A Cell-based MITC3+ Flat Shell Element for Frequency Analyses of Plates and Shells Using Substructuring Methods

A cell-based three-node triangular flat shell element with a bubble node is introduced to analyze frequencies of plates and shells. By smoothing the in-plane strains on sub-triangular domains created by connecting the bubble node to element nodes and applying the divergence theorem to derivatives in the gradient matrices, the integration of corresponding stiffness matrices are transformed from surface to line integrals. To remove the shear locking, the MITC3+ technique for three-node triangular degenerated shell elements with a bubble node is employed. The Craig-Bampton (CB) and enhanced Craig-Bampton (ECB) methods, which are well-known reduced-order modeling techniques based on substructuring strategy, are used for efficiently solving frequency analyses. Numerical results demonstrate the reliability and superiority of the present element, called CS-MITC3+, when combined with the substructuring methods to compute frequencies of plate and shell structures.