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Finite element modelling for a beam on the Winkler type basis with variable rigidity. (English. Russian summary) Zbl 1112.74497
The authors study the design problem for a beam on the Winkler basis, i.e., under the influence of a cross-force which rotates around the axis of the beam; rigidity of the basis is supposed to be a function in the time variable. A general mathematical model is proposed and variational formulations of the boundary value problems in question are obtained. The finite element method is used to determine the stresses of a beam. Results of numerical experiments are given.
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B05 Classical linear elasticity
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators