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arXiv · 2508.13343

Stressability of Semi-Discrete Frameworks

Oleg Karpenkov·Christian Müller·Anna Pratoussevitch
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Abstract

In this paper we study the stressability of semi-discrete frameworks in the plane which are generated by a discrete sequence of smooth curves. We characterize their stressability property by the existence of stresses fulfilling certain difference-differential equation. In particular, we define a semi-discrete height function which we use to generate liftings. Furthermore, we show a semi-discrete analogue of the Maxwell-Cremona lifting property which implies that the stressable semi-discrete frameworks in the plane are precisely the orthogonal projections of semi-discrete conjugate surfaces in 3-space. Finally, we discuss geometric implications for frameworks with vanishing boundary forces and characterize the liftability of frameworks which only consist of two neighboring curves forming one strip.

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Oleg Karpenkov, Christian Müller, Anna Pratoussevitch. 2025-08-18. Stressability of Semi-Discrete Frameworks. https://arxiv.org/abs/2508.13343

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