Large deflection of elastoplastic, non-linear strain-hardening cantilevers

Abstract

This paper concerns the large de ection of elastoplastic, non-linear strain-hardening cantilevers of rectangular cross-section, for which the stress-strain relationship after yielding is described by s K 1 e q . Both the bending moment and axial force are included in the yielding criterion, and the corresponding strain increments obey the associated normality rule. Comparisons between the experimental data and the theoretical predictions are made for mild steel cantilevers subjected to a tip force with an inclined angle f 67 5, 90 and 1578 respectively. R easonable agreement is obtained. The theoretical analysis has described the large de ection behaviour of the cantilever and is in good agreement with tests.

Folding of a plastic fibre under combined shear and compression

“…Hence, no unloading phenomena take place before the beam develop a contact with the end platens. It should be mentioned that, without constraint imposed by the end platens, the unloading indeed happens in a severe deformation phase, as shown by Huang et al [7].…”

“…The critical loading angle depends only on the material hardening exponents. Huang et al [7] found that the critical bending angle is about 40 v for the material with n ¼ 0:07. With the critical bending angle u cr known, the extreme value of the applied force can be calculated from Eq.…”

“…And finite difference methods were adopted to solve nonlinear ordinary differential governing equations. Huang et al [7] introduced the power-law form to represent the material stress-strain relationship after yielding, and the effects of the axial force on the yield criterion and the plastic flow were considered. Lee [3] investigated the case of a cantilever subjected to a combined loading consisting of a uniformly distributed load and a shear load at the free end, and the Runge-Kutta numerical method was used to solve the problem.…”

Large deflection of elastoplastic beams with prescribed moving and rotating ends

“…Thus, the governing equation (10) as well as the constitutive equations (11a) to (11d) should be modi ed accordingly. Even taking these in uences into account, reference [8] demonstrated that the effect of the axial force is negligible for a cantilever, which experiences a large elastoplastic de ection due to the concentrated force applied at its tip. In the present case, the axial strain can be assessed for example 1 with H =Lˆ0:02, as shown in F ig.…”

“…D if culties in the problem lie in both material and geometrical nonlinearities. The large de ection behaviour of an elastoplastic cantilever has been investigated by many authors [1][2][3][4][5][6][7][8][9]. A novel technique making use of the large elastoplastic de ection of a beam is air bending of a slender beam, which was rst proposed and studied by Lippmann and co-workers [10][11][12][13].…”