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Generalizing Jouravski Formulas by Techniques from Differential Geometry

Abstract : We deal with the flexure (flexion inégale) of a Saint-Venant cylinder whose sections we call Bredt-like with variable thickness. We consider a family of sections Dε whose thickness is scaled by a parameter ε. This scaling allows for the construction of an ε-one parameter family of coordinate mappings from a fixed-plane domain D onto Dε. We represent the Helmholtz operator in Dε in terms of a fixed system of coordinates in D and represent the shear stress field in what we call the Bredt basis field, which is not the natural basis associated with any coordinate system. Assuming that the shear stress admits a formal ε power series expansion, we obtain a hierarchy of perturbation problems for its coefficients, finding the well-known Jouravski formula at the lowest iterative step and obtaining its generalization at higher steps - that is, when the section becomes thick. Similar results are obtained for the warping, the resultant shear stress, and the shear shape factors.
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https://hal.archives-ouvertes.fr/hal-00503006
Contributor : Francesco Dell'Isola <>
Submitted on : Friday, July 16, 2010 - 12:27:51 PM
Last modification on : Saturday, July 17, 2010 - 10:14:23 AM
Long-term archiving on: : Thursday, December 1, 2016 - 3:00:10 PM

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  • HAL Id : hal-00503006, version 1

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Francesco Dell'Isola, Giuseppe C. Ruta. Generalizing Jouravski Formulas by Techniques from Differential Geometry. Mathematics and Mechanics of Solids, SAGE Publications, 1997, pp.13. ⟨hal-00503006⟩

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