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A six-node prismatic solid finite element for geometric nonlinear problems in elasticity. (English) Zbl 07318248

Summary: The present work deals with an extended six-node prismatic 3D solid finite element to the analysis of nonlinear geometrical problems. The kinematic formulation is based on a virtual Space Fiber Rotation (SFR) concept which conducts to improve the displacement fields with additional displacement terms, presenting rotational degrees of freedom (DOFs). Once the standard and patch tests for linear validation are previously achieved, the present element is assessed again for large displacement and moderate rotation. For this purpose, the total Lagrangian approach is used and the Green-Lagrange strain Piola-Kirchhoff stress tensors are considered. The material behavior considered in this work is restricted to Saint-Venant-Kirchhoff model for 3D large displacements elasticity To demonstrate the efficiency and accuracy of the developed finite element model, extensive and standard nonlinear benchmarks are presented. The obtained results show a good convergence and accuracy compared to similar finite elements and consequently well capability of the present element to deal with geometric nonlinear problems, including prediction of several limit points.

MSC:

74Cxx Plastic materials, materials of stress-rate and internal-variable type
74Sxx Numerical and other methods in solid mechanics

Software:

ABAQUS
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References:

[1] ABAQUS, Analysis: User’s manual, in, V. 6.11 (2010)
[2] Abed-Meraim, F.; Combescure, A., An improved assumed strain solid-shell element formulation with physical stabilization for geometric non-linear applications and elastic-plastic stability analysis, Internat. J. Numer. Methods Engrg., 80, 1640-1686 (2009) · Zbl 1183.74254
[3] Abed-Meraim, F.; Trinh, V. D.; Combescure, A., Assumed-strain solid-shell formulation for the six-node finite element SHB6: evaluation on non-linear benchmark problems, Eur. J. Comput. Mech./Rev. Eur. Méc. Numér., 21, 52-71 (2012)
[4] Areias, P. M.A.; César de Sá, J. M.A.; António, C. A.C.; Fernandes, A. A., Analysis of 3D problems using a new enhanced strain hexahedral element, Internat. J. Numer. Methods Engrg., 58, 1637-1682 (2003) · Zbl 1032.74661
[5] Ayad, R., Contribution à la modélisation numérique pour l’analyse des solides et des structures, et pour la mise en forme des fluides non newtoniens, (Application à des Matériaux D’emballage [Contribution to the Numerical Modeling of Solids and Structures and the Non-Newtonian Fluids Forming Process. Application to Packaging Materials] (2002), Habilitation to conduct researches, University of Reims: Habilitation to conduct researches, University of Reims Reims, France), (in French)
[6] Ayad, R.; Zouari, W.; Meftah, K.; Zineb, T. B.; Benjeddou, A., Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber, Internat. J. Numer. Methods Engrg., 95, 46-70 (2013) · Zbl 1352.74321
[7] Ayadi, A.; Meftah, K.; Sedira, L., Elastoplastic analysis of plane structures using improved membrane finite element with rotational DOFs, Frattura Integr. Strutt., 14, 148-162 (2020)
[8] Ayadi, A.; Meftah, K.; Sedira, L.; Djahara, H., An eight-node hexahedral finite element with rotational DOFs for elastoplastic applications, Acta Univ. Sapientiae Electr. and Mech. Eng., 11, 54-66 (2019)
[9] Bathe, K., ADINA System Verification Manual (1983), ADINA Engineering, Inc: ADINA Engineering, Inc Wa-tertown, USA
[10] Bathe, K. J., Finite Element Procedures (1996), Prentice hall Englewood Cliffs: Prentice hall Englewood Cliffs NJ
[11] Bischoff, M.; Ramm, E., Shear deformable shell elements for large strains and rotations, Internat. J. Numer. Methods Engrg., 40, 4427-4449 (1997) · Zbl 0892.73054
[12] Bonet, J.; Gil, A. J.; Wood, R. D., Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis (2012), Cambridge University Press · Zbl 1262.74001
[13] Bonet, J.; Wood, R. D., Nonlinear Continuum Mechanics for Finite Element Analysis (1997), Cambridge university press · Zbl 0891.73001
[14] Chrisfield, M., Non-linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials (1991), John Wiley & Sons: John Wiley & Sons New York
[15] Crisfield, M. A., A fast incremental/iterative solution procedure that handles “snap-through”, (Computational Methods in Nonlinear Structural and Solid Mechanics (1981), Elsevier), 55-62 · Zbl 0479.73031
[16] Ghomari, T.; Meftah, K.; Ayad, R.; Talbi, N., A space fibre as added value in finite element modelling for optimal analysis of problems involving contact, Eur. J. Comput. Mech./Rev. Eur. Méc. Numér., 21, 141-157 (2012)
[17] Gruttmann, F.; Stein, E.; Wriggers, P., Theory and numerics of thin elastic shells with finite rotations, Ing.-Arch., 59, 54-67 (1989)
