Quadrilateral shell finite element for analysis of thin-walled reinforced concrete structures

The paper presents the quadrilateral finite element for analysis of thin-walled reinforced concrete structures. The deformation theory of plasticity, formulated in terms of residual strains, is applied for behavior simulation of the both: concrete and steel. Such an approach allows us to simulate a cyclic loading as well as a dynamic one. The stress - strain diagram, proposed by the European Committee on concrete, is used for the compressed zone of concrete. The degradation, caused by the formation of cracks in the tensile zone, is described by the descending branch of the diagram. The symmetric stress-strain diagram, or its exponential approximation, is applied for steel. The compatibility of strains for concrete and steel is adopted. Reinforcements of the given direction are considered as a layer, which works only for compression-tension in this direction. The reinforcements of each direction are presented as a separate layer. We allow for the discrete placement of rods over thickness of the cross section. The Mindlin Reissner shell theory is used for the reduction of a 3D problem to a 2D one; and the mixed interpolation of shear tensorial components is applied to overcome a shear locking effect.