Conference publications

Abstracts

XIX conference

Lattice deployable shells of strips formed by trapezium plates

Grachev V.A, Nayshtut Yu.S.

, 443001, Samara, Str. Molodogvardeyskaya, 194

The paper [1] studies transformed shells of rectilinear strips. The strips are put together of equilateral trapeziums connected with cylindrical hinges made of shape memory materials. The strips are glued together along the surfaces of the specially selected plates. Initially the strips overlap each other residing on the same plane. The middle lines of the strips form a straight line. With package deployment a lattice surface appear, i.e. a shell of the bounded area. It is proved that the formed system is not a “pure” mechanism but it is asymptotically close to it if assembled from thin strips. In this case low force needs to be applied to deploy the original package of strips into a shell.

In the report the line-ups of the paper [1] are carried over the shells that are put together from strips, the middle line of which is an arbitrary plain curvature. The plates comprising a strip meet the only limitation: their thickness should be small compared to length. The angles between the base and the sides of trapeziums could be random. But for the shell to be close to the continuum one, these angles have to “continuously” change and should not differ much from straight angles. The last assumption allows studying geometrical behavior of the shells using the method of Cartan’s moving frame [2] applicable to the nets of six link loops [3].

Mechanical behavior of the deployable shells is studied within the generalized rigid-plastic model [4] where the angles of the plate twist are considered to be additional degrees of freedom. Formulas for ultimate loads are provided.

The proposed structures simulate shells with a local curvature that could widely vary. That is why their application is possible in engineering and biological systems.

References.

1. V.A. Grachev, Yu.S. Nayshtut. Continuum transformed shells of thin strips // Computer research and simulation, 2011, v.3, issue 1. p. 3-29.

2. Cartan E. Les systèmes différentiels extérieurs et leurs applications géométriques, Paris, Hermann, 1945. - 214 p.

3. Phillips J. Freedom in machinery. Cambridge University Press. 2006. 253 p.

4. L.M. Kachanov. Fundamentals of the plasticity theory. М.: Nauka, 1969. 420 p.

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