| 摘要 |
The model elementary flexor is a polyhedral panel represented by a four-angle star-like pyramid which is formed by thin elastic three-angle faces with hinge junctions. It has two symmetry planes which intersect the petals of flexor. An essential geometric property of the flexor is following: when the middle polyhedron is projected into the plane of the boundary, then each face is mapped to a triangle whose doubled intrinsic and extrinsic angles adjacent to the boundary are equal to pi/2-alpha pi/2+alpha respectively, where alpha is the third angle of the three-angle and it belongs to the interval (0,pi/2). As consequence, the presented device is more general than its prototype, the right star-like pyramid "Model ideal flexor", disclosed in UA Patent No. 54692. The invented device belongs to various areas of technique and industry where polyhedral shells with freely changed geometric forms are applied: architecture, aircraft construction, shipbuilding and precise instrument-making. Under small cross loads the panel suffers a non-rigid loss of stability, which is either soft or slow in terms of the dynamical systems theory, and it goes to an adjacent state infinitesimally close to the original equilibrium state, provided that the boundary always slips along its plane. After that, the panel is subject to an overcritical deformation, which is good approximated by an unusual linear bending of its middle polyhedron, as it is predicted by the geometric theory of shells. The deformation is well determined, it goes with a large cross flexure, which is comparable with sizes of the panel, and may be completely controlled numerically. The faces of the panel under the described deformation move approximately as solid plates, whereas the applied efforts discharged basically in hinge junctions joining faces. Such a way to lose the stability, which has been conjectured by L. Euler's static criterion, was unknown in the literature and in practical applications, it was considered just as an abstract idea.
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