Variant of the equations spatial curvilinear rods at the large displacements

摘要

In certain mathematical models, the deformation of the axial line-spatial curve of a rod is described. Deformation by a curve is determined by a tension-compression along a curve, changes curvatures in two mutually perpendicular planes containing tangent, and change of torsion. The parities between displacements of points of a curve, changes curvatures and turns of orts, connected with a curve, can be used as at drawing up of the equations describing deformation spatial curvilinear rod, including at the large displacements and turns, and for construction of finite element approximations. At use of the special description of turn into the received expressions for increments of curvatures and torsion do not enter of curvature of the initial undeformed curve, that is the basis for uniform consideration deformations of rods with breaks and jumps of curvature. Thus the geometry is set on sites. The received parities are correct for any turns at use of Argyris's pseudo- vector. In this article the description deformation of a flat core is generalized on a case spatial curvilinear rod. The method of shout is applied for the decision of a regional task. The example of account is given.