Constrained Cubic Grid Rigidity Decision with Directed Graph and Applications

Anna Mária Takács (), János Katona (), Szabolcs Baják () and Gyula Nagy Kem ()
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Anna Mária Takács: Budapest Business University
János Katona: Obuda University
Szabolcs Baják: Budapest Business University
Gyula Nagy Kem: Budapest Business University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 6, 23 pages

Abstract: Abstract We present a rigidity decision problem of constrained cubic grids in any given bracing pattern. The cubic grid bar and joint frameworks are not rigid. Additional constraints are required for rigidity. These constraints can be pinned down joints and additional bracing elements. Scaffoldings are not rigid cubic grid structures whose specific joints are pinned down. Inserting cable, strut, or rod bracing elements makes the framework rigid. Our model, which provides a linearly complex algorithm, has practical implications in testing the strong connectedness of a corresponding directed graph, contributing to the field of rigidity in structural engineering and motions of cable controlled pinned down cubic mechanisms.

Keywords: Rigidity decision; 3d grid; Bar and joint structure; Cable bracing; Strongly connected graph; Tensegrities; 52C25; 70B15; 70C20; 70Q05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02609-4

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