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 sheardeformable beams and plates. mostly, the literature abounds with traditional equi-spacedlangrange based low order finite element approximations using displacement formulations.however, the finite element models of timoshenko beams and mindlin plates with linearinterpolation of all generalized displacements have suffered from shear locking, which has beenalleviated with the help of primarily reduced/selective integration techniques to obtain acceptablesolutions [1-4]. these kinds of 'fixes' have come into existence because the element stiffnessmatrix becomes excessively stiff with low-order interpolation functions. in this study we proposean alternative spectrally accurate hp/spectral method to model the timoshenko beam theory andfirst order shear deformation theory of plates (fsdt) to eliminate shear and membrane locking.beams and isotropic and orthotropic plates with clamped and simply supported boundaryconditions are analyzed to illustrate the accuracy and robustness of the developed elements. fullintegration scheme is employed for all cases. the results are found to be in excellent agreementwith those published in literature.