A new class of interdependent shape polynomials for the FE dynamic analysis of Timoshenko beam and Mindlin plate

This paper proposes a new class of shape polynomials, able of solving the well known shear-locking phenomena and the high-order time derivative effect problems which can suffer the Mindlin plate model (MPM). These polynomials eliminate the inconsistency of the higher-order spectra because are built on the consistent version of the governing equations proposed by Elishakoff. Using these equations, the new class of interdependent shape polynomials is obtained by introducing of a new kinematic variable: the fictitious deflection. The interdependence of the polynomials ensures that the corresponding FE model is free of locking. Lastly, the interdependent shape polynomials for the Timoshenko beam model (TBM) will be derived as a special case.