On the Analytical Modelling, Global Optimization and Experimental Investigation of the Free-Edge Effect in Composite Laminated Shells

  • Kappel, Andreas (Darmstadt University of Technology)
  • Mittelstedt, Christian (Darmstadt University of Technology)

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The development of efficient computational models concerning the accurate prediction of the optimal layup for general composite laminated shells undergoing different types of thermomechanical loadings is a major challenge, especially when stress concentration phenomena such as the free-edge effect have to be considered. This paper addresses this issue by introducing a semi-analytical approach for the assessment of the three-dimensional stress field in circular cylindrical composite shells with arbitrary layups. The computational model superimposes a novel closed-form analytical solution with a higher-order, displacement-based layerwise approach and the governing equations are derived by means of the minimum total potential energy principle. Enforcing traction-free boundary conditions finally leads to a formulation which enables the full-scale stress assessment in composite laminated shells. A comparison of the numerical results of the presented semi-analytical method with finite element simulations for various structural situations indicates that the developed method works with high accuracy, although being extremely efficient in terms of computational resources. In combination with a restricted, meta-heuristic optimization algorithm, wherein the design variable and the objective function are characterized by the fibre orientation of each lamina and the three-dimensional stress field, it is finally possible to get a detailed insight into the free-edge effect and especially its influence on the fracture behaviour of thick composite laminated shells undergoing thermomechanical loadings. The theoretical results are compared with experimental investigations of L-shaped composite laminates undergoing four-point bending loads and it is found that the global optimization algorithm in conjunction with the highly efficient semi-analytical approach can minimize the delamination tendency and thus can deliver the optimal layup for the considered structural situations.