Evaluating the snappability of bar-joint frameworks
This addresses a specific problem in mechanical engineering or geometry for researchers studying bar-joint frameworks, but appears incremental as it builds on known techniques like averaging and deaveraging.
The paper tackled the problem of measuring the snapping capability of bar-joint frameworks, which can snap between realizations due to elastic deformations, by developing a method based on total elastic strain energy using Hook's law, resulting in theoretical connections between shakiness and snapping.
It is well-known that there exist bar-joint frameworks (without continuous flexions) whose physical models can snap between different realizations due to non-destructive elastic deformations of material. We present a method to measure these snapping capability -- shortly called snappability -- based on the total elastic strain energy of the framework by computing the deformation of all bars using Hook's law. The presented theoretical results give further connections between shakiness and snapping beside the well-known technique of averaging and deaveraging.