hp-Spectral Finite Element Analysis of Shear Deformable Beams and Plates

There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized displacements have suffered from shear locking, which has been alleviated with the help of primarily reduced/selective integration techniques to obtain acceptable solutions [1-4]. These kinds of 'fixe's have come into existence because the element stiffness matrix becomes excessively stiff with low-order interpolation functions. In this study we propose an alternative spectrally accurate hp/spectral method to model the Timoshenko beam theory and first order shear deformation theory of plates (FSDT) to eliminate shear and membrane locking. Beams and isotropic and orthotropic plates with clamped and simply supported boundary conditions are analyzed to illustrate the accuracy and robustness of the developed elements. Full integration scheme is employed for all cases. The results are found to be in excellent agreement with those published in literature.