Refined discrete quadrilateral degenerated shell element by using Timoshenkoʹs beam function

A refined discrete degenerated 20-DOF quadrilateral shell element RQS20 is proposed. The exact displacement function of the Timoshenko’s beam is used as the displacement on the element boundary. The re-constitute method for shear strain matrix is adopted. The proposed element 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. Numerical examples presented show that the new model indeed possesses higher accuracy in the analysis of thin and thick plates/shells, and that it can pass the patch test required for the Kirchhoff thin plate elements. Most important of all, it is free from the membrane and shear locking phenomena for extremely thin plates/shells, on the one hand, and it can also avoid the phenomenon of oscillatory solutions for thick plates/shells case on the other.