A planar finite element formulation for corrugated laminates under transverse shear loading

This paper contributes a planar finite-element unit-cell formulation based on the principle of virtual displacements for simulating the structural as well as the local transverse-shear response of thick-walled corrugated laminates. The theory observes that bending-strain gradients are invariable under constant internal force held in equilibrium by the transverse shear stresses in the corrugated cross-section. It is explained how the load information is transmitted by macro strains which are valid for arbitrary laminates. The unit-cell model assumes periodicity of the corrugation pattern and homogeneity of the global load. Postprocessing aspects include best-fit of the warped cross-section to a vertical plane and extrapolation of the secondary solutions with quadratic polynomials fitted to results at the Barlow points of a Lagrange type finite element with cubic shape functions. Simulation results with the proprietary software show peculiar stress redistributions and it is explained how these are caused by an interplay of geometry, equilibrium, and homogeneous natural boundary conditions. A convergence study along with model verification is included.