Assessment of an Assumed Strain-based Quadrilateral Membrane Element

Authors

  • A. Kherfi Laboratory of Development in Mechanics and Materials (LDMM), University of Djelfa, Algeria
  • K. Guerraiche Mechanical Engineering Department, Faculty of Technology, University of Batna 2, Algeria | NMISSI Laboratory, Faculty of Science and Technology, Biskra University, Algeria
  • K. Zouggar Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Djillali Liabès University of Sidi Bel-Abbès, Algeria
Volume: 12 | Issue: 5 | Pages: 9302-9309 | October 2022 | https://doi.org/10.48084/etasr.5182

Abstract

This paper describes the development of a simple quadrilateral strain-based element for plane stress and strain problems. This element has five nodes, four located at its corners and one at the center. Each of the four corner nodes had two essential external degrees of freedom (u, v), while the center node had three degrees of freedom (u, v, ɵ); the static condensation method was used for the internal node. This element was used for both linear and dynamic analysis. Its performance was assessed using a variety of membrane and axisymmetric analysis problems. The obtained results demonstrated the good performance and accuracy of the proposed element.

Keywords:

strain approach, drilling rotation, quadrilateral element, linear analysis, dynamic analysis, Axisymmetric

Downloads

Download data is not yet available.

References

A. G. da S. Jr, J. A. Martins, and E. C. Romão, "Numerical Simulation of a One-Dimentional Non-Linear Wave Equation," Engineering, Technology & Applied Science Research, vol. 12, no. 3, pp. 8574–8577, Jun. 2022. DOI: https://doi.org/10.48084/etasr.4920

F. Khelil, M. Belhouari, N. Benseddiq, and A. Talha, "A Numerical Approach for the Determination of Mode I Stress Intensity Factors in PMMA Materials," Engineering, Technology & Applied Science Research, vol. 4, no. 3, pp. 644–648, Jun. 2014. DOI: https://doi.org/10.48084/etasr.442

A. Boulenouar, N. Benseddiq, and M. Mazari, "Two-dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis," Engineering, Technology & Applied Science Research, vol. 3, no. 5, pp. 506–510, Oct. 2013. DOI: https://doi.org/10.48084/etasr.363

M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp, "Stiffness and Deflection Analysis of Complex Structures," Journal of the Aeronautical Sciences, vol. 23, no. 9, pp. 805–823, 1956. DOI: https://doi.org/10.2514/8.3664

I. C. Taig and R. I. Kerr, "Some Problems in the Discrete Element Representation of Aircraft Structures," in Matrix Methods of Structural Analysis, F. de Veubeke, Ed. Oxford, UK: Pergamon Press, 1964, pp. 267–316.

K. Y. Sze, "On immunizing five-beta hybrid-stress element models from ‘trapezoidal locking’ in practical analyses," International Journal for Numerical Methods in Engineering, vol. 47, no. 4, pp. 907–920, 2000. DOI: https://doi.org/10.1002/(SICI)1097-0207(20000210)47:4<907::AID-NME808>3.0.CO;2-A

W. Chen and Y. K. Cheung, "Axisymmetric solid elements by the generalized hybrid method," Computers & Structures, vol. 27, no. 6, pp. 745–752, Jan. 1987. DOI: https://doi.org/10.1016/0045-7949(87)90287-2

K. Y. Sze and C. L. Chow, "An incompatible element for axisymmetric structure and its modification by hybrid method," International Journal for Numerical Methods in Engineering, vol. 31, no. 2, pp. 385–405, Feb. 1991. DOI: https://doi.org/10.1002/nme.1620310211

F. Boussem and L. Belounar, "A Plate Bending Kirchhoff Element Based on Assumed Strain Functions," Journal of Solid Mechanics, vol. 12, no. 4, pp. 935–952, Dec. 2020.

R. Ayad, "Éléments finis de plaque et coque en formulation mixte avec projection en cisaillement," Ph.D. dissertation, University of Compiègne, 1993.

K. Guerraiche, "Elements finis d’Elasticite Plane et de Volume Bases Sur l’Approche en Defomation," Ph.D. dissertation, University Mohamed Khider - Biskra, 2014.

Y. Long and Y. Xu, "Generalized conforming quadrilateral membrane element with vertex rigid rotational freedom," Computers & Structures, vol. 52, no. 4, pp. 749–755, Aug. 1994. DOI: https://doi.org/10.1016/0045-7949(94)90356-5

W. Changsheng, Q. Zhaohui, Z. Xiangkui, and H. Ping, "Quadrilateral 4-node Quasi-Conforming Plane Element with Internal Parameters," Chinese Journal of Theoritical and Applied Mechanics, vol. 46, no. 6, pp. 971–976, Nov. 2014.

