Parametric Optimization of Viscoplastic Bars Under Dynamic Axial Loading

The paper formulates the problem of the parametric optimal design of a viscoplastic bar under the impact of axial force, Eq. (4.4), and gives some solutions. The dual approach to the problem has been applied, the minimal residual deflection being the design objective, under the constraint of a constant volume of the bar. The governing equation (2.4) has been derived under the assumption of a power physical law and arbitrarily variable cross section; however, effective calculations have been performed for the linear law (0=1) and for bars of truncated cone shape. Two parameters describe the cross section of this bar, Eq. (3.1), but one of them can be determined from the condition of constant volume of the bar. Hence the parameter of tapering of the cone (A) remains the only design variable in this case. The influence of various parameters which describe the shape of the force impulse (Fig. 2) on the parameter Aopt has been investigated (Figs. 3, 4 and 5).