DEFORMATION OF THIN-WALLED STRUCTURAL ELEMENTS HAVING FIXED AREAS OF FINITE DIMENSIONS ON THE BOUNDARY FRONT SURFACES

Abstract

Solving as an example the plane problem of the mechanics of a rod strip having a fixed finite-length section on one of its front surfaces, we have 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 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 refined Timoshenko shear model, this is possible if the section is fixed only on one of the front surfaces. Exact analytical solutions were found for two simple linear problems of static transverse bending of a flat rod with fixed sections of finite length on one of the front surfaces. One-dimensional finite elements were constructed for modeling unfixed sections of flat rods and sections fixed on one of the front surfaces within the framework of 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 fixed and unfixed sections.