Stress-Responsive Spatial Voronoi Optimization for Lightweight Architectural Shell Structures

Gradient porous structures (GPS) offer significant mechanical and functional advantages over homogeneous counterparts. This paper proposes a computational design framework utilizing spatial Voronoi diagrams to create lightweight, stress-responsive spatial frames optimized for architectural double-curvature arched shell roofing components. The method integrates Solid Isotropic Material with Penalization (SIMP)-based topology optimization (TO) to establish initial stress-informed material distributions, adaptive Voronoi control point (CP) placement guided by localized stress data, and a bi-objective genetic algorithm (GA) optimizing maximum and average displacement. Following optimization, a weighted Lloyd relaxation (LR) refines Voronoi cells into spatial frameworks with varying densities corresponding to stress gradients. Finite Element Analysis (FEA) demonstrates that the optimized Voronoi-driven GPS achieves notable improvements, revealing up to 79.7% material volume reduction and significant improvement in structural efficiency, achieving a stiffness-to-weight ratio (SWR) exceeding 2200 in optimized configurations. Furthermore, optimized structures consistently maintain maximum von Mises (MVM) stresses below 20 MPa, well within the allowable yield strength of the Polyethylene Terephthalate Glycol (PETG) material (53 MPa). The developed framework effectively bridges structural performance, material efficiency, and aesthetic considerations, offering substantial potential for application in advanced, high-performance architectural systems.