Analysis and optimization against buckling of beams interacting with elastic foundation

Abstract

We consider an infinite continuous elastic beam that interacts with linearly elastic foundation and is under compression. The problem of the beam buckling is formulated and analyzed. Then the optimisation of beam against buckling is investigated. As a design variable (control function) we take the parameters of cross-section distribution of the beam from the set of periodic functions and transform the original problem of optimisation of infinite beam to the corresponding problem defined at the finite interval. All investigations are on the whole founded on the analytical variational approaches and the optimal solutions are studied as a function of problems parameters.

Application of pseudo-parameter iteration method to nonlinear deflection analysis of an infinite beam with variable beam cross-sections on a nonlinear elastic foundation

“…For this reason, many efforts have been made to accurately calculate the nonlinear deflection of an infinite beam with variable cross-sections under static loading conditions. To name just a few, Banichuk et al [ 1 ] have formulated and analyzed the buckling problems of an infinite continuous elastic beam that interacts with linearly elastic foundations and is under compression. Zhang and Liu [ 2 ] have investigated the response of an infinite beam resting on the tensionless Winkler foundation subjected to both axial and transverse concentrated loads.…”

Calculating a beam of variable section lying on an elastic foundation

“…The proposed theoretical provisions can be applied to similar structures operating on an elastic foundation. Also in [9], the finite difference method was used to study the operation of beams on an elastic foundation under the assumption of a parabolic change in the distribution of contact pressure with an adjacent elastic medium; there was proposed a method of constructing lines of impact of bending moments in beams on an elastic foundation on the action of an arbitrary external load. For studying continuous beams on elastic supports (bases), finite elements are proposed using the Vlasov foundation model (its modification is proposed), taking into account the effect of shear deformation; the foundation model is a two-parameter elastic medium.…”