Geodesic
An analytical formula for an elastic thin rod shape under composite loading
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 7, pp. 35-42

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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. 
@article{FPM_2005_11_7_a4,
     author = {A. E. Ordanovich},
     title = {An analytical formula for an elastic thin rod shape under composite loading},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {35--42},
     publisher = {mathdoc},
     volume = {11},
     number = {7},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_7_a4/}
}
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A. E. Ordanovich. An analytical formula for an elastic thin rod shape under composite loading. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 7, pp. 35-42. http://geodesic.mathdoc.fr/item/FPM_2005_11_7_a4/