Uncertain initial imperfections via probabilistic and convex modeling: Axial impact buckling of a clamped beam

In the present study the problem of axial impact of a clamped beam with initial imperfections is treated using two uncertainty descriptions. For the deterministic solution, the exact mode and an approximative approach using so called “cosinusoidal polynomials” by Filonenko-Borodich are used. Next, the uncertainty is represented by a convex set and subsequently by random variables. The comparison between both uncertainty descriptions is carried out numerically on the level of the design time of the considered beam.