TWO-DIMENSIONAL THERMOELASTIC PROBLEM FOR A MULTILAYERED FOUNDATION WITH SMOOTH CONTACT BETWEEN LAYERS

Purpose. To obtain analytical expressions describing the thermo-stress-strain state of a layered plate with smooth interlayer contact, resting on a perfectly rigid half-plane, and to illustrate the influence of thermal loads on the stress distribution at its points. Research methods. The Fourier integral transform and the compliance function method are used to solve the problem. Results. An analytical solution is presented for the two-dimensional thermoelastic problem of a single homogeneous layer with boundaries free of shear stresses. The solution is constructed using the Fourier integral transform, which reduces the order of the problem and converts the governing partial differential equations into ordinary differential equations. The components of the thermo-stress-strain state of the layer are represented as combinations of auxiliary functions: normal stresses, vertical displacements, temperature, and heat flux at the upper boundary of the layer. Recurrent relations are obtained between the auxiliary functions of adjacent layers in a multilayered thermoelastic foundation. It is shown that the auxiliary functions of an individual layer are related to each other by linear dependencies, the coefficients of which are referred to as compliance functions. Based on the derived recurrence relations, compliance functions are obtained for the multilayered foundation under the assumption of smooth contact between the layers. As an example of practical application of the proposed method, a two-layer foundation consisting of concrete and steel layers resting on a perfectly rigid half-plane is considered. For this model, the distributions of normal stresses in the upper layer are determined, and the influence of thermal loading on their variation is analyzed. The results demonstrate that accounting for the thermoelastic properties of materials significantly affects the stress formation within the layers of the foundation. The obtained findings may be used in the design of multilayer structures, particularly the foundations of transport infrastructure and buildings subjected to variable thermal fields. Scientific novelty. The compliance function method is extended to the two-dimensional thermoelastic problem of a layered foundation with smooth contact between layers. Practical value. The derived formulas can be used for the strength analysis of building foundations, industrial floor slabs, as well as airfield and pavement structures subjected to high-temperature conditions. The results may also serve as benchmark solutions for validating the proposed problem when solved using alternative methods.