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

مقاله 12، دوره 11، شماره 2 - شماره پیاپی 20، آذر 2021، صفحه 485-511   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.70940.1051

نویسندگان

M. Rezaiee-Pajand^{* 1}؛ Nima Gharaei-Moghaddam²؛ M. Ramezani³

¹Professor of Civil Engineering, School of Engineering, Ferdowsi University of Mashhad, Iran.

²PhD of Structural Engineering, School of Engineering, Ferdowsi University of Mashhad, Iran

³PhD Student of Structural Engineering, School of Engineering, Ferdowsi University of Mashhad, Iran.

چکیده

In this part of the study, several benchmark problems are solved to evalu ate the performance of the existing strain-based membrane elements, which were reviewed in the first part. This numerical evaluation provides a basis for comparison between these elements. Detailed discussions are offered after each benchmark problem. Based on the attained results, it is con cluded that inclusion of drilling degrees of freedom and also utilization of higher-order assumed strain field result in higher accuracy of the elements. Moreover, it is evident that imposing the optimal criteria such as equilib rium and compatibility on the assumed strain field, in addition to reducing the number of degrees of freedom of the element, increases the convergence speed of the resulting strain-based finite elements.

کلیدواژه‌ها

Strain-based formulation؛ Higher-order strain field؛ Equilibrium condition؛ Numerical evaluation؛ Drilling degrees of freedom

مراجع

1. Al Akhrass, D., Bruchon, J., Drapier, S. and Fayolle, S. Integrating a logarithmic-strain based hyperelastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elastoplasticity, Finite Elem. Anal. Des. 86 (2014) 61–70.
2. Belarbi, M.T. and Bourezane, M., On improved Sabir triangular element with drilling rotation, Rev. eur. génie civ., 9(9-10) (2005), 1151–1175.
3. Belarbi, M.T. and Bourezane, M. An assumed strain based on triangular element with drilling rotation, Courier de Savoir, 6 (2005), 117–123.
4. Belarbi, M.T. and Maalem, T. On improved rectangular finite element for plane linear elasticity analysis, Revue Européenne des Éléments Finis, 14(8) (2005), 985–997.

5. Cen, S., Chen, X.M. and Fu, X.R. Quadrilateral membrane element family formulated by the quadrilateral area coordinate method, Comput. Methods Appl. Mech. Eng. 196(41-44) (2007) 4337–4353.
6. Cen, S., Zhou, P.L., Li, C.F. and Wu, C.J. An unsymmetric 4‐node, 8‐DOF plane membrane element perfectly breaking through MacNeal’s theorem, Int. J. Numer. Methods Eng. 103(7) (2015) 469–500.
7. Felippa, C.A. A study of optimal membrane triangles with drilling free doms, Comput. Methods Appl. Mech. Eng. 192(16-18) (2003), 2125–2168.
8. Hamadi, D., Ayoub, A. and Maalem, T. A new strain-based finite element for plane elasticity problems, Eng. Comput. 33(2) (2016), 562–579.
9. MacNeal, R.H., Harder, R.L. A refined four-node membrane element with rotational degrees of freedom, Comput. Struct. 28(1) (1988) 75–84.
10. Madeo, A., Casciaro, R., Zagari, G., Zinno, R. and Zucco, G. A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses, Finite Elem. Anal. Des. 89 (2014) 52–66.
11. Paknahad, M., Noorzaei, J., Jaafar, M.S. and Thanoon, W.A. Analysis of shear wall structure using optimal membrane triangle element, Finite Elem. Anal. Des. 43(11-12) (2007) 861–869.
12. Pian, T.H. and Sumihara, K. Rational approach for assumed stress finite elements, Int. J. Numer. Methods Eng. 20(9) (1984) 1685–1695.
13. Rebiai, C. Finite element analysis of 2-D structures by new strain based triangular element, J. Mech. 35(3) (2018) 1–9.
14. Rebiai, C. and Belounar, L. A new strain based rectangular finite element with drilling rotation for linear and nonlinear analysis, Arch. Civ. Mech.Eng. 13(1) (2013) 72–81.
15. Rebiai, C. and Belounar, L. An effective quadrilateral membrane finite element based on the strain approach, Measurement, 50 (2014) 263–269.
16. Rebiai, C., Saidani, N. and Bahloul, E. A new finite element based on the strain approach for linear and dynamic analysis, Res. J. Appl. Sci. 11(6) (2015) 639–644.
17. Rezaiee-Pajand, M., Gharaei-Moghaddam, N. and Ramezani, M. Two triangular membrane element based on strain, Int. J. Appl. Mech. 11(1) (2019), 1950010.
18. Rezaiee-Pajand, M., Gharaei-Moghaddam, N. and Ramezani, M.R. A new higher-order strain-based plane element, Scientia Iranica. Transaction A, Civil Engineering, 26(4) (2019), 2258–2275.

19. Rezaiee-Pajand, M., Gharaei-Moghaddam, N. and Ramezani, M., Higher-order assumed strain plane element immune to mesh distortion, Eng. Comput. 37(9) (2020), 2957–2981.
20. Rezaiee-Pajand, M., Gharaei-Moghaddam, N. and Ramezani, M., Strainbased plane element for fracture mechanics’ problems, Theor. Appl. Fract. Mech. 108 (2020), 102569.
21. Rezaiee-Pajand, and Ramezani, M. An evaluation of MITC and ANS elements in the nonlinear analysis of shell structures, Mech. Adv. Mater. Struct. (2021) 1–21.
22. Rezaiee-Pajand, M., Ramezani, M. and Gharaei-Moghaddam, N. Us ing higher-order strain interpolation function to improve the accuracy of structural responses, Int. J. Appl. Mech. 12(3) (2020), 2050026.
23. Rezaiee-Pajand, M. and Yaghoobi, M. Formulating an effective general ized four-sided element, Eur. J. Mech. A Solids, 36 (2012), 141–155.
24. Rezaiee-Pajand, M. and Yaghoobi, M. A free of parasitic shear strain formulation for plane element, Research in Civil and Environmental Engineering, 1 (2013) 1–27.
25. Rezaiee-Pajand, M. and Yaghoobi, M. A robust triangular membrane element, Lat. Am. J. Solids Struct. 11(14) (2014), 2648–2671.
26. Rezaiee-Pajand, M. and Yaghoobi, M. An efficient formulation for linear and geometric non-linear membrane elements, Lat. Am. J. Solids Struct. 11(6) (2014), 1012–1035.
27. Rezaiee-Pajand, M. and Yaghoobi, M. Two new quadrilateral elements based on strain states, Civ. Eng. Infrastruct. J. 48(1) (2015), 133–156.
28. 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, Brebbia CA ed., Southampton University (1985), 17–25.
29. Sabir, A.B. and Sfendji, A. Triangular and rectangular plane elasticity finite elements, Thin-Walled Struct. 21(3) (1995), 225–232.
30. Tayeh, S.M. New strain-based triangular and rectangular finite elements for plane elasticity problems, Thesis, The Islamic University, Gaza, 2003.
31. Taylor, R.L., Beresford, P.J. and Wilson, E.L. A non‐conforming element for stress analysis, Int. J. Numer. Methods Eng. 10(6) (1976) 1211–1219.
32. Zhang, G. and Wang, M. Development of eight-node curved-side quadrilateral membrane element using chain direct integration scheme (SCDI) in area coordinates (MHCQ8-DI), Arabian Journal for Science and Engineering, 44(5) (2019) 4703–4724.