The analysis of a free two-layer composite beamon the elastic foundation

Abstract

Abstract
 Introduction. This article offers a methodology for the analysis of a two-layer composite beam on an elastic foundation that represents a one-parameter Winkler model. The behaviour of two-layer beams is described by A.R. Rzhanitsyn in his theory of composite rods that have rigid transverse and elastic-yielding longitudinal connections between layers. The theory of composite rods allows to study the stress-strain state (SSS) of multilayer foundation beams, having a layer featuring low thermal conductivity, and perforated beams.
 Materials and methods. However, analytical solutions to these problems involve certain difficulties; therefore, they are often inapplicable. We propose to apply a numerical method, a method of successive approximations (MSA), developed by professor R.F. Gabbasov at the Department of structural and theoretical mechanics of the Moscow State University of Civil Engineering. MSA has proven to be an effective and highly accurate method designated for analyzing static/dynamic loads, applied to beams, slabs and shells, and for making stability calculations. The difference-based variation of the MSA method has a number of advantages over difference equations of the “classical” finite difference method (FDM). The proposed methodology allows to take into account various types of boundary conditions without involving contour points. Сoncentrated forces, concentrated moments, and piecewise distributed loads can be taken into account as loading types.
 The article describes a problem solving algorithm. The system of initial differential equations is solved using difference analogs. Typical difference equations for regular and boundary points are provided.
 Results. The analysis of a composite free-lying beam on an elastic foundation illustrates the proposed approach. The qua-lity of the analysis results is controlled by performing a numerical study of the solution convergence using several nested meshes.
 Conclusions. The proposed method can be used in the engineering practice of design organizations and the educational process of higher educational institutions training civil engineering specialists.