Large deflections and stability FEM analysis of shear deformable compressed anisotropic flat panels

This paper deals with the non-linear analysis of multilayered axially compressed plates in the static elastic conservative cases. A finite element model based on a Reissner-Mindlin theory involving von Kármán nonlinearity is developed. Results related to the classical Kirchhoff plate approximations are obtained via application of a penalty technique to the shear correction factor. The numerical investigations have concerned the large deflections and postbuckling behaviour of symmetrically and non-symmetrically anisotropic flat panels. The main conclusions are: (1) the non-linear effects very much depend on lay-up and boundary conditions, moreover for the asymmetric laminated long plates the snapping-type instability occurs; (2) the shear deformation effects are very much subordinate to both multilayered lay-up and load levels, furthermore they are greater in the large deflections field; (3) it has been observed that in the neighbourhood of a singularity (of buckling point type) of the tangent stiffness matrix, the use of an arc-length type algorithm could lead to a new buckled path and that happens without employing an appropriate turning bifurcation algorithm with an accompanying eigenvalues calculation, but via a non-convergent iteration in the loadstep.