Abstract
The present work proposes an approach to determining the linear and angular displacements of a rigid rectangular slab lying without friction on an elastic layer. The approach is based on the orthogonal polynomial method, in which the distribution of contact stresses is sought in the form of a double series of Chebyshev polynomials of the first kind with a weight, which allows one to identify a feature in the contact stresses at the slab faces. The Green’s function for the elastic layer is also expanded into a four-fold series in these polynomials using four uses of the quadrature formula. Using the orthogonality of the adopted Chebyshev polynomials with weight reduces the problem under consideration to an infinite system of linear algebraic equations, which is solved by the truncation method. Two examples are given for a rigid square plate on an elastic layer under loading by concentrated symmetrically applied force and moment. For comparison, the results of M.I. Gorbunov-Posadov are given in the case of the plate being located on an elastic half-space.
Published Version
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