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Complex potential function in elasticity theory: shear and torsion solution through line integrals

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Abstract

Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.

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References

  1. England A.H.: Complex Variable Methods in Elasticity. Wiley-Interscience, New York, NY (1971)

    MATH  Google Scholar 

  2. Dettman J.: Applied Complex Variables. Dover, New York (1984)

    MATH  Google Scholar 

  3. Muskhelishvili N.I.: Some Basic Problems of Mathematical Theory of Elasticity. P. Noordhoff LTD, Groningen (1953)

    MATH  Google Scholar 

  4. Sokolnikoff I.S.: Mathematical Thoery of Elasticity. McGraw-Hill, New York, NY (1956)

    Google Scholar 

  5. Timoshenko S., Goodier J.N.: Theory of Elasticity. McGraw-Hill, New York, NY (1951)

    MATH  Google Scholar 

  6. Ziegler F.: Mechanics of Solid and Fluids, 2nd reprint of 2nd edn. Springer, New York, NY (1998)

    Google Scholar 

  7. Timoshenko S.P.: Strength of Materials—Part1, 2nd edn. Van Norstad, New York, NY (1940)

    Google Scholar 

  8. Love E.A.H.: A Treatise on the Mathematical Theory of Elasticity. Dover, New York, NY (1944)

    MATH  Google Scholar 

  9. Truesdell, C.: History of Classical Mechanics. Die Naturwissenschaften 63, Part. II: the 19th and 20th Centuries, pp. 119–130. Springer, Berlin (1976)

  10. Di Paola M., Pirrotta A., Santoro R.: De Saint-Venant flexure-torsion problem handled by line element-less method (LEM). Acta Mech. 217, 101–118 (2011)

    Article  MATH  Google Scholar 

  11. Di Paola M., Pirrotta A., Santoro R.: Line element-less method (LEM) for beam torsion solution (Truly no-mesh method). Acta Mech. 195, 349–363 (2008)

    Article  MATH  Google Scholar 

  12. Barone, G., Pirrotta, A., Santoro, R.: Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM. Eng. Anal. Bound. Elem. 35, 895–907 (2011)

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  1. Dipartimento di Ingegneria Civile Ambientale e Aerospaziale (DICA), Università degli Studi di Palermo, Viale delle Scienze, 90128, Palermo, Italy

    Antonina Pirrotta

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  1. Antonina Pirrotta
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Correspondence to Antonina Pirrotta.

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Pirrotta, A. Complex potential function in elasticity theory: shear and torsion solution through line integrals. Acta Mech 223, 1251–1259 (2012). https://doi.org/10.1007/s00707-012-0628-x

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  • DOI: https://doi.org/10.1007/s00707-012-0628-x

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