Saint Venant Problem for a Naturalh Twisted Rod in Nonlinear Moment Elasticity Theory

摘要

Problems of tension, compression, torsion, and bending of a naturally twisted rod loaded by end forces and moments are analyzed from the standpoint of three-dimensional elasticity theory of micropolar continua possessing moment stresses and subjected to severe strains. These spatial problems are reduced to two-dimensional nonlinear boundary value problems for a planar region having the form of a rod cross section. The allowance for moment stresses is of interest, in particular, for mechanics of composite and nanostructural materials. In the framework of classical linear elasticity theory, the Saint Venant problem for a naturally twisted rod was investigated in [1, 2]. The nonlinear theory of bending and torsion of prismatic bodies without allowance for moment stresses was developed in [3-7].