Stegantsev E. The boundary problems for the elastic multilayer foundations of the periodical structure

The thesis for the Candidate of physical and mathematical sciences degree on specialty 01.02.04 - mechanics of a deformable solid body. - Zaporozhe National University, Zaporozhe, 2009. The technique of the determination of the stresses and displacements in the layers of the elastic multilayer foundation of the periodical structure has been developed. This technique is based on Hankel integral transformation, Fourier integral transformation and the compliance function technique for the solution in quadratures of the basic boundary problems of the elasticity theory for the elastic multilayer medium. The compliance function technique has been extended to the new type of the foundations. One has considered an axisymmetrical torsion, the planar deformation and the space deformation of the multilayer foundation of the periodical structure. The singular integral equation for the contact problem of the torsion of the elastic multilayer foundation of the periodical structure has been obtained. This equation has been approximately solved with the help of the new quadrature formula, which has been obtained in the thesis. The procedure of the a priori estimation of the maximum difference between the stresses in the multilayer foundation of the periodical structure and the multilayer foundation of the stack structure under the same load has been developed. The new approach to the determination of the elastic characteristics of the two-layer foundation has been proposed. The numerical results and the new mechanical relationships have been given. Key words: elastic multilayer foundation of the periodical structure, Hankel integral transformation, Fourier integral transformation, compliance function technique, contact problem, homogenization, effective shift moduli.