A topological counting rule for shells

2025/10/12 by Nassar, Hussein
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Soft Condensed Matter (cond-mat.soft)

paper · doi:10.48550/arxiv.2510.10683

Abstract

Holding a shell in their hands, one can apply six loads: three by pulling and shearing, and three by bending and twisting. Here, it is shown that the shell will resist exactly three load cases and comply with the other three, provided the shell is simply connected, meaning it has no holes and no handles.

Citations

• Cracking Down on Fracture to Functionalise Damage
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• Effective isometries of periodic shells
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Related

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• Shells without drilling rotations: a representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory
• Symmetries in the linear theory of the deformation of thin shells
• The Sturdiness of the Shell Model: Informal Review