Geodesic
The one-dimensional micropolar theory of elastic rods basic parities construction
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 52-61

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The reduction from a three-dimensional problem of the asymmetrical theory of elasticity to one-dimensional by means of splitting a three-dimensional problem on set of two-dimentional and one-dimensional problems is carried out. Kinematic parameters with which it is necessary to involve are specified that together with system Kirchoff differential equations to receive the closed system of the equations of the one-dimensional micropolar theory of cores. Other geometrical sizes are found from parities defining them. Conditions with which should satisfy factors in closing parities are received. The contribution to these parities which introduces the account moment pressure is estimated. For the one-dimensional theory the common decision at presence stiffnesse is specified to symmetry. 
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     title = {The one-dimensional micropolar theory of elastic rods basic parities construction},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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A. A. Iliykhin; D. V. Timoshenko. The one-dimensional micropolar theory of elastic rods basic parities construction. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 52-61. http://geodesic.mathdoc.fr/item/ISU_2008_8_4_a7/