Mechanics of Thin-Walled Structural Elements with Boundary Front Surfaces Having Fixed Areas
V. N. Paimushin1,2, V. M. Shishkin3
1Tupolev Kazan National Research Technical University, Kazan, Russia
2Kazan Federal University, Kazan, Russia
3Vyatka State University, Kirov, Russia
Keywords: flat rod, fixed section, refined Timoshenko model, transverse bending
Abstract
By solving the plane problem of the mechanics of a rod strip having a fixed finite-length section on one of its front surfaces, it has been shown that when studying deformation processes with consideration of the compliance of the fixed section, it is necessary to take into account the change in the stress-strain state parameters and the mathematical models used for their description. This change occurs across the boundary between the unfixed and fixed sections. Within the framework of the classical Kirchhoff-Love model, it is impossible to take into account the compliance of the fixed section of the rod. However, within the framework of the simplest refined Timoshenko shear model, this is possible if the section is fixed only on one of the front surfaces. Exact analytical solutions of two simplest linear problems of static transverse bending of a flat rod with fixed sections of finite length on one of the front surfaces are found. One-dimensional finite elements for modeling unfixed sections of flat rods and sections on one of the front surfaces were constructed using the refined Timoshenko shear model. Numerical experiments were performed, showing the necessity of taking into account the change in the rod strain-stress parameters across the boundary between the fixed and unfixed sections.
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