# On the mechanical behaviour of laminated curved beams: a simple model which takes into account the warping effects

• Volume: 1, Issue: 3, page 223-233
• ISSN: 1120-6330

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## Abstract

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A mechanical one-dimensional model which describes the dynamical behaviour of laminated curved beams is formulated. It is assumed that each lamina can be regarded as a Timoshenko's beam and that the rotations of the cross sections can differ from one lamina to another. The relative displacements at the interfaces of adjacent laminae are assumed to be zero. Consequently the model includes a shear deformability, due to the warping of the cross beam section consequent to the variability of the laminae rotations, but it is not able to describe the phenomena of the interfacial slip and of the delamination. By means of the principle of virtual work a variational formulation of the motion equations is carried out, which is useful in view of a successive numerical approach. The constitutive assumption at the basis of the analysis carried out is that of an orthotropic linear elastic behaviour in the single lamina.

## How to cite

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Ascione, Luigi, and Fraternali, Fernando. "On the mechanical behaviour of laminated curved beams: a simple model which takes into account the warping effects." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.3 (1990): 223-233. <http://eudml.org/doc/244230>.

@article{Ascione1990,
abstract = {A mechanical one-dimensional model which describes the dynamical behaviour of laminated curved beams is formulated. It is assumed that each lamina can be regarded as a Timoshenko's beam and that the rotations of the cross sections can differ from one lamina to another. The relative displacements at the interfaces of adjacent laminae are assumed to be zero. Consequently the model includes a shear deformability, due to the warping of the cross beam section consequent to the variability of the laminae rotations, but it is not able to describe the phenomena of the interfacial slip and of the delamination. By means of the principle of virtual work a variational formulation of the motion equations is carried out, which is useful in view of a successive numerical approach. The constitutive assumption at the basis of the analysis carried out is that of an orthotropic linear elastic behaviour in the single lamina.},
author = {Ascione, Luigi, Fraternali, Fernando},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Composite materials; Curved beams; Dynamics; Constitutive relations; one-dimensional model; dynamical behaviour; Timoshenko beam; shear deformability; laminae rotations; principle of virtual work; constitutive assumption; orthotropic linear elastic behaviour in the single lamina},
language = {eng},
month = {9},
number = {3},
pages = {223-233},
publisher = {Accademia Nazionale dei Lincei},
title = {On the mechanical behaviour of laminated curved beams: a simple model which takes into account the warping effects},
url = {http://eudml.org/doc/244230},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Ascione, Luigi
AU - Fraternali, Fernando
TI - On the mechanical behaviour of laminated curved beams: a simple model which takes into account the warping effects
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/9//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 3
SP - 223
EP - 233
AB - A mechanical one-dimensional model which describes the dynamical behaviour of laminated curved beams is formulated. It is assumed that each lamina can be regarded as a Timoshenko's beam and that the rotations of the cross sections can differ from one lamina to another. The relative displacements at the interfaces of adjacent laminae are assumed to be zero. Consequently the model includes a shear deformability, due to the warping of the cross beam section consequent to the variability of the laminae rotations, but it is not able to describe the phenomena of the interfacial slip and of the delamination. By means of the principle of virtual work a variational formulation of the motion equations is carried out, which is useful in view of a successive numerical approach. The constitutive assumption at the basis of the analysis carried out is that of an orthotropic linear elastic behaviour in the single lamina.
LA - eng
KW - Composite materials; Curved beams; Dynamics; Constitutive relations; one-dimensional model; dynamical behaviour; Timoshenko beam; shear deformability; laminae rotations; principle of virtual work; constitutive assumption; orthotropic linear elastic behaviour in the single lamina
UR - http://eudml.org/doc/244230
ER -

## References

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1. MINDLIN, R. D. - DERESIEWICZ, H., Timoshenko's shear coefficient for flexural vibrations of beams. Technical Report n° 10, ONR Project NR064-388, Dep. Civ. Eng., Columbia University, New York1953.
2. GOODMAN, L. E. - SUTHERLAND, J. G., Discussion of paper, Flexural vibrations in uniform beams according to Timoshenko theory, by R. A. Anderson. J. Appl. Mech., 21, 1954, 202-204. Zbl0052.42405
3. COWPER, G. R., The shear coefficient in Timoshenko's beam. J. Appl. Mech., 33, 1966, 335-340. Zbl0151.37901
4. WHITNEY, J. M., Shear correction factor for orthotropic laminates under static loads. J. Appl. Mech., 40, 1973, 302-304.
5. BHIMARADDI, A. - CARR, A. J. - MOSS, P. J., Generalized finite element analysis of laminated curved beams with constant curvature. Comput. Struct., 31, 1989, 309-317.
6. YUAN, F. G. - MILLER, R. E., A new finite element for laminated composite beams. Comput. Struct., 31, 1989, 737-745. Zbl0685.73032
7. ASCIONE, L. - FRATERNALI, F., Sulla statica delle travi ad asse curvo. Rep. Inst. Civ. Eng., Univ. of Salerno, n° 17, 1989.
8. VINSON, J. R. - SIERAKOWSKI, R. L., The behaviour of structures composed of composite materials. Martinus Nijhoff Publishers, Dordrecht1987. Zbl0624.73068

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