arXiv subjects

JiaHao Li

Publications and source records attributed to JiaHao Li.

2 recordsLinked to original sources

arXiv2026

Inverse design of a magneto-elastica for shape-morphing

Slender magnetic elements provide a versatile platform for programmable shape-morphing under remote magnetic actuation. However, a general and physically interpretable framework for the inverse design of a 'magneto-elastica' under prescribed boundary conditions remains lacking. In this work, we develop an explicit analytical formulation for the inverse design of a magneto-elastica based on the integral form of the moment equilibrium equations. Compared with purely local differential formulations, this integral approach makes the global constraints imposed by boundary conditions and moment balance explicit, and enables a systematic characterization of the feasible design space. We identify the key dimensionless parameters that govern the competition between magnetic torques and elastic restoring moments and show that the applied boundary conditions are an essential ingredient. We obtain closed-form solutions for the beam tapering profiles required to generate desired actuated shapes in the cases of clamped--free and clamped--clamped configurations; in the latter case, this includes analytical expressions for the boundary reactions. The formulation recovers the classical inverse elastica in the absence of magnetic fields and reveals a linear scaling between curvature deviation and magnetic mismatch. A tessellation strategy based on stiffness tailoring is further proposed for the design of discretized morphing surfaces. The theoretical predictions are validated against discrete elastic rod simulations and experiments across representative geometries. This work establishes a consistent analytical framework for the inverse design of a magneto-elastica and provides new insight into magnetically-induced shape programming in slender structures.

cond-mat.soft↗

arXiv2025

Inverse Elastica: A Theoretical Framework for Inverse Design of Morphing Slender Structures

Inverse 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 optimizations, is highly efficient yet remains challenging, particularly for cases involving arbitrary boundary conditions (BCs). Here, we develop a systematic theoretical framework, termed inverse elastica, for the direct determination of the undeformed configuration from a target deformed shape along with prescribed BCs. Building upon the classical elastica, inverse elastica is derived by supplementing the geometric equations of undeformed configurations. The framework shows three key features: reduced nonlinearity, solution multiplicity, and inverse loading. These principles are demonstrated through two representative models: an analytical solution for a two-dimensional arc and a numerical continuation study of the inverse loading of a three-dimensional helical spring. Furthermore, we develop a theory-assisted optimization strategy for cases in which the constrains of the undeformed configurations cannot be directly formulated as BCs. 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.

cond-mat.soft↗