Improvement of Calculation Technique for Flexible Orthotropic Plates on Elastic Base. Part 1: Calculation Theory

The paper considers a rectangular orthotropic insulated slab on an elastic foundation, modeled by an elastic homogeneous isotropic layer rigidly connected to a non-deformable foundation. Elastic and nonlinear calculations of this plate opening. The calculation of a flexible orthotropic slab on an elastic foundation in a nonlinear formulation is carried out iteratively by the method of B. N. Zhemochkin. To determine the coefficients of the canonical equations and free terms, a mixed method of structural mechanics was used. The deflections of a slab with a pinched normal in the main system of the mixed method due to the action of a concentrated force are determined by the Ritz method when the deflections are represented as a power polynomial in a new original expression, which is proposed by the author for the first time in the studies. This expression satisfies not only the boundary conditions of the pinched slab in terms of displacements, but also the biharmonic equation. In nonlinear calculations, when finding the variable (secant) stiffness for the Zhemochkin section,  at each iteration, the “stiffness – curvature” dependence is used for each of the X and Y directions, approximated by a nonlinear function, the nature of the dependence of which graphically indicates the nonlinear-elastic operation of the orthotropic plate and its deformation taking into account crack formation and crack opening. The algorithm for the above solution is implemented using the Wolfram Mathematica 11.3 computer program.

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