Contact problems of multilayer slabs interaction on an elastic foundation

Abstract

Abstract A mathematical model and a method to assess the internal force factors in multilayer strip – slab on elastic foundation under various static loads were developed in the paper. A detailed review of well-known publications on assessing the stress-strain state and dynamic behavior of various structures interacting with the base is given. A closed system of integro-differential equations describing the strain process in multilayer slabs on an elastic foundation was derived. The problem under consideration was reduced (using the Chebyshev polynomial) to the solution of infinite systems of algebraic equations. The regularities of infinite systems of algebraic equations were proved and the corresponding estimates were obtained. A number of terms of the Chebyshev polynomial for obtaining a solution to the problem with the required accuracy was determined. The efficiency of the method was shown on the example of test problems.