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Finite Element Analysis of 2-D Structures by New Strain Based Triangular Element

Published online by Cambridge University Press:  08 February 2018

C. Rebiai
C. Rebiai*
Affiliation:
Mechanical Engineering Department University of Batna2Fésdis, Algeria
*
*Corresponding author ([email protected])
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Abstract

In this investigation, a new simple triangular strain based membrane element with drilling rotation for 2-D structures analysis is proposed. This new numerical model can be used for linear and dynamic analysis. The triangular element is named SBTE and it has three nodes with three degrees of freedom at each node. The displacements field of this element is based on the assumed functions for the various strains satisfying the compatibility equations. This developed element passed both patch and benchmark tests in the case of bending and shear problems. For the dynamic analysis, lumped mass with implicit/explicit time integration are employed. The obtained numerical results using the developed element converge toward the analytical and numerical solutions in both analyses.

Keywords

Strain approachLinear analysisDynamic analysisLumped mass
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 3 , June 2019 , pp. 305 - 313
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

REFERENCES

Zouari, W., Hammadi, F. and Ayad, R., “Quadrilateral Membrane Finite Elements with Rotational DOFs for the Analysis of Geometrically Linear and Nonlinear Plane Problems,” Computers and Structures, 173, pp. 139–149 (2016).Google Scholar
Nodargi, N. A. and Bisegna, P., “A Novel High-Performance Mixed Membrane Finite Element for the Analysis of Inelastic Structures,” Computers and Structures, 182, pp. 337–353 (2017).Google Scholar
Madeo, A., Zagari, G. and Casciaro, R., “An Isostatic Quadrilateral Membrane Finite Element with Drilling Rotations and No Spurious Modes,” Finite Element in Analysis and Design, 50, pp. 21–32 (2012).Google Scholar
Huang, M., Zhao, Z. and Shen, C., “An Effective Planar Triangular Element with Drilling Rotation,” Finite Element in Analysis and Design, 46, pp. 1031–1036 (2010).Google Scholar
Belarbi, M. T. and Maalam, T., “On Improved Rectangular Finite Element for Plane Linear Elasticity Analysis,” Revue Européenne des éléments Finis, 14, pp. 985–997 (2005).Google Scholar
Allman, D. J., “A Quadrilateral Finite Element Including Vertex Rotations for Plane Elasticity Analysis,” International Journal of Numerical Methods in Engineering, 26, pp. 717–730 (1988).Google Scholar
Kim, J., Varadan, V. V. and Varadan, V. K., “Efficacy of Drilling Degrees of Freedom in the Finite Element Modeling of P-and SV-Wave Scattering Problems,” Journal of Mechanics, 16, pp. 103–108 (2000).Google Scholar
Ibrahimobigovic, A., Taylor, R. L. and Wilson, E. L., “A Robust Quadrilateral Membrane Finite Element with Drilling Degrees of Freedom,” International Journal of Numerical Methods in Engineering, 30, pp. 445–457 (1990).Google Scholar
Taylor, R. L. and Simo, J. C., “Bending and Membrane Elements for Analysis of Thick and Thin Shells,” Proceeding of NUMETA Conference, Swansea (1985).Google Scholar
Sheng, G. G. and Wang, X., “The Geometrically Nonlinear Dynamic Responses of Simply Supported Beams under Moving Loads,” Applied Mathematical Modelling, 48, pp. 183–195 (2017).Google Scholar
Rebiai, C. and Belounar, L., “A New Strain Based Rectangular Finite Element with Drilling Rotation for Linear and Nonlinear Analysis,” Archives of Civil and Mechanical Engineering, 13, pp. 72–81 (2013).Google Scholar
Rebiai, C. and Belounar, L., “An Effective Quadrilateral Membrane Finite Element Based on the Strain Approach,” Measurement, 50, pp. 263–269 (2014).Google Scholar
Rebiai, C., Saidani, N. and Bahloul, E., “A New Finite Element Based on the Strain Approach for Linear and Dynamic Analysis,” Research Journal of Applied Science, Engineering and Technology, 11, pp. 639–644 (2015).Google Scholar
Tang, L., Ding, S., Xie, Y. and Huo, Y., “A Multilayer Nodes Update Method in FEM Simulation of Large Depth Fretting, Wear,” Wear, 301, pp. 483–490 (2013).Google Scholar
Hu, Z., Lu, W., Thouless, M. D. and Barber, J. R., “Simulation of Wear Evolution Using Fictitious Eigenstrains,” Tribology International, 82, pp. 191–194 (2015).Google Scholar
Hu, Z., Lu, W., Thouless, M. D. and Barber, J. R., “Effect of Plastic Deformation on the Evolution of Wear and Local Stress Fields in Fretting,” International Journal of Solids and Structures, 82, pp. 1–8 (2016).Google Scholar
Liu, G. R., Nguyen-Thoi, T. and Lam, K. Y., “An Edge-Based Smoothed Finite Element Method (ES-FEM) for Static, Free and Forced Vibration Analyses of Solids,” Journal of Sound and Vibration, 320, pp. 1100–1130 (2009).Google Scholar
Sabir, A. B., “A Rectangular and Triangular Plane Elasticity Element with Drilling Degrees of Freedom,” Proceedings of the Second International Conference on Variational Methods in Engineering, Southampton University, Berlin (1985).Google Scholar
Belarbi, M. T. and Bourezane, M., “An Assumed Strain Based on Triangular Element with Drilling Rotation,” Courier de Savoir, 6, pp. 117–123 (2005).Google Scholar
ABAQUS 6.11., Analysis User’s Manual (2011).Google Scholar
Pian, T. H. and Sumihara, K., “Rational Approach for Assumed Stress Finite Elements,” International Journal for Numerical Methods in Engineering, 20, pp. 1685–1695 (1984).Google Scholar
Yunus, S. M., Saigal, S. and Cook, R. D., “On Improved Hybrid Finite Elements with Rotational Degrees of Freedom,” International Journal for Numerical Methods in Engineering, 28, pp. 785–800 (1989).Google Scholar
Sze, K. Y., Chen, W. and Cheung, Y. K., “An Efficient Quadrilateral Plane Element with Drilling Degrees of Freedom Using Orthogonal Stress Modes,” Computers & Structures, 42, pp. 695–705 (1992).Google Scholar
Mac-Neal, R. H. and Harder, R. L., “A Proposed Standard Set of Problems to Test Finite Element Accuracy,” Finite Element in Analysis and Design, 11, pp. 3–20 (1985).Google Scholar
Cook, R. D., “A Plane Hybrid Element with Rotational Degrees of Freedom and Adjustable Stiffness,” International Journal of Numerical Methods in Engineering, 24, pp. 1499–1508 (1987).Google Scholar
Smith, I. M. and Griffith, D. V., Programming the Finite Element Method, 2nd Edition, John Wiley & Sons, University of Manchester, United Kindom, Hermès (1988).Google Scholar
Smith, I. M. and Griffith, D. V., Programming the Finite Element Method, 4th Edition, John Wiley & Sons, Ltd, United Kindom (2004).Google Scholar