The Pipes–Pagano-problem revisited: Elastic fields in boundary layers of plane laminated specimens under combined thermomechanical load

This paper addresses the development of a layerwise variational approach to free-edge effects in layered plates with arbitrary layups under thermomechanical load. In the course of this method, the physical layers of the laminate are discretized into an arbitrary number of mathematical layers through the plate thickness in each of which a C0-continuous displacement field is formulated. Beside terms corresponding to Classical Laminate Plate Theory, the layerwise displacement fields consist of unknown inplane functions in the layer interfaces and a linear interpolation through the layer thickness. The inplane functions are governed by systems of coupled Euler–Lagrange second order differential equations which are derived from the principle of minimum elastic potential and which in the presently considered cases allow for a closed-form analytical solution. The boundary conditions of traction free laminate edges are satisfied in an average sense by using an integral formulation. The present approach is straightforwardly applied, requires astonishingly low computational effort and is in excellent agreement with the results of other authors. Even though a discretization scheme is employed, the method allows for closed-form solutions for all state variables in the considered laminate which renders this approach a semi-analytical methodology.