Mixed shell element for static and buckling analysis of variable angle tow composite plates

A mixed quadrilateral 3D finite element, obtained from the Hellinger-Reissner functional, is presented for linear static and buckling analyses of variable-angle tow (VAT) composite plates. Variable-angle tows describe curvilinear fiber paths within composite laminae and are a promising technology for tailoring the buckling and post-buckling capability of plates. Due to the variable stiffness across the planform of the VAT plates, pre-buckling stresses can be tailored and redistributed towards supported edges, thereby greatly improving the buckling load. A linear mixed element called MISS-4 is used as starting point for this work. The element presents a self-equilibrated and isostatic state of stress. The kinematics lead to element compatibility matrix calculations based solely on the interpolation along element edges. The drilling rotations do not require penalty functions or non-symmetric formulations, thus avoiding spurious energy modes. The buckling analysis is reliably performed via a co-rotational formulation. In this work VAT plates with linear fiber angle variation in one direction, and constant stiffness properties in the orthogonal direction are studied. Numerical examples of VAT plates subjected to different loads and boundary conditions are investigated herein. The convergence of displacements, stress resultants and buckling loads are presented, and comparisons with numerical results, obtained using the S4R finite element of Abaqus and the pseudo-spectral Differential Quadrature Method, are shown.