Application of mesh-free methods in the wing rigidity analysis to support automation of UAV design

Modern aircraft design, including both manned aircraft and unmanned aerial vehicles (UAVs), faces computational challenges balancing aerodynamic efficiency, structural integrity, and weight optimization within practical timeframes. Conventional high-fidelity methods create bottlenecks that limit the design space exploration essential for UAV development. This paper presents a computational framework that integrates mesh-free structural analysis with generative knowledge-based engineering (KBE) and surrogate modelling for the optimization of rapid automated UAV wing design. The methodology combines the formalization of classical aerodynamic and structural mechanics knowledge with programmable CAD integration using the open-source Python package CadQuery. The developed framework automatically generates parametric wing geometries, extracts geometric properties, including cross-sectional moments of inertia and volumes, and performs structural analysis without mesh generation or finite element preprocessing. Aerodynamic loads are estimated using reusable meta-models from CFD studies stored as B-spline approximations in SplineCloud, enabling decoupled workflows and rapid evaluation.The mesh-free algorithm implements the numerical integration of beam bending equations, incorporating distributed aerodynamic and gravitational loads with variable cross-sectional properties. This eliminates the computational overhead of mesh generation while maintaining sufficient accuracy for preliminary design. The workflow is embedded in a KBE wing model, automating geometry generation and structural evaluation for swept wings with variable materials and geometries. The validation studies used three NACA airfoil families (2410, 2412, 2415) across aspect ratios (6-9), sweep angles (12°-18°), and spans (500-2500 mm). Individual evaluations completed in ~20 seconds versus hours/days for FEM simulations, achieving 2-3 orders of magnitude efficiency improvement. Generated 2nd-order meta-models enable sub-millisecond response evaluations suitable for iterative optimization requiring thousands of evaluations. This research advances automated design methodologies, providing computationally efficient alternatives to high-fidelity approaches while maintaining engineering accuracy for preliminary optimization. Open-source implementation ensures accessibility for the UAV design community. Future work will focus on FEM validation, aeroelastic coupling, and extensions to complex configurations.