The Finite Elements Research for Calculation of Thin-Walled Bar Systems

Structural mechanics

This article is written to continue the article of recent issue of the journal (Lalin V.V., Rybakov V.A. The finite elements for design of building walling made of thin-walled beams) considered the creating of 4 types of finite elements – depending on a way of function approximation of deformations (torsion and warping):

1. Linear approximation of torsional functions with a 2-central finite element having 4 transitions; 2. Square-law approximation of torsional functions and linear approximation of warping function with a 3-central finite element having 5 transitions;
3. Square-law approximation of functions of torsional and warping functions with a 3-central finite element having 6 transitions
4. Cubical approximation of functions of torsional with a 2-central finite element having 4 transitions

In the article we continue realization of finite elements method algorithms and we consider some test examples about the torsion of the thin-walled beam having various boundary conditions on the ends. Also the given problems are considered from the point of view of search of static power factors at the constrained torsion: a bimoment, a sectorial torsion moment and the moment of free torsion.

Formulas for cross-sectional form for channel influence factor calculation, which are necessary for application of the semisheared theory of thin-walled beams, are received. Analytical decisions for the basic power factors and deformations under the semisheared theory for simple schemes most often meeting in engineering practice loaded by in regular intervals distributed loading with excenterisity are received. Convergence of the offered finite elementswhich speed depends on the type of basic functions approximation is shown on concrete examples.

Recommendations and conclusions concerning application of various finite elements are formulated.