Reddyʹs layerwise laminate plate theory for the computation of elastic fields in the vicinity of straight free laminate edges

Reddyʹs layerwise laminate plate theory is employed for the closed-form analysis of free-edge effects in layered plates of arbitrary non-orthotropic layups. The approach consists of the subdivision of the physical laminate layers into an arbitrary number of mathematical layers through the plate thickness. In each interface, a set of unknown displacement functions with respect to the inplane width coordinate is introduced while in the thickness direction layerwise linear Lagrangian interpolation polynomials are employed. The unknown inplane functions are determined from the governing Euler–Lagrange differential equations, derived from the principle of minimum potential energy. A solution approach in the form of decaying exponential functions leads to closed-form analytical representations for all free-edge state variables in a straightforward manner while in the inner laminate regions, the stress state corresponding to Classical Laminate Plate Theory is recovered exactly. The present approach is applicable on a standard personal computer, needs insignificant computational effort even in cases of thick laminates consisting of a high number of layers and is in excellent agreement with reference results from the literature.