Modeling of composite plates with an arbitrary hole location using the variable separation method

In this paper, a method to compute explicit solutions for laminated plate with arbitrary hole position is presented using a variable separation method. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x,y, the transverse coordinate z and the coordinates XT,YT of the hole position. As the parameterized problem involves the geometry, a mapping transformation is introduced to refer to a fixed reference configuration. This choice yields to an iterative process that consists of solving a 2D and three 1D problems successively at each iteration. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element Method is used. The functions of XT and YT are discretized with linear interpolations. Mechanical tests with different numbers of layers are performed to show the accuracy of the method and its capacity to capture local effects and 3D state of the stress near the curved free-edge.