TL;DR
This paper establishes conditions for the infinitesimal rigidity of non-Euclidean braced grids in the plane, using matroid theory to characterize the combinatorial structure of braces with various diagonal configurations.
Contribution
It provides necessary and sufficient conditions for rigidity in non-Euclidean norms, extending classical results to more general metric settings.
Findings
Rigidity conditions depend on a matroid structure of the brace configuration.
Component rectangles can have 0, 1, or 2 diagonal braces.
The paper characterizes rigidity using combinatorial and geometric criteria.
Abstract
Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial part of the conditions is given in terms of a matroid for the bicoloured bipartite multigraph defined by the braces.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Computational Geometry and Mesh Generation