Elastic Analysis of Three-Layer Concrete Slab Based on Numerical Homogenization with an Analytical Shear Correction Factor

Sandwich structures are widely used in construction, as well as in the aviation, spaceship, and electronics industries. The interesting result, among others, is the fact that individual layers can be freely selected to meet the planned requirements. In the case of sandwich structures in construction, they must meet the requirements of load-bearing capacity, thermal, and acoustic insulation, and additionally, they must be resistant to biological and chemical corrosion. The paper presents calculation algorithms for Hoff’s three-layer panels. In the first case, the well-known and proven method of finite differences in variation terms was used, assuming actual geometrical and material parameters. In the second case, the numerical homogenization method of the layered panel was used, replacing the stiffnesses of individual layers with a homogeneous equivalent plate with substitute stiffness corrected in shearing by an analytically derived shear correction factor. A comparative analysis of the results of the calculations with the use of both approaches was carried out. A good agreement between the displacement values and the calculated cross-sectional forces was obtained. On this basis, it can be assumed that the static analysis of a slab by simplified methods using numerical homogenization with an analytical shear correction factor is appropriate and can be applied to layer structures.