Static analysis of a two-layer beam with a flexible interlayer connection

Abstract

This research aims to develop an algorithm that allows for the analysis of the influence of interlayer connections on the static responseof double-layer beams. Since their construction uses the advantages of different materials, multilayer beams are widely used in the constructionindustry. The critical element of these types of structures is the connection between layers, the stiffness of which can significantly affect thestatic response of the system, and therefore its strength. The Euler-Bernoulli model was used to describe the double-layer beams. In the paper,the compliance of normal displacements in multilayer and double-layer beams was considered based on the research of other authors. It wasalso assumed that the tangential interactions at the connection of layers were tangential forces that are proportional to the relative tangentialdisplacement (slip) of these layers. This general approach eliminates the need for a broader analysis of the connection (its description andstructure) with regard to the applied “connector” between the layers. Using equilibrium equations and the adopted assumptions, a system ofdisplacement equations was derived. This system is formed by three coupled second- and fourth-order differential equations, the exact solution ofwhich is a nontrivial mathematical problem. This system was solved using the finite sine and cosine Fourier transform. Although the algorithmpresented in the paper was used to solve a specific set of equations that describe a simply supported beam, the formulas derived in the paperallow for solving beams with other support schemes. The Fourier transformation method, after appropriate modifications (changing the boundaryconditions and, in some cases, changing the sine to cosine transformation and vice versa), can be used to solve beams that have other supportconditions. To verify the correctness and effectiveness of the described method, two numerical examples were solved. In the first one, theinfluence of the variable value of the tangential stiffness of the connection on the values ??and distribution of internal forces (including theinfluence on the values ??of normal stresses) was analyzed. In the second example, calculations were performed for an example taken from theliterature, and the obtained results were compared with the results obtained by other authors. The analyzed examples confirmed the significantinfluence of the tangential stiffness of the layer connection on the static response of the system. Furthermore, they confirmed the correctness andhigh accuracy of the method that was used to solve the problem.