The computation of the bar’s torsional stiffness based on the film-type analogy

The article suggests a torsional stiffness estimation algorithm for the bars of the arbitrary cross-sections based on the minimization of the full mechanical potential of the deformed cross-section film-type analogy. We have calculated the bar’s stress-strain state with due consideration of the rectangular and cruciform cross-sections warpage under torsion. The calculation shows that for the most commonly encountered square section the accuracy of torsional stiffness estimate by means of the film-type analogy method exceeds 95 % of the parameter value defined by the analytical method of the elasticity theory. For the cruciform cross-section bar, which is not described in the elasticity theory reference-books, we have discovered the connection between the torsional stiffness and the film deflection shape parameter along the axis perpendicular to the cross section’s plane. The article provides the recommendations on establishing the number of points of the discrete film-type analogy and the composition of variables by which the displacements of these points are set.

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