Geometrically Nonlinear Inelastic Analysis of Timoshenko Beams on Inelastic Foundation

In this paper a Boundary Element Method (BEM) is developed for the geometrically nonlinear inelastic analysis of Timoshenko beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on inelastic tensionless Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. To account for shear deformations, the concept of shear deformation coefficients is used. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed plasticity (fiber) approach exploiting three-dimensional material constitutive laws and numerical integration over the cross-sections. An incremental iterative solution strategy along with an efficient iterative process are employed, while the arising boundary value problem is solved employing the boundary element method. Numerical examples are worked out confirming the accuracy and the computational efficiency of the proposed beam formulation, as well as the significant influence of the geometrical nonlinearity and the shear deformation effect in the response of a beam-foundation system.