On the Strain–Stress State of Locally Loaded Layered Composite Slabs

Two versions of the semi-analytical finite-element method are developed within the framework of the three-dimensional theory of elasticity. In the first version, the unknown functions are subject to a polynomial finite-element approximation in the planar coordinate X, expanded into Fourier series in the coordinate Y, and are approximated by known polynomials in coordinate Z (thickness). In the second version, linear polynomials are used for the approximation in the coordinate X and the Fourier series are applied in the coordinate Y. The distributions of the unknown functions over the thickness are obtained by analytically solving the appropriate system of differential equations. The reason of developing the two versions of the method is their approximation and arithmetic errors. The stress–strain state of a layered composite slab under local normal and tangential loading is calculated. The site of load application is square with side length equal to the slab thickness. Three types of boundary conditions on a slab bottom surface (free, clamped and resting on an elastic foundation) are considered.