Deformation of multilayered physically nonlinear concrete slabs by quasi-static loads

Abstract

Three-layer concrete slabs are considered where each layer is formed of its concrete grade. These slabs are widely used in the construction industry, particularly in the construction of agricultural buildings and structures; thus, calculating these slabs under the external loads and forces caused by their weight is an important and relevant task. It is assumed that the concretes are non-linearly formed, and the ratios between stresses and strains are taken as the third-order polynomials with different coefficients for the different grades of concrete. The slabs are supposed to be sufficiently thin, and the Kirchhoff-Lyav hypotheses are valid. The equations of the Genka-Ilyushin deformation theory are used as the equations for the state of phase materials of the considered hybrid slabs. The complete systems of resolving equations are obtained, the equations are solved by the Bubnov-Galerkin method, and the resulting systems of algebraic equations are solved numerically in the Maple mathematical package. The graphs of the slabs' deflection and the deformation values at each point of the slab are obtained. The significant difference is shown in the maximum deflections and deformations with and without considering the slab's weight.