Andreev, A. B.; Maximov, J. T.; Racheva, M. R. Finite element modelling for a beam on the Winkler type basis with variable rigidity. (English. Russian summary) Zbl 1112.74497 Sib. Zh. Vychisl. Mat. 8, No. 1, 23-30 (2005). 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. Reviewer: N. I. Alexandrova (Novosibirsk) MSC: 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 Keywords:finite element method; Winkler type basis; dynamic stress PDF BibTeX XML Cite \textit{A. B. Andreev} et al., Sib. Zh. Vychisl. Mat. 8, No. 1, 23--30 (2005; Zbl 1112.74497)