Journal of Applied and Computational Mechanics

In-Plane Shear-Axial Strain Coupling Formulation for Shear-‎Deformable Composite Thin-Walled Beams

Document Type : Research Paper

Authors

1 School of Engineering and Sciences, Tecnológico de Monterrey, Calle del Puente 222 , Tlalpan, 14380, Mexico

2 School of Engineering and Sciences, Tecnológico de Monterrey, General Ramon Corona 2514, Zapopan, 45138, Mexico‎

3 School of Engineering and Sciences, Tecnológico de Monterrey, Av. Eugenio Garza Sada 2051 Sur, Monterrey, 64849, Mexico‎

Abstract

This paper presents an improved description of the in-plane strain coupling in Librescu-type shear-deformable composite thin-walled beams (CTWB). Based on existing descriptions for Euler-type CTWB, an analogous formulation for shear-deformable CTWB is here developed by building, via the Mindlin–Reissner theory and an orthotropic constitutive law of the shell wall, an alternate equation for the in-plane shear force which effectively couples the axial and shear in-plane strains. It is observed that this strain coupling formulation includes some of the transversal (out-of-plane) shear strain terms, thus also functioning as a path for transferring transversal shear energy to the in-plane strain field and therefore improving shear-deformability. The performance of the new CTWB model is compared against that of previously available CWTB (i.e. Euler-type with strain coupling and Timoshenko-type without strain coupling) for several aspect ratios, fibre-orientations and laminate types. Error measures are calculated by comparing several relevant stiffness coefficients and displacement shapes to reference results provided by corresponding 3D shell-based ANSYS finite-element models. Results indicate that for cases involving significant shear energy (i.e. short aspect ratios) and/or in-plane shear-axial strain coupling (i.e. off-axis or asymmetric/unbalanced laminates), the new CTWB model proposed in this work can attain an accuracy level comparable to that associated to more sophisticated models, two to three orders of magnitude larger, at a fraction of the computational cost.

Keywords

Main Subjects

[1] Alfio Q., Gianluigi R., Reduced order methods for modeling and computational reduction, Springer International Publishing, Switzerland, 2014.
[2] Oliver, J., Caicedo, M., Huespe, A. E., Hernández, J. A., Roubin, E., Reduced order modeling strategies for computational multiscale fracture, Computer Methods in Applied Mechanics and Engineering, 313, 2017, 560-595.
[3] Cambronero-Barrientos F., Díaz-del-Valle J., Martínez-MartínezJ.A., Beam element for thin-walled beams with torsion, distortion, and shear lag, Engineering Structures, 143, 2017, 571–588.
[4] Librescu L., Song O., Thin-walled composite beams – theory and application, Springer, 2006.
[5] Volovoi V., Hodges, D. H., Theory of anisotropic thin-walled beams, Journal of Applied Mechanics, 67(3), 2000, 453-459.
[6] Carrera E.,  Giunta G., Refined beam theories based on a unified formulation, International Journal of Applied Mechanics, 2(1), 2010, 117-143.
[7] Vlasov V.Z., Thin-Walled Elastic Bars (in Russian), 2nd ed., Fizmatgiz, Moscow, 1959.
[8] Timoshenko S. An Introduction to the Theory of Elasticity, Nature, 138, 1936 54–55.
[9] Lee J., Flexural analysis of thin-walled composite beams using shear-deformable beam theory, Composite Structures, 70, 2005, 212–222.
[10] Vo T.P., Lee J., Flexural-torsional behavior of thin-walled composite box beams using shear-deformable beam theory, Engineering Structures, 30, 2008, 1958–1968.
[11] Cortínez V.H., Piovan M.T., Stability of composite thin-walled beams with shear deformability, Composite Structures, 84, 2006, 978–990.
[12] Vo T.P., Lee J., Flexural-torsional coupled vibration and buckling of thin-walled open section composite beams using shear-deformable beam theory, International Journal of Mechanical Sciences, 51, 2009, 631–641.
[13] Vo T.P., Lee J., Geometrically nonlinear theory of thin-walled composite box beams using shear-deformable beam theory, International Journal of Mechanical Sciences, 52, 2010, 65–74.
[14] Alsafadie R., Hjiaj M., Battini J.M., Three-dimensional formulation of a mixed corotational thin-walled beam element incorporating shear and warping deformation, Thin-Walled Structures, 49, 2011, 523–533.
[15] Machado S.P., Saravia C.M., Shear-deformable thin-walled composite Beams in internal and external resonance, Composite Structures, 97, 2013, 30–39.
[16] Vieira R.F., Virtuoso F.B.E., Pereira E.B.R., A higher order thin-walled beam model including warping and shear modes, International Journal of Mechanical Sciences, 66, 2013, 67–82.
[17] Vieira R.F., Virtuoso F.B.E., Pereira E.B.R., Definition of warping modes within the context of a higher order thin-walled beam model, Computers & Structures, 147, 2015, 68–78.
[18] Vieira R.F., Virtuoso F.B.E., Pereira E.B.R., Buckling of thin-walled structures through a higher order beam model, Computers & Structures, 180, 2017, 104–116.
[19] Zhang C., Wang S., Structure mechanical modeling of thin-walled closed-section composite beams, Part 1: Single-cell cross section, Composite Structures, 113, 2014, 12–22.
[20] Cárdenas, D., Elizalde, H., Jáuregui-Correa, J. C., Piovan, M. T., Probst, O., Unified theory for curved composite thin-walled beams and its isogeometrical analysis, Thin-Walled Structures, 131, 2018, 838-854.
[21] Rana S., Fangueiro R., Advanced composite materials for aerospace engineering: processing, properties and applications, Woodhead Publishing, United Kingdom, 2016.
[22] Chortis D.I. Structural Analysis of Composite Wind Turbine Blades, Springer International Publishing, Heidelberg, 2013.
[23] Ye L., Feng P., Yue Q., Advances in FRP Composites in Civil Engineering, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011.
[24] Dinker, A., Agarwal, M.,  Agarwal, G. D., Heat storage materials, geometry and applications: A review, Journal of the Energy Institute, 90(1), 2017 1-11.
[25] Cottrell J.A., Hughes T.J.R., Bazilevs Y., Isogeometric Analysis, John Wiley & Sons, Ltd, Chichester, UK, 2009.
[26] Hughes T.J.R., Cottrell J.A., Bazilevs Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194, 2005, 4135–4195.
[27] Sherar, P.A., Variational based analysis and modelling using B-splines, Ph.D. Thesis, Applied Mathematics & Computing Group,Cranfield University, Cranfield, 2004.
Journal of Applied and Computational Mechanics
Volume 7, Issue 2
April 2021
Pages 450-469