On the determination of transverse shear stiffnesses of orthotropic plates

Abstract

Since the classical Kirchhoff plate theory neglects the transverse shear strains, it does not include constitutive equations for the transverse shear force-transverse shear strain interactions. In this case, the transverse shear forces can be calculated from the equilibrium equations.¶For thick, laminated and sandwich plates, the transverse shear strains should be taken into account and the relevant constitutive equations have a significant influence on the correct estimation of the deflections or the stress resultants, and due to this fact we need refined theories. There are two different possibilities to formulate such refined theories which are able to describe both homogeneous and inhomogeneous in the thickness direction plates. The first is based on the assumption of an equivalent single layer, the second on a layerwise formulation. Equivalent single layer theories, which limit the analysis to the estimation of global characteristics, are mostly prefered. The simplest refinement of the classical plate theory are the so-called first order shear deformation theories. The quality of such theories depends on the correct determination of the effective stiffnesses. Many theories result in identical stiffnesses for bending, tension/compression, in-plane shear and torsion. Differences can be obtained for the transverse shear stiffnesses.¶In this contribution, different proposals for the transverse shear stiffnesses with values based on a deformable directed surface theory will be compared. In the case of homogeneous isotropic plates, the transverse shear stiffness estimated due to the deformable surface theory is in agreement with Mindlin's proposal. On the other hand, for isotropic symmetric sandwiches with thin face sheets and a very soft core Reissner's approximation can be obtained.