A proof of the convexity of a set of lamination parameters

Akian, Jean‐Luc

doi:10.1002/mma.7854

Cited by 3 publications

(1 citation statement)

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“…The optimization of fibre angles of composite laminates is known to be a non-convex design problem: results are sensitive to starting points and convergence is not guaranteed [43]. By defining the composite structure with lamination parameters instead of fibre angles the design space can be transformed into a convex design problem under certain conditions [44][45][46][47]. A second optimization step is then required to translate the lamination parameters into a manufacturable layup of fibre angles.…”

Section: Optimization Formulationmentioning

confidence: 99%

Increasing reliability of axially compressed cylinders through stiffness tailoring and optimization

Lincoln

Pirrera

Groh

2023

Phil. Trans. R. Soc. A.

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The capabilities of the rapid tow shearing (RTS) process are explored to reduce the well-known imperfection sensitivity of axially compressed cylindrical shells. RTS deposits curvilinear carbon fibre tapes with a fibre-angle-thickness coupling that enables the in situ manufacturing of embedded rings and stringers. By blending the material’s elastic modulus and wall thickness smoothly across the cylindrical surface, the load paths can be redistributed favourably with a minimal-design approach that contains part count and weight while ameliorating imperfection sensitivity. A genetic algorithm that incorporates realistic manufacturing imperfections and axial stiffness penalty is used to maximize the 99.9% reliability load of straight fibre (SF) and RTS cylinders. The axial stiffness penalty ensures that reliability does not come at the expense of stiffness. The first-order second-moment method is used to calculate statistical moments that enable an estimate of the 99.9% reliability load. Due to the fibre-angle-thickness coupling of RTS, buckling data are normalized by mass and thickness. Compared to a quasi-isotropic laminate, which corresponds to the optimal eight-layer design for a perfect cylinder, the optimized SF and RTS laminates have a 6% and 8% greater 99.9% normalized reliability load. By relaxing the axial stiffness penalty, the performance benefit can be increased such that SF and RTS cylinders exceed the 99.9% normalized reliability load of an eight-layer quasi-isotropic laminate by 23% and 37%, respectively. Both improvements (with and without penalty functions) stem largely from a reduction in the variance of the buckling-load distribution, thereby demonstrating the potential of fibre-steered cylinders in reducing the imperfection sensitivity of cylindrical shells. This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.

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