Study With The Chebyshev Series Method Of A Strip On An Elastic Nonlinear Winkler-Pasternak-type Foundation
Free (open access)
This paper describes the procedure and results of theoretical investigations into the beam-soil foundation interaction. Actual pressure versus soil settlement response is represented by a nonlinear Winkler-Pasternak relation. The resulting nonlinear governing differential equation is solved using Chebyshev polynomials. The iterative numerical procedure adopted to solve the resultant system of simultaneous equations is presented. The numerical results are plotted in the form of a chart and, for a range of values of non-dimensional parameters γ, Z and V, and load Q, they are compared with the available F.D.M. results and are found to be in good agreement. Keywords: contact problems, Chebyshev polynomials, Winkler-Pasternak-type soil, nonlinear foundation, numerical methods. 1 Introduction The theory of beams, plates and shells supported on elastic foundations has been the subject of numerous investigations. The simplest approach depends on the assumption that the intensity of the foundation reaction at any point is proportional to the deflection of the structure at that point (Winkler-Pasternak model). As an extreme case, the foundation is represented as elastic half-space [l]. The first of the models provides a simpler solution to the problem of contact between structure and foundation, and for this reason it has been the one most adopted up to now. The problem, in its simplest formulation, appears as linear elastic. However, it does not have sufficient generality in the description of the
contact problems, Chebyshev polynomials, Winkler-Pasternak-type soil, nonlinear foundation, numerical methods.