Conference publications

Abstracts

XXII conference

Solids based on thin plates

Grachev V.A., Neustadt Yu.S.

Samara State Architectural and Building University 194 Molodogvardeyskaya Str., Samara, 443096, Russia

The presentation 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 free-dom. The structure is deployable – initially it is close to a small diameter one-dimensional manifold that occupies significant volume after deployment.

The set of plates represents a net of the Bricard’s and Schatz’s symmetric mechanisms connected with cylindrical hinges. Once assembled, the net remains flexible with a small number of degrees of freedom.

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 de-scribed 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.

The presentation summarizes the results of the papers [1, 2] for three-dimensional manifolds. As a result a “field machine” is designed, the frame of which consists of the set of thin plates.

References.

1. V. A. Grachev, Yu. S. Neustadt. Lattice deployable shells assembled from strips of trapezium plates //Computer research and simulation. 2012, v. 4, No. 1, p. 63-73 (in Russian).

2. V. A. Grachev, Yu. S. Neustadt. Ultimate load theorems for rigid-plastic solids with internal degrees of freedom and their application to continuum lattice shells // Computer research and simulation. 2013, v. 5, No. 3, p. 423-432 (in Russian).

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