Non-Linear Analysis of Composite Plates and Shells Using a New Shell Element

One of the most popular approaches in the finite element analysis of plates and shells is using an assemblage of facet triangular elements built by combining a membrane and a plate bending element to model the curved surface. Due to the lack of a drilling degree of freedom in most triangular membrane elements, these elements may cause rotational singularity in the stiffness matrix. One approach to overcome this problem is using membrane elements with in-plane (or drilling) rotational degree of freedom. Although some elements with drilling degree of freedom have been derived, most of them suffer from aspect ratio locking. Recently, Felippa [

1

] developed an optimal membrane element with drilling degree of freedom. Its response for in-plane pure bending is not dependent on the aspect ratio. There are several triangular plate bending elements to combine with a membrane element. Batoz et al. [

2

] studied several triangular Kirchhoff plate bending elements and showed that Discrete Kirchhoff Triangle (DKT) [

3

], is the most reliable triangular element for analysis of thin plates. Katili [

4

] developed a discrete Kirchhoff-Mindlin triangular plate bending element called DKMT which is capable to include the transverse shear effects in thick plates, and coincides with the DKT element in case of thin plates. As a result, both thin and thick plates can be modeled with this element.

In the present work, a new shell element for both thin and thick plates is developed by combining the DKMT plate bending element and the optimal membrane triangular element (also called OPT). The membrane-bending coupling effect of composite laminates is incorporated in the formulation, and inconsistent stress stiffness matrix and tangent stiffness matrix are formulated. Using co-rotational method and the tangent stiffness matrix, this new shell element is used to solve problems with geometric nonlinearity and the results are compared with analytical solutions or those available in the literature. The behavior and advantages of the new element are studied.