Keywords: beam on nonlinear foundation, Winkler foundation, inelastic analysis, distributed plasticity, boundary element method.

In engineering practice we often come across the analysis of beams on or in a soil foundation. Piles, pile-columns and pile groups embedded in the soil medium as well as beams-columns resting on the soil half space are the most common examples. Analysis of civil engineering structures based on elastic constitutive equations is most likely to lead to extremely conservative designs not only due to the significant difference between first yield in a cross section and full plasticity but also as a result of the unaccounted for yet significant reserves of strength that are enabled only after inelastic redistribution along members takes place. Thus, material nonlinearity is important for investigating the ultimate strength of a beam that resists bending loading, while distributed plasticity models are acknowledged in the literature to capture more rigorous material nonlinearities than cross sectional stress resultant approaches or lumped plasticity idealizations.

In this investigation the inelastic analysis of beams of doubly symmetric simply or multiply connected constant cross-sections resting on an inelastic foundation is presented employing the boundary element method (BEM). The beam is subjected to arbitrarily distributed or concentrated bending loading along its length, 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 model exploiting material constitutive laws and numerical integration over the cross sections. An incremental - iterative solution strategy is adopted to restore global equilibrium along with an efficient iterative process to integrate the inelastic rate equations. The arising boundary value problem is solved employing the BEM [1]. The essential features and novel aspects of the present formulation compared with previous ones are summarized as follows:

1. The formulation is a displacement based one taking into account inelastic redistribution along the beam axis by exploiting material constitutive laws and numerical integration over the cross sections.
2. The inelasticity of the soil medium is taken into account.
3. An incremental-iterative solution strategy is adopted to restore global equilibrium of the beam. Integration of the inelastic rate equations is performed for each monitoring station with an efficient iterative process and stress resultants are obtained employing incremental strains.
4. The beam is supported by the most general nonlinear boundary conditions, while its cross section is an arbitrary doubly symmetric one.
5. To the authors' knowledge, the BEM has not yet been used for the solution of the aforementioned problem.

Accurate results are obtained using a relatively small number of nodal points across the longitudinal axis, while the procedure developed retains most of the advantages of a BEM solution over a domain approach.

1

J.T. Katsikadelis, "Boundary Elements: Theory and Applications", Elsevier, Amsterdam-London, United Kingdom, 2002.

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