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A review of some integral equations for solving the Saint-Venant torsion problem

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Summary

It has been attempted to write down a complete collection of integral equations and functional equations for solving the classical Saint-Venant's torsion problem, to a large extent using Green's third identity and a unified notation for the systematic compilation. Some of the equations are well known, others seem to be new. Nearly all the equations are interpreted physically. Known and unknown connections among the equations are pointed out.

Zusammenfassung

Es wird hier der Versuch gemacht ein vollständiges Verzeichnis von Integralgleichungen und Funktionalgleichungen zur Lösung des klassischen Saint-Venant'schen Torsionsproblems aufzustellen-weitgehend mit Hilfe der dritten Green'schen Identität und unter Verwendung einheitlicher Bezeichnungen, um dadurch eine systematische Zusammenstellung zu erreichen. Einige von diesen Gleichungen sind wohlbekannt-andere dagegen werden hier vermutlich zuerst angegeben; beinahe alle Gleichungen werden physikalisch gedeutet. Bekannter und unbekannter Beziehungen zwischen den Gleichungen sind angegeben.

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Authors and Affiliations

  1. Laboratory of Applied Mathematical Physics, The Technical University of Denmark, DK-2800, Lyngby, Denmark

    Søren Christiansen

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  1. Søren Christiansen
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Additional information

The present work is partly based upon material which was compiled for an invited lecture give on July 3, 1975 at the Institute of Technical Mechanics, The Technical University of Aachen, The Federal Republic of Germany.

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Christiansen, S. A review of some integral equations for solving the Saint-Venant torsion problem. J Elasticity 8, 1–20 (1978). https://doi.org/10.1007/BF00044507

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