Analysis of isotropic and composite laminated plates and shells using a differential quadrature hierarchical finite element method

A p-version curved composite laminated shell element has been developed using the modified high order bases of a differential quadrature hierarchical finite element method (DQHFEM). The theoretical model of the shell is based on a layerwise theory with linear expansion in each layer. Exact geometry is established using the CAD technique of Non-Uniform Rational B-splines. As a result, the FEM discretization errors of geometry are eliminated. To solve the coupling difficulty of elements with different parameterization that commonly exists in complicated models, a novel method based on interpolation on arc length coordinates is proposed in this work. Even though the computational efficiency based on a layerwise theory is not as fast as those based on the equivalent single-layer theory, it produces as accurate results as the 3D theory and uses less DOFs as well as less input data than the 3D model. Additionally, because of the high convergence rate of the p-version FEM and the exact representation of the geometric model, the present elements are expected to produce more accurate results than the conventional h-version flat shell elements with the same number of DOFs. Numerical examples are provided to illustrate the accuracy as well as versatility of the present elements.