Bending of elastic beams on winkler-type viscoelastic foundations with unilateral constraints

A solution algorithm is presented for the analysis of unilateral, frictionless contact between a beam and a viscoelastic foundation. The foundation is modelled as a Winkler-type viscoelastic medium, to which the time integration method [ Mech. Teoret. i Stos. 22 , 209–233 (1984)] was applied. The problem was formulated in the form of a variational inequality, from which, after space discretization by the finite element method, a linear complementarity problem was derived. The solution method covers the time-discontinuities of loads and both loading (reloading) and unloading processes. The applicability of the algorithm is illustrated by selected numerical solutions to some examples.