Analysis of thickness locking in classical, refined and mixed multilayered plate theories

Abstract

Abstract This paper discusses the thickness locking (TL) mechanism, also known as Poisson locking, which is caused by the use of simplified kinematic assumptions in the plate analysis. Bending and vibration problems have been analyzed for isotropic, orthotropic and multilayered, composite plates. TL has been investigated for a large variety of plate theories: thin plate theory (TPT), First order shear deformation theory (FSDT), higher order theories (HOT), mixed theories and layer-wise (LW) theories. Transverse normal stress σ zz and strain ϵ zz zero conditions are discussed. Penalty numbers have been introduced to force ϵ zz = 0 condition in the three-dimensional solution and refined plate theories. The unified formulation has been used to implement the whole considered plate modelings. Analytical closed form solutions have been considered. A comprehensive numerical investigation has been performed. The following main conclusions have been acquired. (1) TL is strongly due to the coupling between transverse normal strain and in-plane strain in the constitutive law (Poisson effect). (2) TL appears if and only if transverse normal strains ϵ zz are assumed constant in the thickness directions (that happens for TPT, FSDT and HOT with constant and linear transverse displacement expansion in the thickness direction). (3) TL can lead to large error (about 25% for deflections and 15% for circular frequency) in thin, isotropic plate analysis. (4) TL reduces significantly in orthotropic and laminated plates. (5) The use of LW models introduces benefits vs TL. (6) Mixed methods do not make any improvements with respect TL. (7) Penalties technique on elastic coefficients can be efficiently used to enforce ϵ zz = 0 conditions in 3D solutions as well as in HOT, mixed and layer-wise plate theories.