Abstract
The paper deals with the problem of studying the static equilibrium of thin orthotropic rectangular plates resting on a three-parameter elastic base. To solve this problem, a mathematical model of a thin reinforced concrete slab as a homogeneous orthotropic plate with an averaged Huber's modulus is constructed. A mathematical model of a three-parameter elastic foundation is proposed, taking into account the friction between the lower surface of the plate and the foundation. The developed method for analyzing the equilibrium of such plates allows obtaining an exact solution of the equilibrium equation, taking into account the boundary and surface conditions at individual nodes. During the numerical implementation of the developed approach, a procedure for generating such nodes is proposed. The solution of the equilibrium equation is presented as the sum of the deflection force functions and its shape functions multiplied by unknown parameters, which are interpreted as the degree of freedom of the plate. This approach made it possible to satisfy the boundary and surface conditions with high accuracy. On the basis of the obtained solutions, the stress-strain state of a thin homogeneous orthotropic square plate completely clamped along the contour is analyzed for the case when the plate is subjected to a distributed load on its upper part and rests on an elastic base. On the basis of the solutions obtained in this work and formulas obtained by other authors, a comparative analysis of the results for the case of three types of elastic bases is carried out: a three-parameter base, a Winkler base, and a plate with a free bottom surface. Based on numerical calculations, it was found that the elastic base significantly reduces the deflection, tilt and moment in the plate. The results obtained for the Winkler model and the three-parameter model differ by 3% and 1,5% for deflections and moments, respectively. It is established that the results obtained within the proposed model practically do not depend on the coefficient of friction between the lower surface of the plate and the foundation.
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