Conference publications

Abstracts

XVII conference

Stable shell forms composed of plates

Grachev V.A., Nayshtut Yu.S.

Samara State Architectural and Civil Engineering University, Russia, 443001, Samara, Str. Molodogvardeyskaya, 194 Ph.: (846) 336-87-78, е-mail: neustadt99@mail.ru

This report covers transformed shells of rectilinear strips. The rectilinear strips are put together of two different size equal-angle trapeziums that are joined with ideal cylindrical hinges. The strips are specially stuck together.

If the trapeziums of the bigger sizes are equipped with additional non-ideal hinges in such a way that it takes work to “unfold” them, unwrapping of the strip package first results in formation of the negative Gauss curvature shell. Then maximum surface area is attained and further unwrapping leads to the following: radii of the main curvatures R1, R2 (related to the curvature lines 1, 2) change places, i.e. R1 and R2 become curvature radii along the lines 2, 1.

Something similar happens when solid anisotropic thin shells are designed [1]. Similar transformations occur with deployable shells [2].

Geometrical behavior of the proposed shells is studied based on the analysis of Bricard's six-loop linkages [3] and the possibility to introduce "continuous internal variables” while analyzing the nets composed of trapeziums (that do not differ much from rectangles). The last assumption is equal to Cartan's method of moving hedron when used for latticed shells.

The proposed mechanical model explains different stable forms of latticed shells based on of the theory of plasticity [4] and acceptance of the following hypothesis: transformed shells of the trapeziums allow only twist (that is considered elastic) and the hinges are ideal rigidly plastic elements.

References.

1. Norman A. D., Golabchi M. R., Seffen K.A.,Guest S. D. Multistable Textured Shell Structures //Advanced Science and Technology, vol. 54: (2008), 168-173

2. Grachev V.A., Nayshtut Yu. S. Transformed systesms based on six-loop linkages // Mathematics, computer, education, issue 15 (2), 2008, 131-139 (in Russian)

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

4. Kachanov L. M. Fundamentals of the theory of plasticity. М.: Science, 1969. 420 p. (in Russian)

• view as PDF