Study of Elastic Properties and Stress-Strain State of a Rod Loaded Using a Cable
Authors: Naumov A.M. | Published: 06.08.2015 |
Published in issue: #8(665)/2015 | |
Category: Calculation and Design of Machinery | |
Keywords: flat curved rod, method of successive loadings, associated basis, Cartesian basis, transformation matrix, state vector |
Spatial and flat rods, or structural elements that can be reduced to the model of a rod are very widely used in engineering, instrumentation, power engineering, systems of active and passive vibration isolation, etc. This paper presents a methodology for calculating the flat curved elastic rod, loaded using an inextensible cable, with large displacements, i.e. in the nonlinear formulation. The forces acting on the rod from the cable, are neither dead nor follower, and can be classified as the so-called feedback forces, the magnitude and direction of which depend on the linear and angular displacements of points of their application. This complicates the formulation of the boundary conditions in the problem of mechanics rods. An original approach is proposed to the application of the method of successive loadings in the study of a stress-strain state (SSS) of the rod itself as well as its elastic properties. The re-sults of a numerical study of loading the rod by an inextensible cable are presented. They demonstrate the potentials of the proposed algorithm to solve such problems. The described method of numerical calculations of deep deformation of flat rods can be fairly easily applied to spatial rod structures of arbitrary complex geometry.
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