The finite elements approximation has been analyzed. The shifted penalization and the method of nonsmooth optimization can be used in order to obtain numerical results. C. Chinosi, L. Della Croce and T. Scapolla Hierarchic finite elements for thin plates and shells. We consider the numerical approximation of thin plate and shell structures. The plate model is described following the Reissner-Mindlin assumptions while the shell is described using the Naghdi formulation.
Plates exhibit shear locking and shells show both shear and membrane locking.
Several techniques to avoid the numerical locking have been proposed. Here we solve the problems using a family of high order hierarchic finite elements. We present several numerical results that show the robustness of the finite elements, able to avoid in many circumstances the locking behavior. T.W. Chiu and A.H. Berney. Absolute instabilities of a finite length vortex street with external axial velocities.