Enhancement of MITC3+ flat shell element using curvature corrections

An enhancement of the MITC3+ flat shell element using curvature corrections is proposed. Herein, the corrected curvature field is established through the utilization of corrected nodal derivatives that satisfy the discrete divergence consistency (DCC). The concept of DDC in this study is derived from the orthogonality condition between resultant bending stress (bending moments) and curvature (bending strain) differences within the Hu-Washizu three-field variational principle. In the context of membrane behavior, we employ the Allman-like triangular element with drilling degrees of freedom (DOFs), ensuring both the true rotation of drilling DOFs within elasticity and the effective elimination of spurious energy modes. Through numerical results, the proposed method exhibits exceptional performance in addressing plate and shell structural problems, outperforming the MITC3+. Remarkably, using the constant base demonstrates the highest level of robustness.