A four-nodes shell Finite Element (FE), obtained from the Hellinger-Reissner variational principle with assumed stress and displacement fields [1, 2, 3], is reformulated for the analysis of reinforced concrete structures. The nonlinear material behaviour is described through a plastic model under the assumption of small strain/displacement fields. The structural response of the element is obtained by integration also along the shell thickness direction. The concrete is described through the confinement-sensitive plasticity-based constitutive law proposed in [4] which is a non-associated model not requiring the often difficult calibration of several parameters, but it is expressed only in terms of the uniaxial compressive strength of the concrete. At a negligible computational cost, the presence of steel rebars is computed by defining material layers contributing through a one-dimensional response. The proposed approach can be readily used for modelling additional material layers as in the case of retrofitting of existing structures. Computational efficiency and accuracy are assessed by comparing the proposed shell strategy and 3D FE models in static-nonlinear analyses.

References

[1]  Liguori, F. S., Madeo, A., "A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures", International Journal for Numerical Methods in Engineering, 122 (17), 4575-4608 (2021).

[2]  Madeo, A., Liguori, F. S., Zucco, G., Fiore, S., "An efficient isostatic mixed shell element for coarse mesh solution", International Journal for Numerical Methods in Engineering, 122 (1), 82-121 (2021)

[3]  Bilotta, A., Turco, E., "Elastoplastic analysis of pressure-sensitive materials by an effective three-dimensional mixed finite element", ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 97 (4), 382-396 (2017).