Gradient optimization of a four-pointed star-shaped zero-Poisson’s-ratio honeycomb structure

Abstract

Morphing-wing structures require an optimal balance among large deformation capability, out-of-plane load bearing, and low structural mass while eliminating parasitic transverse warping. This study presents a gradient-tailoring optimization framework for a four-pointed star-shaped zero-Poisson’s-ratio honeycomb core applied to a variable-camber morphing trailing edge. The design methodology integrates nonlinear finite-element (FE) analysis, central composite response-surface screening, and a constrained multi-island genetic algorithm to assess layer-wise wall-thickness, wall-length, and coupled gradients under a prescribed deflection target and yield-strength limit. Results reveal that wall-thickness grading governs load redistribution at the highly stressed fixed end, achieving a 17.7% maximum stress reduction and a 6.9% mass reduction, whereas wall-length grading predominantly controls structural compliance and cell volume, reducing mass by 8.5% with negligible stress relief (0.9%). The coupled gradient achieves the superior trade-off, yielding an 11.0% mass reduction alongside a 16.9% stress reduction for the PA6 engineering design. To validate the nonlinear deformation behavior, 3D-printed thermoplastic polyurethane (TPU) specimens were tested under a five-point weighted-bending setup, and the captured digital image correlation (DIC) displacement profiles matched well with the corresponding TPU-FE verification. This work provides an effective structural metamaterial solution and parametric gradient strategy for continuous variable-camber morphing wings.