Iterative technique for a beam lying on a transversely isotropic foundation

Abstract

The effect of the foundation heterogeneity on the mechanical behaviour of a beam on Vlasov soils is discussed. According to a refined Vlasov soil model, the static problem of beams lying on transversely isotropic soils can be solved by an iterative method. In this paper, based on the energy variational principle, the differential equations for beams under an axial force on refined Vlasov foundations are derived. The methods for solving the internal forces and deformations of beams lying on refined elastic foundations are given. Additionally, an equation for the attenuation parameters is also established, and the characteristic parameters of the refined model are solved by iterative technique. Numerical results show that the foundation heterogeneity have a influence on the deformations and internal forces of the beam-soil system. Moreover, relatively accurate characteristic parameters can be obtained through the iterative process. The refined Vlasov model has broad application prospects.