M. Rezaiee-Pajand and M. Yaghoobi, "Formulating an effective generalized four-sided element," European Journal of Mechanics - A/Solids, vol. 36, pp. 141–155, Nov. 2012. DOI: https://doi.org/10.1016/j.euromechsol.2012.02.012

M. S. Djoudi and H. Bahai, "A cylindrical strain-based shell element for vibration analysis of shell structures," Finite Elements in Analysis and Design, vol. 40, no. 13, pp. 1947–1961, Aug. 2004. DOI: https://doi.org/10.1016/j.finel.2003.11.008

A. B. Sabir and A. C. Lock, "A curved, cylindrical shell, finite element," International Journal of Mechanical Sciences, vol. 14, no. 2, pp. 125–135, Feb. 1972. DOI: https://doi.org/10.1016/0020-7403(72)90093-8

D. G. Ashwell, A. B. Sabir, and T. M. Roberts, "Further studies in the application of curved finite elements to circular arches," International Journal of Mechanical Sciences, vol. 13, no. 6, pp. 507–517, Jun. 1971. DOI: https://doi.org/10.1016/0020-7403(71)90038-5

A. B. Sabir and A. Sfendji, "Triangular and rectangular plane elasticity finite elements," Thin-Walled Structures, vol. 21, no. 3, pp. 225–232, Jan. 1995. DOI: https://doi.org/10.1016/0263-8231(94)00002-H

A. Belounar, "Eléments finis membranaires et flexionnels à champ de déformation pour l’analyse des structures," Ph.D. dissertation, University Mohamed Khider - Biskra, 2019.

S. J. Fenves, N. Perrone, and A. R. Robinson, Numerical and Computer Methods in Structural Mechanics. New York, NY, USA: Elsevier, 2014.

J.-L. Batoz and G. Dhatt, Modélisation des structures par éléments finis. Sainte-Foy, France: Presses Université Laval, 1990.

M. Rezaiee-Pajand, N. Gharaei-Moghaddam, and M. Ramezani, "Review of the strain-based formulation for analysis of plane structures Part II: Evaluation of the numerical performance," Iranian Journal of Numerical Analysis and Optimization, vol. 11, no. 2, pp. 485–511, Sep. 2021.

D. Boutagouga, "A Review on Membrane Finite Elements with Drilling Degree of Freedom," Archives of Computational Methods in Engineering, vol. 28, no. 4, pp. 3049–3065, Jun. 2021. DOI: https://doi.org/10.1007/s11831-020-09489-z

M. T. Belarbi and A. Charif, "Développement d’un nouvel élément hexaédrique simple basé sur le modèle en déformation pour l’étude des plaques minces et épaisses," Revue Européenne des Éléments Finis, vol. 8, no. 2, pp. 135–157, Jan. 1999. DOI: https://doi.org/10.1080/12506559.1999.10511361

K. Guerraiche, L. Belounar, and L. Bouzidi, "A New Eight Nodes Brick Finite Element Based on the Strain Approach," Journal of Solid Mechanics, vol. 10, no. 1, pp. 186–199, Mar. 2018.

L. Belounar and K. Guerraiche, "A new strain based brick element for plate bending," Alexandria Engineering Journal, vol. 53, no. 1, pp. 95–105, Mar. 2014. DOI: https://doi.org/10.1016/j.aej.2013.10.004

L. Belounar and M. Guenfoud, "A new rectangular finite element based on the strain approach for plate bending," Thin-Walled Structures, vol. 43, no. 1, pp. 47–63, Jan. 2005. DOI: https://doi.org/10.1016/j.tws.2004.08.003

F. Boussem, A. Belounar, and L. Belounar, "Assumed strain finite element for natural frequencies of bending plates," World Journal of Engineering, vol. ahead-of-print, no. ahead-of-print, Jan. 2021. DOI: https://doi.org/10.1108/WJE-02-2021-0114

A. Belounar, F. Boussem, M. N. Houhou, A. Tati, and L. Fortas, "Strain-based finite element formulation for the analysis of functionally graded plates," Archive of Applied Mechanics, vol. 92, no. 7, pp. 2061–2079, Jul. 2022. DOI: https://doi.org/10.1007/s00419-022-02160-y

A. Belounar, S. Benmebarek, and L. Belounar, "Strain based triangular finite element for plate bending analysis," Mechanics of Advanced Materials and Structures, vol. 27, no. 8, pp. 620–632, Apr. 2020. DOI: https://doi.org/10.1080/15376494.2018.1488310

M. S. Djoudi and H. Bahai, "A shallow shell finite element for the linear and non-linear analysis of cylindrical shells," Engineering Structures, vol. 25, no. 6, pp. 769–778, May 2003. DOI: https://doi.org/10.1016/S0141-0296(03)00002-6

M. Bourezane M, "An Efficient Strain Based Cylindrical Shell Finite Element," Journal of Solid Mechanics, vol. 9, no. 3, pp. 632–649, Jan. 2017.

