Bending of multilayer beam slabs lying on an elastic half-space

Mathematical models and analytical methods for solving contact problems of multilayer beam slabs lying on an elastic base are developed, considering the reactive normal and shear pressures of the base. In this case, an elastic filler is inserted between each pair of beam slabs. The rigidity of the filler placed between the slabs can differ in each layer. Each slab beam is subject to external loads and pressure of the filler. The stiffness coefficients of beam slabs are discrete and variable. The lower beam slab, which has a two-way connection with the elastic base, is under the influence (except for external loads) of reactive normal and shear pressure of the base. The mathematical model of the problem includes closed systems of integro-differential equations with corresponding boundary conditions. To solve the problem, an analytical method based on the approximation of Chebyshev orthogonal polynomials was used. The solution to the problem is reduced to the study of infinite systems of algebraic equations. The regularity of the resulting infinite system of equations is proven. To solve it, the reduction method was used. A test example is considered and a numerical solution to algebraic equations is obtained. The internal force factors arising in the beam slab are also investigated. Based on the analysis of numerical results, some new results were identified, i.e., a significant influence of the filler and the reactive pressure of the base on the internal force factors of the beam slab, etc.