Stability of slender beams and frames resting on 2D elastic half-space

Abstract

Making use of a mixed variational formulation based on the Green function of the substrate, which assumes as independent fields the structure displacements and the contact pressure, a simple and efficient Finite Element-Boundary Integral Equation (FE-BIE) coupling method is derived and applied to the stability analysis of beams and frames resting on an elastic half-plane. Slender Euler-Bernoulli beams with different combinations of end constraints are considered. The examples illustrate the convergence to the existing exact solutions and provide new estimates of the buckling loads for different boundary conditions. Finally, nonlinear incremental analyses of rectangular pipes with compressed columns and free or pinned foundation ends are performed, showing that pipes stiffer than the soil may exhibit snapthrough instability

Static analysis of shear flexible beams and frames in adhesive contact with an isotropic elastic half-plane using a coupled FE–BIE model

“…However, possible constraint equations among displacements or rotations of the foundation beam can be included into the total potential energy of the beam-substrate system (Eq. (22)) by means of a penalty approach, as illustrated in [28,29].…”

“…In [26], an analogous mixed formulation was used for the analysis of Timoshenko beams in frictionless contact with the substrate, whereas in [27] structural elements with no bending stiffness, such as bars and thin coatings, were investigated. In [28,29], using Euler-Bernoulli and Timoshenko beam theory, respectively, the coupled FE-BIE method was applied to the buckling analysis of beams and frames in frictionless contact with the substrate. To the authors' knowledge, the present proposal to use the FE-BIE model for the plane strain or plane stress static analysis of shear deformable beams and frames in adhesive contact with the substrate represents a new contribution.…”

Nonlinear Analysis of RC Box Culverts Resting on a Linear Elastic Soil

“…The assemblage of global stiffness matrices K a , K b and load vectors f a , f b from the corresponding element matrices K ai , K bi and load vectors f ai , f bi is as usual. However, with a penalty approach it is possible to include constraint equations into functional ∏ (Tullini et al, 2013a;2013b).…”

“…An analogous formulation was used by Tullini and Tralli (2010;Tullini et al., 2012) for the analysis of Timoshenko beams in frictionless contact with the substrate and of bars and thin coatings (i.e., mono-dimensional elements without bending stiffness), respectively. The same mixed model was used by Tullini et al (2013a;2013b) for the analysis of elastic instability of beams and frames in frictionless contact with the substrate.…”

Buckling of a Timoshenko beam bonded to an elastic half-plane: Effects of sharp and smooth beam edges

“…By using a coupled FE-BIE formulation involving the half-plane Green function, Tullini et al (2012Tullini et al ( , 2013 numerically solved the buckling problem of Timoshenko beam in contact with an elastic half-plane under various BCs. Except for the Gallagher work ( Gallagher, 1974 ), concerning E-B beam model, the aforementioned investigations are based on numerical approaches and, to Authors knowledge, a comprehensive analytical study on the stability of a Timoshenko beam bonded to an elastic half-plane cannot be found in Literature.…”