A Stress-Constrained Topology Optimisation Framework for Concurrent Material Distribution and Fibre Orientation in Composite Structures

  • Ullah, Zahur (Durham University)
  • Swarbrick, Benjamin (Durham University)
  • Gao, Guifeng (Durham University)
  • STEFANO, GIANI (Durham University)

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This study presents a stress-constrained topology optimisation (TO) framework for fibre-reinforced polymer composites (FRPCs) aimed at achieving high-performance and failure-resistant structures under complex loading conditions [1]. The proposed approach simultaneously optimises material distribution and fibre orientation by treating material density and fibre angle as independent design variables, resulting in two design variables per finite element. Structural compliance is minimised subject to a global volume constraint and stress constraints. The stress constraints are evaluated using the Tsai-Wu failure criterion and aggregated via a p-norm measure to ensure a differentiable and computationally efficient formulation [2]. A complete analytical derivation of sensitivities for both the objective and constraint functions with respect to the design variables is provided, enabling robust and efficient gradient-based optimisation. The framework accommodates complex geometries through both structured and unstructured meshes imported from external preprocessors such as Coreform Cubit, and allows for the inclusion of design and non-design domains. The resulting constrained optimisation problem is solved using the Method of Moving Asymptotes (MMA) [3]. The proposed framework is validated through a range of numerical examples, including multi-load case problems and realistic applications involving a composite bicycle frame and crank. References [1]. Ma, G., Yang, W. and Wang, L. 2022. Strength-constrained simultaneous optimization of topology and fiber orientation of fiber-reinforced composite structures for additive manufacturing. Advances in Structural Engineering 25(7), pp. 1636–1651. [2]. Mirzendehdel, A.M., Rankouhi, B. and Suresh, K. 2018a. Strength-based topology optimization for anisotropic parts. Additive Manufacturing 19, pp. 104–113. [3]. Svanberg, K. 1987. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering 24, pp. 359–373.