States of self-stress in symmetric frameworks and applications

Schulze, Bernd; Millar, Cameron; Mazurek, Arek; Baker, William F.

doi:10.1016/j.ijsolstr.2021.111238

Cited by 1 publication

(7 citation statements)

References 25 publications

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“…The symmetries might be destroyed by the transformation, but this might not be important to the designer (in fact, the designer may want to destroy certain symmetries). Larger groups of symmetry operations can help to detect more states of self-stress and more mechanisms which are not otherwise detected -this is discussed in greater depth in Schulze et al 4 In that paper, an example with higher order symmetry; four mirror symmetries and…”

Section: Increasing the Number Of States Of Self-stressmentioning

confidence: 98%

“…An accompanying paper develops the mathematical background further. 4 This paper is aimed at a more engineering based audience as opposed to the other paper which is written for a more mathematically literate audience. However, readers are referred to the accompanying paper for more rigorous discussion of the underlying mathematics.…”

Section: Structural 'Counts'mentioning

confidence: 99%

“…The accompanying paper 4 describes the derivation of the symmetry adapted count using a block diagonalisation of the equilibrium matrix. This paper tries to explain this in a simple way.…”

Section: Theorymentioning

confidence: 99%

“…An example based on a Desargues framework is given on Page 13. A similar basis change can be applied to the mechanism space (this is explored more in the accompanying paper 4 ). This block diagonalisation of the equilibrium matrix was first described by Kangwai and Guest 15 (see also Schulze 16 and Owen and Power 17 ).…”

Section: Theorymentioning

confidence: 99%

“…If the structure requires a boundary structure for horizontal equilibrium, then, for this paper, the boundary structure is idealised as a horizontal reaction truss so that all horizontal forces are resolved within the idealised structure. 5 The accompanying paper 4 tackles frameworks with horizontal supports as well.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Symmetry and the design of self-stressed structures

Millar,

Schulze,

Mazurek

et al. 2023

International Journal of Space Structures

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The symmetry adapted counting rule for mechanisms and states of self-stress in symmetric frameworks is presented in an accessible and intuitive manner with the aim of empowering engineers who design such structures. By simply counting nodes and bars, it is possible to detect states of self-stress and mechanisms beyond the standard Maxwell-Calladine count. This methodology is first introduced without the need to understand the underlying group theory before being applied to a range of example frameworks. Design problems focusing on gridshells are discussed – it is noted that placing bars on lines of mirror symmetry tend to increase the number of states of self-stress in a framework, which can be desirable. This paper reformulates common symmetric frameworks and introduces simple rules regarding how to obtain a greater number of states of self-stress. By allowing for the design of states of self-stress, the forces in the structure can be designed with greater control.

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Section: Increasing the Number Of States Of Self-stressmentioning

confidence: 98%

Section: Structural 'Counts'mentioning

confidence: 99%

“…The accompanying paper 4 describes the derivation of the symmetry adapted count using a block diagonalisation of the equilibrium matrix. This paper tries to explain this in a simple way.…”

Section: Theorymentioning

confidence: 99%