Accurate Stress Fields in Composite Ply-Drops Using Variable Kinematics Wedge Element

  • van den Broek, Sander (University of Bristol)
  • Greaves, Peter (Offshore Renewable Energy Catapult)
  • Weaver, Paul (University of Bristol and Limerick)
  • Pirrera, Alberto (University of Bristol)

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Functional requirements for structures often involve complex geometry and varying stiffness and strength requirements. For example, wind turbine blades experience more stress near the root, requiring thicker materials, while thin aerodynamic shapes are required near the tip. Ply drops, which terminate plies in a laminated composite, are used to achieve transitions in stiffness and shape. Ply termination results in sudden changes in both geometry and material properties within the laminate. Stress concentrations formed within these ply drops can lead to failure, e.g. initiating delamination. To mitigate these potential failures and interactions between ply drops that may be placed close together, the design of ply terminations requires an evaluation of the internal stresses near and through the resin pocket of the ply drop. Only simple ply drops can be solved analytically through closed-form solutions, interactions between ply drops are highly nonlinear, requiring a numerical approach. Gaining sufficient accuracy using traditional finite element approaches requires a significant amount of h-refinement (a very fine mesh), making its use prohibitive for large structures. The current work extends previous work by the authors in the use of variable kinematics continuum elements applied to ply-drops. Extending the previous work, a different type of variable kinematics element is developed and applied to the problem. While the previous element was based on a unified formulation approach, the implemented element is not decomposed into two separate kinematic descriptions. The use of such decomposed shape functions adds constraints to the mesh, requiring all elements to face in identical directions, which is difficult to achieve in complex geometry. This problem can be mitigated by the use of elements that are kinematically agnostic with respect to their orientation, simplifying the analysis of more complex geometry and the mesh generation process. In addition, local p-refinement can be easily extended without causing compatibility issues. Analysis of ply drops requires both hexahedron and wedge (prism) elements. The hexahedron element is identical to that used by Szabo et al. and by the authors in previous work. The wedge element, based on the element described by Solin, has been developed to improve its convergence characteristics and to ass