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MODELS IN PHYSICS AND TECHNOLOGY
Solids composed of thin plates
V. A. Grachev, Yu. S. Nayshtut Samara State Architectural and Building University, 194 Molodogvardeyskaya Str., Samara, 443096, Russia
Abstract:
The paper demonstrates a fractal system of thin plates connected with hinges. The system can be studied using the methods of mechanics of solids with internal degrees of freedom. The structure is deployable — initially it is close to a small diameter one-dimensional manifold that occupies significant volume after deployment. The geometry of solids is studied using the method of the moving hedron. The relations enabling to define the geometry of the introduced manifolds are derived based on the Cartan structure equations. The proof substantially makes use of the fact that the fractal consists of thin plates that are not long compared to the sizes of the system. The mechanics is described for the solids with rigid plastic hinges between the plates, when the hinges are made of shape memory material. Based on the ultimate load theorems, estimates are performed to specify internal pressure that is required to deploy the package into a three-dimensional structure, and heat input needed to return the system into its initial state.
Keywords:
fractal system, thin plates, continuum solid, Cartan moving hedron, ultimate load, rigid plastic solid, shape memory.
Received: 25.08.2014 Revised: 15.09.2014
Citation:
V. A. Grachev, Yu. S. Nayshtut, “Solids composed of thin plates”, Computer Research and Modeling, 6:5 (2014), 655–670
Linking options:
https://www.mathnet.ru/eng/crm351 https://www.mathnet.ru/eng/crm/v6/i5/p655
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Abstract page: | 73 | Full-text PDF : | 36 | References: | 18 |
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