Infinitesimal Bendings of Surfaces with an Edge Under Certain Boundary Conditions.
R. E. Gibson Library bulletin translation series,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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Infinitesimal bendings of surfaces of positive curvature with a smooth edge are examined. Given on the surface is a continuous field R of simple rays along the edge. To be sought is the existence of infinitesimal surface bendings under which edge points shift by a given value sigma s in the direction of R. The necessary and sufficient conditions of solution of the problem, imposed on the function sigma s, are found. As a corollary of these conditions follow the rigidity of surfaces with sleeve joints of a special form and a strengthening of A.V. Pogorelovs theorem on the rigidity of surfaces when the distances between edge points and some fixed point are stationary. Author
- Theoretical Mathematics