, includes a correct treatment of transverse shear distor- tion. A preferred mode of instability is identified having a wave-length in reasonable agreement with that obtained experimentally by other workers.
A method is presented for solving the three-dimensional axisymmet- ric field equations for a perfectly plastic material which obeys the von-Mises yield criterion and the Levy-Mises flow law. The method is used for the particular case in which a small axisymmetric perturbed flow is superposed on a uniform flow without flow reversal taking place. The method then leads to solving a fourth order differen- tial equation for the velocity potential. The special case of a thick cylindrical shell under compressive flow is examined. The solution so obtained, being derived from the three dimensional theory, includes a correct treatment of transverse shear distor- tion. A preferred mode of instability is identified having a wave-length in reasonable agreement with that obtained experimentally by other workers.