A. Mousa, "Strain-Based Finite Element Analysis of Stiffened Cylindrical Shell Roof," American Journal of Civil Engineering, vol. 5, no. 4, Jul. 2017. DOI: https://doi.org/10.11648/j.ajce.20170504.15

H. Guenfoud, M. Himeur, H. Ziou, and M. Guenfoud, "A consistent triangular thin flat shell finite element with drilling rotation based on the strain approach," International Journal of Structural Engineering, vol. 9, no. 3, 2018. DOI: https://doi.org/10.1504/IJSTRUCTE.2018.093673

A. B. Sabir and M. S. Djoudi, "Shallow shell finite element for the large deflection geometrically nonlinear analysis of shells and plates," Thin-Walled Structures, vol. 21, no. 3, pp. 253–267, Jan. 1995. DOI: https://doi.org/10.1016/0263-8231(94)00005-K

C. Rebiai and L. Belounar, "A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis," Archives of Civil and Mechanical Engineering, vol. 13, no. 1, pp. 72–81, Mar. 2013. DOI: https://doi.org/10.1016/j.acme.2012.10.001

A. Belounar, L. Belounar, and A. Tati, "An assumed strain finite element for composite plates analysis," International Journal of Computational Methods, Jul. 2022. DOI: https://doi.org/10.1142/S0219876222500347

A. Belounar, F. Boussem, and A. Tati, "A Novel C0 Strain-Based Finite Element for Free Vibration and Buckling Analyses of Functionally Graded Plates," Journal of Vibration Engineering & Technologies, Jun. 2022. DOI: https://doi.org/10.1007/s42417-022-00577-x

M. Rezaiee-Pajand, N. Gharaei-Moghaddam, and M. Ramezani, "Strain-based plane element for fracture mechanics’ problems," Theoretical and Applied Fracture Mechanics, vol. 108, Aug. 2020, Art. no. 102569. DOI: https://doi.org/10.1016/j.tafmec.2020.102569

A. B. Sabir, "A Rectangular and Triangular Plane Elasticisy Elements with Drilling Degrees of Freedom," in Proceedings of the Second International Conference on Variational Methods in Engineering, 1985, pp. 17–25.

L. Bouzidi, L. Belounar, and K. Guerraiche, "Presentation of a new membrane strain-based finite element for static and dynamic analysis," International Journal of Structural Engineering, vol. 10, no. 1, pp. 40–60, Jan. 2019. DOI: https://doi.org/10.1504/IJSTRUCTE.2019.101431

C. Rebiai, N. Saidani, and E. Bahloul, "A New Finite Element Based on the Strain Approach for Linear and Dynamic Analysis," Research Journal of Applied Sciences, Engineering and Technology, vol. 11, no. 6, pp. 639–644, Jul. 2015. DOI: https://doi.org/10.19026/rjaset.11.2025

R. Winkler and D. Plakomytis, "A New Shell Finite Element with Drilling Degrees of Freedom and its Relation to Existing Formulations," in Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), Crete Island, Greece, 2016, pp. 2803–2842. DOI: https://doi.org/10.7712/100016.1998.11192

R. H. Macneal and R. L. Harder, "A proposed standard set of problems to test finite element accuracy," Finite Elements in Analysis and Design, vol. 1, no. 1, pp. 3–20, Apr. 1985. DOI: https://doi.org/10.1016/0168-874X(85)90003-4

Y. K. Cheung, Y. X. Zhang, and W. J. Chen, "A refined nonconforming plane quadrilateral element," Computers & Structures, vol. 78, no. 5, pp. 699–709, Dec. 2000. DOI: https://doi.org/10.1016/S0045-7949(00)00049-3

W. Zouari, F. Hammadi, and R. Ayad, "Quadrilateral membrane finite elements with rotational DOFs for the analysis of geometrically linear and nonlinear plane problems," Computers & Structures, vol. 173, pp. 139–149, Sep. 2016. DOI: https://doi.org/10.1016/j.compstruc.2016.06.004

P. G. Bergan and C. A. Felippa, "A triangular membrane element with rotational degrees of freedom," Computer Methods in Applied Mechanics and Engineering, vol. 50, no. 1, pp. 25–69, Jul. 1985. DOI: https://doi.org/10.1016/0045-7825(85)90113-6

R. D. Cook, D. S. Malkus, M. E. Plesha, and R. J. Witt, Concepts and Applications of Finite Element Analysis, 4th Edition. Hoboken, NJ, USA: John Wiley & Sons, Ltd, 2001.

S. Timoshenko and S. Woinowsky-krieger, Theory of Plates and Cells. New York, NY, USA: Mc Graw-Hill, 1959.

I. M. Smith, D. V. Griffiths, and L. Margetts, Programming the Finite Element Method. Chichester, UK: John Wiley & Sons, 2013.

Downloads

How to Cite

[1]
A. Kherfi, K. Guerraiche, and K. Zouggar, “Assessment of an Assumed Strain-based Quadrilateral Membrane Element”, Eng. Technol. Appl. Sci. Res., vol. 12, no. 5, pp. 9302–9309, Oct. 2022.

Metrics

Abstract Views: 781
PDF Downloads: 577

Metrics Information

Most read articles by the same author(s)