Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations

This paper presents numerical evaluations related to the multilayered plate elements which were proposed in the companion paper (Part 1). Two-dimensional modellings with linear and higher-order (up to fourth order) expansion in the z-plate=layer thickness direction have been implemented for both displacements and transverse stresses. Layer-wise as well as equivalent single-layer modellings are considered on both frameworks of the principle of virtual displacements and Reissner mixed variational theorem. Such a variety has led to the implementation of 22 plate theories. As far as nite element approximation is concerned, three quadrilaters have been considered (four-, eight- and nine-noded plate elements). As a result, 22×3 di erent nite plate elements have been compared in the present analysis. The automatic procedure described in Part 1, which made extensive use of indicial notations, has herein been referred to in the considered computer implementations. An assessment has been made as far as convergence rates, numerical integrations and comparison to correspondent closed-form solutions are concerned. Extensive comparison to early and recently available results has been made for sample problems related to laminated and sandwich structures. Classical formulations, full mixed, hybrid, as well as three-dimensional solutions have been considered in such a comparison. Numerical substantiation of the importance of the ful lment of zig-zag e ects and interlaminar equilibria is given. The superiority of RMVT formulated nite elements over those related to PVD has been concluded. Two test cases are proposed as ‘desk-beds’ to establish the accuracy of the several theories. Results related to all the developed theories are presented for the rst test case. The second test case, which is related to sandwich plates, restricts the comparison to the most signi cant implemented nite elements. It is proposed to refer to these test cases to establish the accuracy of existing or new higher-order, re ned or improved nite elements for multilayered plate analyses.