On the solution of a non-linear parabolic equation with a floating boundary arising in a problem of plastic impact of a beam

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Abstract
The deformation of a cantilever beam with strain rate sensitivity subjected to impact loading at its base has been studied in [11] by an approximate method in which the inertia forces in the plastic region are neglected. If these forces are taken into account, the equation of motion in the plastic region is a fourth order non-linear parabolic differential equation with a floating boundary, i.e. one whose position varies with time and must be found as part of the solution. A numerical solution of this equation is presented here. The results show that the bending moment in the plastic region varies nearly linearly. This result implies that the shear force is nearly constant in the plastic region, and hence that the inertia forces in the plastic region are small in comparison with the shear force in the same region.