[18] Klinkel, S.; Wagner, W., A geometrical non-linear brick element based on the EAS-method, Internat. J. Numer. Methods Engrg., 40, 4529-4545 (1997) · Zbl 0899.73539
[19] Kuo-Mo, H., Nonlinear analysis of general shell structures by flat triangular shell element, Comput. Struct., 25, 665-675 (1987) · Zbl 0604.73084
[20] Leicester, R., Finite deformations of shallow shells (Shallow shell deformations based on nonlinear equations solved by Newton-Raphson iteration), Amer. Soc. Civ. Eng. Eng. Mech. Div. J., 94, 1409-1423 (1968)
[21] Meek, J. L.; Tan, H. S., Instability analysis of thin plates and arbitrary shells using a faceted shell element with loof nodes, Comput. Methods Appl. Mech. Engrg., 57, 143-170 (1986) · Zbl 0591.73085
[22] Meftah, K., Modélisation Numérique des Solides Par éléments Finis Volumiques Basés sur le Concept SFR [Numerical Modeling of 3D Structure by Solid Finite Elements Based Upon the SFR Concept] (Space Fiber Rotation) (2013), University of Biskra: University of Biskra Algeria, (in French)
[23] Meftah, K.; Ayad, R.; Hecini, M., A new 3D 6-node solid finite element based upon the “Space Fibre Rotation” concept, Eur. J. Comput. Mech./Rev. Eur. Méc. Numér., 22, 1-29 (2012)
[24] Meftah, K.; Sedira, L., A four-node tetrahedral finite element based on space fiber rotation concept, Acta Univ. Sapientiae Electr. Mech. Eng., 11, 67-78 (2019)
[25] Meftah, K.; Sedira, L.; Zouari, W.; Ayad, R.; Hecini, M., A multilayered 3D hexahedral finite element with rotational DOFs, Eur. J. Comput. Mech., 24, 107-128 (2015) · Zbl 1327.74136
[26] Meftah, K.; Zouari, W.; Sedira, L.; Ayad, R., Geometric non-linear hexahedral elements with rotational DOFs, Comput. Mech., 57, 37-53 (2016) · Zbl 1382.65414
[27] Mostafa, M., An improved solid-shell element based on ANS and EAS concepts, Internat. J. Numer. Methods Engrg., 108, 1362-1380 (2016)
[28] Ooi, E. T.; Rajendran, S.; Yeo, J. H., Extension of unsymmetric finite elements US-QUAD8 and US-HEXA20 for geometric nonlinear analyses, Eng. Comput., 24, 407-431 (2007) · Zbl 1198.74101
[29] Reddy, J. N., An Introduction to Nonlinear Finite Element Analysis (2004), Oxford University Press: Oxford University Press USA
[30] Reese, S., On a physically stabilized one point finite element formulation for three-dimensional finite elasto-plasticity, Comput. Methods Appl. Mech. Engrg., 194, 4685-4715 (2005) · Zbl 1221.74075
[31] Simo, J. C.; Rifai, M. S., A class of mixed assumed strain methods and the method of incompatible modes, Internat. J. Numer. Methods Engrg., 29, 1595-1638 (1990) · Zbl 0724.73222
[32] Surana, K. S., Geometrically nonlinear formulation for the curved shell elements, Internat. J. Numer. Methods Engrg., 19, 581-615 (1983) · Zbl 0509.73082
[33] Sze, K.; Chan, W., A six-node pentagonal assumed natural strain solid-shell element, Finite Elem. Anal. Des., 37, 639-655 (2001) · Zbl 1015.74072
[34] Sze, K. Y.; Liu, X. H.; Lo, S. H., Hybrid-stress six-node prismatic elements, Internat. J. Numer. Methods Engrg., 61, 1451-1470 (2004) · Zbl 1075.74682
[35] Sze, K.; Liu, X.; Lo, S., Popular benchmark problems for geometric nonlinear analysis of shells, Finite Elem. Anal. Des., 40, 1551-1569 (2004)
[36] Thomas, G.; Gallagher, R. H., A Triangular Thin Shell Finite Element: Nonlinear Analysis (1975), National Aeronautics and Space Administration
[37] Tian, R.; Yagawa, G., Generalized nodes and high-performance elements, Internat. J. Numer. Methods Engrg., 64, 2039-2071 (2005) · Zbl 1122.74524
[38] Trinh, V. D.; Abed-Meraim, F.; Combescure, A., A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element, J. Mech. Sci. Technol., 25, 2345-2364 (2011)
[39] Vasios, N., Nonlinear Analysis of Structures the Arc Length Method: Formulation (2015), (PhD Student)
[40] Wagner, W., Stability analysis of shells with the finite element method, (Nonlinear Analysis of Shells by Finite Element. Nonlinear Analysis of Shells by Finite Element, CISM Courses and Lectures (1992), Springer-Verlag: Springer-Verlag Vienna)
[41] Wang, J.; Wagoner, R. H., A practical large-strain solid finite element for sheet forming, Internat. J. Numer. Methods Engrg., 63, 473-501 (2005) · Zbl 1140.74560
[42] Yamakawa, S.; Shimada, K., Converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for FEM accuracy and efficiency, Internat. J. Numer. Methods Engrg., 80, 74-102 (2009) · Zbl 1176.74200
[43] Yuqiu, L.; Yin, X., Generalized conforming triangular membrane element with vertex rigid rotational freedoms, Finite Elem. Anal. Des., 17, 259-271 (1994) · Zbl 0814.73061
[44] Zhang, Y. X.; Cheung, Y. K., A refined non-linear non-conforming triangular plate/shell element, Internat. J. Numer. Methods Engrg., 56, 2387-2408 (2003) · Zbl 1062.74632
[45] Zouari, W.; Assarar, M.; Meftah, K.; Ayad, R., Free vibration analysis of homogeneous piezoelectric structures using specific hexahedral elements with rotational DOFs, Acta Mech., 226, 1737-1756 (2015)
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