On the theory of thick slabs on an elastic foundation
Static problems are investigated covering the deformation of a thick elastic slab with an arbitrary smooth boundary that rests without friction on a linearly deformable foundation. The slab is loaded by a normal distributed load on the upper face. Lur'e's symbolic method is used to investigate the state of stress and strain of the slab. A class of homogeneous solutions corresponding to a free upper face and the condition of linear elastic-contact of the slab with the foundation on the lower face of the slab is isolated. This last condition is a relation realized by the integral operator of the contact problem for a linearly deformable foundation between the settling of the slab and the contact stress. It is shown that the homogeneous solution determined in this manner can be of three kinds: potential, vortical, and harmonic. There is also a certain elementary solution. The problem here of finding the characteristic numbers of the potential solution reduces to seeking the eigenvalues of the integral operator mentioned. The axisymmetric problem of the deformation of a thick circular slab in a Winkler foundation is considered as an example.
two-dimensional Fredholm integral equation of second kind
characteristic numbers of the potential solution
eigenvalues of the integral operator mentioned
scientific article; zbMATH DE number 4022829