SPECIFIED CALCULATION OF COMPOSITE PLATES ON THE ELASTIC BASIS UNDER THE ACTION OF LOCALIZED LOADS

Abstract

The qualitative and reliable calculation of plates on elastic bases is one of the main elements of the design of complex building constructions. There is an extremely large number of calculation methods, that are not always perfect. These mathods do not provide clear answers to important issues arising in building constructions. These questions relate to both problem. The first of this problem consists of the choosing models of elastic bases. The second problem consists of choosing of calculation models of shells and plates. In particular, in most cases, shells and plates, which are used in building structures, are anisotropic. So, the choice of their design models for such elements is an extremely important issue. The paper is aimed at the axisymmetric problem of bending an infinite transversal-isotropic plate on an elastic basis (elastic half-space), which can be the models of road slabs or airfield pavement, which are under the action of localized loads. On the basis of the equations of the generalized model of transversally isotropic plates, the solution of problem for the case of the plates on elastic bases is obtained. This solution corresponds to the case of the influence of localized loads. The contact displacements and stresses on the section surface are determined with accounting for the deformation of the transverse shear and compression. Obtained results coincide with the results of the classical theory of thin plates, when in the obtained equations are neglected by the listed refinements. The obtained results coincide with S. Lukasevych’s results, when in the given formulas the members, which are corresponded transverse compression deformations, do not accoun for. Values of the contact displacements and pressures in the boundary of the plate and the elastic basis, which depend on the ratios of their modulus of elasticity, is summarized in the comparative table and the corresponding figures. Механіка та математичні методи / Mechanics and mathematical methods No1, 2019 Стор. 35-45 / Page 35-45 ________________________________________________________________________________ ________________________________________________________________________________ Шваб’юк В. І., Ротко С. В., Бондарский О. Г., Шваб’юк В. В. https://doi.org/10.31650/2618-0650-2019-1-1-35-45 36 The obtained results indicate that the classical theory of thin plates gives very low values of the contact displacements and pressures compared with the results of the refined theory of transtropic plates of medium thickness.