Numerical Analysis of 2D Elastic Torsion Problem for a Rod by the Method of Matched Sections

Authors

  • Kostiantyn Slovak Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» , Ukraine image/svg+xml https://orcid.org/0009-0001-0266-7672
  • Igor Orynyak Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» , Ukraine image/svg+xml https://orcid.org/0000-0003-4529-0235
  • Kirill Danylenko Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» , Ukraine image/svg+xml https://orcid.org/0009-0007-6101-6582

DOI:

https://doi.org/10.20535/2521-1943.2025.9.4(107).340386

Keywords:

Method of matched sections, transfer matrix method, elastic plane body, torque, angle of rotation, boundary conditions

Abstract

Torsion problem is treated here as Saint Venant’s semi-inverse task for prismatic bars, which allows to consider 2D geometry instead of 3D one. The novelty of the paper is that at the first time it tackles the problem by the method of matched section, MMS, – a new numerical approach for multiphysics problems. Like finite element method it supposes the continuous distribution of all parameters within the element, and like volume element method it keeps the conservation laws and equilibrium for each element and the body as a whole. The main idea of MMS is to substitute the partial differential equations (stemmed from required conservation laws) by the ordinary ones by introducing the additional constants, which can be later found from the continuity conditions at the center of element. The governing equations for torsion are broken out on two independent (along each coordinate axis passed through the centers of the opposite sides) equations, which relate two governing parameters (angle of rotation and torque) at the beginning with those at the end of the element. Each element contains 8 unknowns, so 4 above connection equations are supplemented by continuity conditions between elements and the boundary conditions. In addition to rectangular element the simplified version of the triangular one is proposed which is used to account for the outer boundary configuration. Numerical verification is performed for different shapes of cross-section and for composite cross-section. The results show the efficiency of the method, and high accuracy is attained even for small grids.

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Published

2025-12-29

How to Cite

[1]
K. Slovak, I. Orynyak, and K. Danylenko, “Numerical Analysis of 2D Elastic Torsion Problem for a Rod by the Method of Matched Sections”, Mech. Adv. Technol., vol. 9, no. 4(107), pp. 401–408, Dec. 2025.

Issue

Vol. 9 No. 4(107) (2025)

Section

Mechanics

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Copyright (c) 2025 Костянтин Словак, Ігор Ориняк, Кірілл Даниленко

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