Torsion problem: stress statement and solution by the boundary element method

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Abstract

The formulation of the problem of torsion regarding stresses and its solution by the boundary elements method are described. The main advantage of the problem formulation in stresses is direct determination of stresses in the cross-section, unlike the classical formulation, when the result of the approximate solution is the Prandtl stress function values, and the determination of stresses is brought down to numerical differentiation. The boundary integral equation of the second kind is obtained to formulate the problem with respect to stresses. The procedure for solving the problem by the boundary elements method is described, the system of solving equations is compiled. Solutions of test problems on torsion of rods with rectangular and channel cross-sections are presented. Comparison of the calculation results with known analytical solutions illustrates the reliability and permissible engineering accuracy of the obtained solutions.

About the authors

Vladimir V. Lalin

Peter the Great St. Petersburg Polytechnic University; RUDN University

Author for correspondence.
Email: vllalin@yandex.ru
ORCID iD: 0000-0003-3850-424X

Dr.Sc., Professor of the Higher School of Industrial, Civil and Road Construction of the Institute of Civil Engineering

St. Petersburg, Russian Federation; Moscow, Russian Federation

Daniil A. Semenov

Peter the Great St. Petersburg Polytechnic University

Email: dan290797@gmail.com
ORCID iD: 0000-0002-9144-1412

PhD student of the Higher School of Industrial, Civil and Road Construction of the Institute of Civil Engineering

St. Petersburg, Russian Federation

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