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Torsion of an elastic rod whose cross-section is a parallelogram, trapezoid, or triangle, or has an arbitrary shape by the method of transformation to a rectangular domain

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Abstract

A coordinate transformation is used to take the domain of the rod cross-section to a rectangular domain for which the spectra of eigenfunctions and eigenvalues are known. The torsion function is represented as a generalized Fourier series to reduce the problem to solving a closed linear system of algebraic equations for the expansion coefficients. It is shown that these Fourier series converge absolutely, because the expansion coefficients decrease by a cubic law depending on the term number. We prove that the approximate solution in the form of a finite sum of the Fourier series converges to the exact solution. This theorem is generalized to the case of a rod cross-section of arbitrary shape.

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Authors and Affiliations

  1. Voronezh State Technological Academy, pr-t Revolyutsii 19, Voronezh, 394000, Russia

    A. D. Chernyshov

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  1. A. D. Chernyshov
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Correspondence to A. D. Chernyshov.

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Original Russian Text © A.D. Chernyshov, 2014, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2014, No. 2, pp. 132–144.

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Chernyshov, A.D. Torsion of an elastic rod whose cross-section is a parallelogram, trapezoid, or triangle, or has an arbitrary shape by the method of transformation to a rectangular domain. Mech. Solids 49, 225–236 (2014). https://doi.org/10.3103/S0025654414020125

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  • DOI: https://doi.org/10.3103/S0025654414020125

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