A Computational Framework for the Dimensioning and Performance Evaluation of Continuous Shape-Morphing Surfaces

Continuous shape-morphing surfaces require carefully optimized actuator arrays to accurately render complex physical profiles. However, evaluating the spatial resolution and required control effort for different actuator layouts remains a significant design challenge. This paper presents a comprehensive computational framework for the evaluation and dimensioning of continuous shape-morphing surfaces modeled via Kirchhoff-Love plate theory. By simulating maximum-curvature peaks and directional Gaussian ridges, we quantitatively extract geometric performance metrics such as spatial resolution, shape isotropy, and directional dependence, alongside the required localized actuation forces. The framework is used to systematically compare four fundamental actuator layouts (square, rectangular, triangular, and honeycomb). The results demonstrate that morphing efficacy is highly spatially dependent, fluctuating significantly based on the target profile’s alignment and lateral shift relative to the underlying actuator grid. This framework serves as a versatile design tool to optimize physical actuator layouts and dimension hardware requirements for future real-world applications.