On the use of transverse shear stress homogeneous and non-homogeneous conditions in third-order orthotropic plate theory

This paper discusses the influence of non-homogeneous transverse shear stresses conditions on the accuracy of plate theories formulated in terms of displacement variables. The case of a third-order plate theories is considered and the attention has been focused on cylindrical bending problems. The following three models are developed and compared: (1) the ‘original’ third model with five displacement variables; (2) the ‘reduced’ third-order model with three displacement variables obtained by imposing ‘homogeneous’ stress conditions with correspondence to the plate top-surface; (3) the modification of case 2 which considers ‘non-homogeneous’ stress conditions. Variationally consistent governing equations have been derived by employing the principle of virtual displacement in the linear-elastic, static case. Closed form solutions results have been obtained for both stresses and displacements in the case of harmonic loadings and simply supported boundary conditions. The following main conclusions have been reached by the conducted numerical investigation: The use of non-homogeneous boundary conditions lead to a general improvement with respect to model 2 results. The ‘original’ model leads in general to better response evaluation than the other two models; an exception is made for the transverse shear stresses calculated by Hooke law for which case model 3 leads to the most accurate results.