Fast and reliable analysis of free-edge stress fields in a thermally loaded composite strip by a layerwise laminate theory

A layerwise theory for the analysis of free-edge effects in thermally loaded symmetric laminates with arbitrary layups is developed. The laminate under investigation is decomposed into an arbitrary number of mathematical layers through the thickness. The theory approach employs displacement terms according to Classical Laminate Plate Theory which are upgraded by layerwise displacement functions. The additional layerwise displacement functions consist of unknown inplane functions and linear thickness terms. The principle of minimum potential energy yields the governing Euler–Lagrange equations which allow for a closed-form analytical solution for the inplane functions, thus characterizing this method as a semi-analytical one. The underlying boundary conditions of traction free edges are fulfilled in an integral sense. The present results are in excellent agreement with accompanying finite element computations