Axiomatic/asymptotic evaluation of multilayered plate theories by using single and multi-points error criteria

This paper deals with refined theories for multilayered composites plates. Layer-Wise (LW) and Equivalent Single Layer (ESL) theories are evaluated by means of axiomatic–asymptotic approach. Theories with forth order displacement fields in the thickness layer/plate direction z are implemented by referring to the Unified Formulation by Carrera. The effectiveness of each term of the made expansion is evaluated by comparing the related theories with a reference solution. As a result a reduced model is obtained which preserve the accuracy of the full-model (model that include the whole terms of the z-expansion) but it removes the not-significant terms in the same expansion (those terms that do no improve the results according to a given error criteria). Various single-point and multi-point error criteria have been analyzed and compared in order to establish such an effectiveness: error localized in an assigned point along z, error localized at each interface, error located at the z-value corresponding to the maximum value of the considered variables, etc. Applications are given in case of closed form solutions of orthotropic cross-ply, rectangular, simply supported plates loaded by bisinusoidal distribution of transverse pressure. Symmetrically and unsymmetrical laminated cases are considered along with sandwich plates. It is found the reduced model is strongly influenced by the used localized error and that in same case the reduced model which is obtained by of single point criteria can be very much improved by the use of multi-point criteria.