Nonlinear analysis of a crossing-beams system on an elastic with usage of the Mathematica software

Belarusian State University of Transport, 246653 Gomel, Belarus

^* Corresponding author: kozunova@gmail.com

Abstract

In this paper, the authors consider the method of calculating an infinite system of cross beams on an elastic base by the variationaldifference method. The system of cross beams on an elastic base is most often modeled as shallow strip foundations for buildings of various functional purposes. The variation-difference method is one of the numerical and analytical methods for calculating building structures, it is based on the variational principles of the Ritz-Timoshenko method and on the minimum of the total potential energy of the entire system according to the Lagrange principle, and is also close to the real operating conditions of the foundation – base. A single-layer isotropic artificial base was used as an elastic base in the work, as an elastic layer limited in thickness. The algorithm of nonlinear calculation is based on the use of the iterative method of elastic solutions. The physical nonlinearity of the material of reinforced concrete beams is taken into account through the asymptotic dependence “Moment-curvature”. Numerical approbation of the results of elastic and nonlinear calculations of the system of cross beams on an elastic base was carried out using the MATHEMATICA software package.