The modal behavior of the MITC3+ triangular shell element

•The static modal behavior of the MITC3+ shell element is investigated in detail.•We provide insight into how shear locking occurs on the mode level.•The performance of the MITC3+ shell element is presented in dynamic mode solutions. In this paper, we investigate the static and dynamic modal behavior of the MITC3+ triangular shell element (Lee and Bathe, 2004; Lee et al., 2014). We focus on bending-dominated situations because such shell problems are particularly difficult to solve when using low-order elements. For comparison, the pure displacement-based (DISP3), MITC3 and MITC4 shell elements are also studied. First, static mode solutions are performed for a single right-angled shell element and an assemblage of two right-angled shell elements. The detailed strain fields are established in the bending modes. This study provides insight into how shear locking occurs on the mode level. We then analytically show how the MITC3+ shell element properly represents the pure bending conditions in a two-sided clamped plate problem. Considering free plate and free hyperboloid shell problems, we finally present the excellent performance of the MITC3+ shell element in dynamic mode solutions.