Mechanical Cloaking of Cutouts in Laminated Plates

The presence of a central cutout in thin, plate-like structures often results in a reduction in load-carrying capacity due to a removal of bending stiffness at the unsupported central region. This paper presents a design approach that minimizes the mechanically detrimental effect of a central circular cutout on the buckling performance of a flat, square, simply supported plate under uniaxial compression, for a hole diameter-to-plate-width ratio of 𝐷/𝑙𝑦 = 0.3. We consider the potential design of a holed laminated plate to have the performance of an unholed target design by application of the variable-angle Continuous Tow Shearing (CTS) process to generate periodic stiffness variations, in order to significantly disrupt and redirect prebuckling stresses. Parallelized population-based optimization approaches are used to find structural solutions which can meet the target unholed plate performance with lowest mass increase. Both holed straight fiber and fiber-steered designs are found which give near-identical structural performance to an optimum unholed eight-ply straight fiber plate of square aspect ratio ([±45]_2s). The holed eight-ply straight fiber plate gives near identical prebuckling stiffness and within ±3% buckling load of the holed plate for a 21% mass increase where ply-level orientations ([±79/±54]_s) and ply-level thicknesses ([(1.22𝑡₀)₂/(1.37𝑡₀)₂]_s) are allowed to vary. Comparatively, the eight-ply holed CTS fiber-steered plate ([±90⟨33|21⟩¹⁰/±90⟨52|2⟩⁴]_s) achieves within 1% of the prebuckling stiffness and ±1% of the buckling load of the target unholed plate for a 9% mass increase. Stress analysis is conducted to identify the governing mechanics that account for the improved performance of the CTS fiber steered plate. We find that the fiber-steered solution removes high-magnitude stresses away from the hole boundary to a region of higher stiffness within the plate, which are produced by the fiber angle-ply thickness coupling of the CTS process. Overall, the findings of the present work indicate a suitable direction for future research and the need to further investigate the non-intuitive mechanics arising from CTS fiber steering for application to future aerostructural research and development.