A CS-MITC18+ flat shell element for static and frequency analyses of laminated composite plate and shell structures

A new cell-based smoothed three-node triangular flat shell element is developed in this study to analyze laminated composite plates and shells based on the first-order shear deformation theory. The proposed flat shell element has 18 degrees of freedom with the truly drilling degrees of freedom derived from the Allman-type displacement approximations. The bending behaviors are represented by the C⁰-type displacement approximations enriched by the cubic bubble function. The membrane and bending strains are smoothed on the sub-triangular domains defined by the straight lines connecting the elements’ nodes to the bubble nodes at the centroid. This cell-based smoothed approach transforms the numerical integration of the membrane and bending stiffness matrices from the surfaces to boundary lines of the sub-triangular domains. The transverse shear strains are re-interpolated according to the MITC3 + technique to overcome the shear locking phenomenon. The accuracy and convergence of the suggested flat shell element, namely, CS-MITC18+ element, are evaluated through several laminated composite plates and shells discretized by regularly or irregularly triangular mesh. Numerical results show the excellent performance of the new CS-MITC18+ flat shell element in the static and frequency analyses of the various laminated composite plate and shell structures.