Minimizing the mass of an aircraft's structure reduces the cost of materials and manufacturing, as well as fuel consumption and atmospheric emissions. During the preliminary design when many alternative configurations and load cases need to be considered, fast and reliable analysis tools are required. The specialist software VICONOPT [1] is designed for efficient, accurate buckling and vibration analysis and optimum design of plates and panels. VICONOPT avoids the modelling and computational costs of finite element analysis by employing the exact stiffness analysis and the Wittrick-Williams algorithm. Previous work has enabled the incorporation of damage such as delaminations in composite structures to study their effect on the buckling and post buckling behaviour but the type of delamination which could be studied was limited.

In this paper a novel hybrid method uses VICONOPT to model the undamaged parts of the structure in combination with finite elements (FE) in the area of the damage. Specifically, VICONOPT is used to calculate exact dynamic stiffness matrices for undamaged rectangular strips, while the FE method is used to calculate the stiffness and mass matrices for a rectangular strip containing the damaged region. The vibration behaviour of composite plates containing delaminations of different sizes and positions is studied. The results show the ability of the hybrid method to handle through-the-length delaminations efficiently. Further results for a plate containing a single rectangular delamination are compared with a smeared method [2] and an approximation method based on exact stiffness analysis. Close agreement is seen for small delaminations, but as the delamination size increases local vibration effects occur and differences are observed due to the different ways the embedded delamination is modelled. The paper will also include comparisons against results from commercial FE software.

[1] D. Kennedy, M. Fischer and C.A. Featherston, “Recent developments in exact strip analysis and optimum design of aerospace structures”, Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 221(4):399-413 (2007).

[2] M. Damghani, D. Kennedy and C.A. Featherston, “Global buckling of composite plates containing rectangular delaminations using exact stiffness analysis and smearing method”, Computers and Structures, 134:32-47 (2014).