A layer-wise plasticity-based approach for the analysis of reinforced concrete shell structures using a mixed finite element

The analysis of reinforced concrete shell structures accounting for material nonlinearity is addressed. The structural response is numerically evaluated using a mixed shell finite element and a plasticity-based material behaviour. The finite element is a quadrilateral with four nodes and is based on self-equilibrated assumed stresses. The kinematic fields are interpolated only along the element boundary by polynomials up to the third order. The generalised shell stresses are evaluated through layer-wise integration of the Cauchy pointwise stresses. This allows appropriated three-dimensional elastoplastic constitutive equation to be employed and to include multiple reinforcing layers. The integration of the constitutive laws is performed using a dual decomposition method which preserves the assumed stress interpolation. Results, including civil engineering applications, show that the proposed approach is reliable and accurate in evaluating the static nonlinear equilibrium path. Additionally, the mixed finite element shows a quadratic rate of convergence in the collapse load and low error even for coarse meshes.