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Lookup NU author(s): Dr Weicheng Huang
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© 2025 Elsevier LtdInverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the forward equations to identify optimal designs. Such methods, however, are computationally intensive and often susceptible to local minima issues. In contrast, solving the inverse problem theoretically, which can bypass the need for extensive forward simulations, is highly efficient yet remains challenging, particularly for cases involving arbitrary boundary conditions, such as clamped-free and clamped-clamped boundary conditions. Here, we develop a systematic theoretical framework based on Kirchhoff rod model, termed inverse elastica, for the direct determination of the undeformed configuration from a target deformed shape along with prescribed BCs. Building upon the classical Kirchhoff rod model, inverse elastica is derived by supplementing the geometric equations of undeformed configurations. Compared to forward solving of Kirchhoff rod model, inverse elastica shows several features: reduced nonlinearity, inverse loading and solution multiplicity. Building upon inverse elastica, we develop a theory-assisted optimization strategy for cases in which the constrains of the undeformed configurations cannot be directly formulated as boundary conditions. Using this strategy, we achieve rational inverse design of complex spatial curves and curve-discretized surfaces with varying Gaussian curvatures. Our theoretical predictions are validated through both discrete elastic rod simulations and experiments. While grounded in theory, the engineering value of inverse elastica is demonstrated through design of a deployable and conformable hemispherical helical antenna. This work thus provides a novel strategy for inverse design of morphing slender structures, opening new avenues for applications in morphing structures, soft robotics, deployable radio-frequency systems, architectural design, and beyond.
Author(s): Li J, Huang W, Zhu Y, Yu L, Sun X, Liu M, Wu H
Publication type: Article
Publication status: Published
Journal: Journal of the Mechanics and Physics of Solids
Year: 2026
Volume: 208
Print publication date: 01/02/2026
Online publication date: 20/12/2025
Acceptance date: 18/12/2025
ISSN (electronic): 0022-5096
Publisher: Elsevier Ltd
URL: https://doi.org/10.1016/j.jmps.2025.106488
DOI: 10.1016/j.jmps.2025.106488
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