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. (2000). 73K10, 73K20. Mathematics Subject Classification

On the bending of viscoelastic plates made of polymer foams

“…In the case of isotropic and symmetric over the thickness plates the effective stiffness tensors have the following structure [5][6][7]38]:…”

“…Such a model can be accepted in the case of plates with constant or slowly changing thickness. For the linear variant the identification of the elastic stiffness tensors considering changing properties was proposed in [4][5][6]. Using the techniques presented in these articles the static boundary-value problems for FGM plates made of metal foams which behave elastically are solved in [7].…”

On the Eigenfrequencies of an Ordered System of Nanoobjects

“…In [1][2][3]23] a new approach to the determination of the effective stiffness tensors was proposed. The idea of this approach is based on the comparison of the exact solutions of the three-dimensional elasticity and the corresponding solutions of Equations (1)- (6) for several test problems of the elastostatics such as tension and bending, plane shear, and torsion.…”

“…From this point of view they may consider the nanocomposite based on an oriented array of nanocrystals or nanotubes as a transversally isotropic material. We propose to extend the procedure [1,2,23] to the case of such materials. Finally, one obtains the components of the effective stiffness tensors which depend not only on the bulk elastic properties and the thickness of the plate but also on the surface tension.…”

“…In the last section of this paper we discuss the methods of identifications of elastic properties of a nanocomposite plate using the approach [1][2][3]23]. …”