A 4-node quasi-conforming Reissner–Mindlin shell element by using Timoshenko's beam function

In the paper, we propose a new 4-node quadrilateral shell element with six degrees of freedom per node within the framework of assumed displacement quasi-conforming method. In order to improve membrane behavior, the drilling degrees of freedom are added. The exact displacement function of Timoshenko's beam, from which the interpolated inner-field function is derived, is used as the string net function on the element boundary in the bending part. The re-constitution technique for the shear strain terms is adopted. The proposed element preserves all the advantages of the quasi-conforming method: explicit stiffness matrix, convenient post processing and free from membrane locking and shear locking, which can be used for the analysis of both moderately thick and thin plates/shells, and the convergence for the very thin case can be ensured theoretically. The numerical tests and comparisons with other existing solutions in the literatures suggest that the present element is efficient and accurate.

► We present a 4-node flat shell element within the framework of assumed displacement quasi-conforming technique.
► The drilling degrees of freedom are added to improve membrane behavior.
► Timoshenko's beam function is used as the string net function in the bending part.
► The re-constitution technique for the shear strain terms is adopted.
► Several numerical examples are presented, and the results are in good agreement with references.