Dynamic analysis of beam-soil interaction systems with material and geometrical nonlinearities

In this paper a Hybrid Domain Boundary Element Method is developed for the geometrically nonlinear dynamic analysis of inelastic Euler-Bernoulli beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on viscous inelastic Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse dynamic loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. A displacement based formulation is developed and inelastic redistribution is modelled through a distributed plasticity (fibre) approach. A uniaxial hysteretic law is considered for the evolution of the plastic part of the normal stress following the phenomenological hysteresis model, while hysteretic force-displacement model is also employed in order to describe the inelastic behaviour of the Winkler springs. Numerical integration over the beam cross sections is performed in order to resolve the hysteric parts of the stress resultants. Application of the boundary element technique yields a system of nonlinear Differential-Algebraic Equations, which are written in state-space form and solved by an incremental-iterative solution strategy. Numerical examples are worked out confirming the accuracy and the computational efficiency of the proposed beam formulation, as well as the significant influence of material and geometrical nonlinearities in the response of beam-soil interaction systems.