A Unified Formulation for Multilayered Plate Elements based on PVD and RMVT

摘要

This paper presents a uni ed formulation of classical and re ned nite, plate elements for bending and vibrations analysis of layered composites structures. Classical formulation which are based on displacement assumptions and Principle of Virtual Displacement (PVD) applications, are compared to advanced mixed elements which are formulated on the basis of Reissner's Mixed Variational Theorem (RMVT). Finite elements which preserve the independence of the number of the independent variables from the numbers of the ?? ?layers (Equivalent Single Layer Models) as well as those elements in which the number of the unknown variables remains ?? ?dependent (Layer Wise Models) are both considered. Linear up-to-fourth order expansions in the thickness direction are treated for the unknown stress and displacement variables. Extensive use of indicial notations has been made. As a results nite element matrices have been all written in terms of a few fundamental nuclei which have only terms. Some results have been proposed to assess and compare the implemented elements. It is shown that the a priori ful llment of the interlaminar continuity for transverse stresses makes mixed models more attractive than other available models that violate such a continuity.