Semi-analytical Model for the Close-Range Stress Analysis of Transverse Cracks in Composite Plates

In this paper, an efficient method for the computation of the stress state in the vicinity of transverse cracks in symmetric fibre-reinforced composite laminated plates under tensile load is presented. To determine the stress field, the solution of the Classical Lamination Theory (CLT) of the uncracked structure is superimposed with a so-called “internal solution” which is based on a subdivision of the layers into an arbitrary number of numerical plies. The displacement field of the composite laminated plate is approximated by introducing a priori unknown interface displacement functions. By employing the principle of minimum total potential energy, the governing equations are obtained in a closed-form manner and yield a quadratic eigenvalue problem, which is solved numerically. In order to obtain a full description of the state variables, the underlying boundary conditions as well as the continuity conditions have to be utilized. Comparisons with two-dimensional finite element studies indicate that the semi-analytical method is able predict the stress field with similar accuracy while only using a fraction of the underlying computational effort.