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Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach

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Abstract

The purpose of this study is to calculate the torsional rigidity and maximum shear stresses of arbitrarily shaped orthotropic composite or functionally graded material sections on the basis of a hybrid finite element approach. A hybrid finite element based on a Hellinger–Reissner functional is presented. A set of numerical examples is solved to verify the proposed method, and a parametrical study is also performed.

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Abbreviations

D :

Diameter

\(G_{zx},G_{zy}\) :

Shear modulus of elasticity

\(G_{zy}^b , G_{zy}^t\) :

Shear moduli at the bottom and top sides of an FGM section

GJ :

Torsional rigidity

\(Q_{x},\,Q_{y}\) :

Internal shear force components

T :

Torsional moment

\(\beta \) :

Torsional rigidity factor

\(\phi \) :

Saint-Venant’s stress function

\(\theta \) :

Angle of twist per unit length

\(\bar{{\tau }}_{\max }\) :

Maximum shear stress factor

[D]:

Differential operator matrix

[G]:

Nodal forces corresponding to assumed stress field

[N]:

Shape functions

[P]:

Interpolation matrix for stress

\(\{q\}\) :

Displacement components

\(\{w\}\) :

Displacements

\(\{\beta \}\) :

Stress parameters

\(\{\sigma \}\) :

Internal forces

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Authors and Affiliations

  1. Faculty of Civil Engineering, Istanbul Technical University, 34469, Istanbul, Turkey

    Kutlu Darılmaz, Engin Orakdöğen & Konuralp Girgin

Authors
  1. Kutlu Darılmaz
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  2. Engin Orakdöğen
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  3. Konuralp Girgin
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Correspondence to Konuralp Girgin.

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Darılmaz, K., Orakdöğen, E. & Girgin, K. Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach. Acta Mech 229, 1387–1398 (2018). https://doi.org/10.1007/s00707-017-2067-1

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  • DOI: https://doi.org/10.1007/s00707-017-2067-1

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