General nonlinear theory of rods and its applications to the solution of particular problems
Basing on method developed in the theory of shells, the general
nonlinear theory of flexible rods [1] is formulated (1987), where all the basic
types of deformation: bending, torsion, tension, transversal shear are taken
into account. Use of the rotation (turn) tensor allowed to write down the equations
in a compact form, convenient for the mathematical analysis. In
contradistinction to previous theories, the proposed theory describes
the experimentally discovered Pointing effect (the contraction of a rod
under torsion). The developed theory was applied to analyse the series of
particular problems [2, 3]. A new method [4 - 6] was suggested (2005) for the
construction of elastic tensors, and their structure has been determined.
In this work the new theory of symmetry of tensors, determined in the space
with two independent orientations, is essentially used. All elastic constants
were found for plane curvilinear rods.
- Goloskokov D.P., Zhilin ð.á. General nonlinear theory of elastic rods with application
to the description of the Pointing effect // Deposited in VINITI N 1912-V87. Dep. 20 p. (In Russian.)
- Zhilin P.A., Tovstik T.P. Rotation
of a rigid body based on an inertial rod // Mechanics and Control. Proc. of St. Petersburg
State Technical University. 1995. N 458. P. 78-83. (In Russian).
- Zhilin P.A., Sergeyev A.D., Tovstik T.P. Nonlinear
theory of rods and its application // Proc. of XXIV Summer School - Seminar
“Nonlinear Oscillations in Mechanical Systems”. St. Petersburg. 1997. P. 313-337. (In Russian.)
- Zhilin P.A. Advanced problems in mechanics. Selection of articles. V. 1. St. Petersburg. Edition of IPME RAS. 2006. 306 p. (In Russian.)
- Zhilin P.A. Advanced problems in mechanics. Selection of articles. V. 2. St. Petersburg. Edition of IPME RAS. 2006. 271 p.
- Zhilin P.A.Applied mechanics. Theory of thin elastic rods.
Tutorial book. St. Petersburg State Polytechnical University. 2007. 101 p. (In Russian.)