Abstract
An analytical method to determine the interlaminar stresses in laminates with ply drop-offs is presented. The mechanisms that cause interlaminar stresses are identified and divided into effects due to global and local discontinuities. The former type of discontinuity arises due to the overall laminate construction, such as the differences in laminate properties from the undropped region to the dropped region and due to the termination of the plies. The latter type of discontinuity arises due to the geometric and related details of the ply drop-offs in the drop-off region. In the current work, the interlaminar stresses due to the global effects of ply drop-offs are obtained via consideration of a simplified model of a laminate with ply drop-offs based on the assumption that the drop-off zone has no effective length and that the load transfer from the terminated plies to the continuous plies occurs completely in the undropped region. Mathematically, closed-form expressions for the interlaminar stresses are obtained by assuming a priori a set of admissible stress fields that depends on known functions in the thickness direction and arbitrary functions in the lengthwise direction. The principle of minimum complementary energy along with appropriate boundary conditions are then used to obtain the final form of the interlaminar stresses. The results from the current work are validated through comparisons with results from previous finite element analysis from the literature for a free-edge problem, which the current method can also be used to analyze, and for laminates with external and internal ply drop-offs. The current method allows one to obtain the overall stress field efficiently and, thus, can be used to examine many different laminate configurations. The contribution to the overall stress field due to the global effects of ply drop-offs and its importance as well as possible extensions to obtain more accurate local stress fields are discussed.
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