An analytical formula for an elastic thin rod shape under composite loading

A. E. Ordanovich

M. V. Lomonosov Moscow State University

Abstract: The Euler problem on stability of a thin elastic rod under compressing forces is widely known. In a number of papers this problem is generalized to finding the shape of such a rod at simultaneous action of a compressing force and a torsional moment. The shape is determined by solving of a complex nonlinear boundary value problem by numerical methods. In this paper, an approach providing a full analytical solution of the problem for a broad range of external conditions is discussed.

UDC: 539.371

 English version: Journal of Mathematical Sciences (New York), 2007, 146:3, 5820–5825

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