摘要
By employing large deformation governing equations expressed in the form of finite difference, the dynamic responses of an elastic, perfectly plastic cantilever subjected to an oblique impact at its tip was numerically studied. Through analyzing the instantaneous distribution of the yield function （φ = ｜M/Mo｜ ＋ （N/No）^2）, bending moment and axial force during the early stage of the response, the elastic-plastic deformation mechanism and the influence of axial component of an oblique impact on the dynamic response of a cantilever beam were discussed. The present analysis shows that the deformation mechanism of an elastic-plastic cantilever subjected to an oblique impact consists of four phases, i.e. ‘the expanding compressed plastic region＇ mode; the ‘generalized traveling plastic hinge＇ and ‘shrinking plastic region＇ mixed mode; the ‘stationary plastic hinge＇ mode and ‘elastic vibration＇ mode. Compared with the two-phase deformation mode obtained by using the rigid, perfectly plastic approach, the mode of shrinking plastic region that occurred instantly after the oblique impact and the mode of stationary hinge were both confirmed. The primary features of the deformation mechanism are captured by both analysis methods. It has also been found that the beam＇s deformation is mainly controlled by the axial component of the oblique impact in the early phase of the dynamic response, the deformation mechanism is obviously different from the case of a transverse impact. With further development of the response, the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section. At the same time, the bending moments along the cantilever develop gradually and dominate the beam＇s deformation. The numerical results indicate that the mass, impact speed and oblique angle are the important factors that influence the elastic-plastic dynamic response of a cantilever beam.
By employing large deformation governing equations expressed in the form of finite difference, the dynamic responses of an elastic, perfectly plastic cantilever subjected to an oblique impact at its tip was numerically studied. Through analyzing the instantaneous distribution of the yield function （φ = ｜M/Mo｜ ＋ （N/No）^2）, bending moment and axial force during the early stage of the response, the elastic-plastic deformation mechanism and the influence of axial component of an oblique impact on the dynamic response of a cantilever beam were discussed. The present analysis shows that the deformation mechanism of an elastic-plastic cantilever subjected to an oblique impact consists of four phases, i.e. ‘the expanding compressed plastic region＇ mode; the ‘generalized traveling plastic hinge＇ and ‘shrinking plastic region＇ mixed mode; the ‘stationary plastic hinge＇ mode and ‘elastic vibration＇ mode. Compared with the two-phase deformation mode obtained by using the rigid, perfectly plastic approach, the mode of shrinking plastic region that occurred instantly after the oblique impact and the mode of stationary hinge were both confirmed. The primary features of the deformation mechanism are captured by both analysis methods. It has also been found that the beam＇s deformation is mainly controlled by the axial component of the oblique impact in the early phase of the dynamic response, the deformation mechanism is obviously different from the case of a transverse impact. With further development of the response, the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section. At the same time, the bending moments along the cantilever develop gradually and dominate the beam＇s deformation. The numerical results indicate that the mass, impact speed and oblique angle are the important factors that influence the elastic-plastic dynamic response of a cantilever beam.
基金
Supported by the Key Project of Chinese Ministry of Education (No.02084).
