In spite of some drawbacks, finite element methods based on nodal rather than Gaussian integration present major advantages, especially in the context of elastoplastic or elastoviscoplastic problems—notably the elimination of locking problems due the plastic or viscoplastic incompressibility condition, and the reduction of computation and storage requirements pertaining to internal variables. This paper investigates another potential advantage of such methods, namely the possibility to account exactly—instead of approximately like with Gaussian integration—for conditions of prescribed traction on external surfaces, and continuity of the traction-vector across internal interfaces separating different materials. The technique proposed is somewhat similar to that classically used to satisfy plane stress conditions in 2D elastoplastic problems: it consists, when using the constitutive law to evaluate the stresses from the strains, in adjusting the out-of-plane components of the strain, so as to enforce either identity of the traction-vector and its prescribed value on external surfaces, or identity of the traction-vectors on both sides of internal interfaces. The examples provided for both traction-free boundaries and interfaces between materials evidence the efficiency of the technique.
Accepté le :
Publié le :
Yabo Jia 1 ; Jean-Baptiste Leblond 2, 3 ; Jean-Michel Bergheau 1
CC-BY 4.0
@article{CRMECA_2022__350_G1_57_0,
author = {Yabo Jia and Jean-Baptiste Leblond and Jean-Michel Bergheau},
title = {Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods},
journal = {Comptes Rendus. M\'ecanique},
pages = {57--83},
publisher = {Acad\'emie des sciences, Paris},
volume = {350},
year = {2022},
doi = {10.5802/crmeca.103},
language = {en},
}
TY - JOUR AU - Yabo Jia AU - Jean-Baptiste Leblond AU - Jean-Michel Bergheau TI - Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods JO - Comptes Rendus. Mécanique PY - 2022 SP - 57 EP - 83 VL - 350 PB - Académie des sciences, Paris DO - 10.5802/crmeca.103 LA - en ID - CRMECA_2022__350_G1_57_0 ER -
%0 Journal Article %A Yabo Jia %A Jean-Baptiste Leblond %A Jean-Michel Bergheau %T Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods %J Comptes Rendus. Mécanique %D 2022 %P 57-83 %V 350 %I Académie des sciences, Paris %R 10.5802/crmeca.103 %G en %F CRMECA_2022__350_G1_57_0
Yabo Jia; Jean-Baptiste Leblond; Jean-Michel Bergheau. Exact satisfaction of boundary and interface conditions in nodal-integration-based finite element methods. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 57-83. doi : 10.5802/crmeca.103. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.103/
[1] A stable finite element for the Stokes equations, Calcolo, Volume 21 (1984), pp. 337-344 | DOI | MR | Zbl
[2] The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Upper Saddle River, NJ, 1987
[3] Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991 | DOI
[4] Finite Element Procedure, Prentice-Hall, Upper Saddle River, NJ, 1996
[5] Benchmark tests based on the Couette viscometer—II: thermo-elasto-plastic solid behaviour in small and large strains, Comput. Math. Appl., Volume 67 (2014), pp. 1482-1496 | DOI | MR | Zbl
[6] A stable P1/P1 finite element for finite strain von Mises elasto-plasticity, Comput. Methods Appl. Mech. Eng., Volume 324 (2017), pp. 537-545 | DOI | MR | Zbl
[7] A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications, Commun. Numer. Methods Eng., Volume 14 (1998), pp. 437-449 | DOI | MR | Zbl
[8] Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes, Int. J. Numer. Methods Eng., Volume 47 (2000), pp. 1549-1568 | DOI | Zbl
[9] An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications, Commun. Numer. Methods Eng., Volume 17 (2001), pp. 551-561 | DOI | Zbl
[10] Locking-free continuum displacement finite elements with nodal integration, Int. J. Numer. Methods Eng., Volume 76 (2008), pp. 1020-1043 | DOI | MR | Zbl
[11] Reformulation of nodally integrated continuum elements to attain insensitivity to distortion, Int. J. Numer. Methods Eng., Volume 90 (2012), pp. 805-818 | DOI | MR | Zbl
[12] Linear tetrahedral element for problems of plastic deformation, Meccanica, Volume 50 (2015), pp. 3069-3086 | DOI | MR | Zbl
[13] A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems, Comput. Struct., Volume 87 (2009), pp. 14-26 | DOI
[14] A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes, Comput. Methods Appl. Mech. Eng., Volume 199 (2010), pp. 3005-3027 | DOI | MR | Zbl
[15] A stabilized conforming nodal integration for Galerkin mesh-free methods, Int. J. Numer. Methods Eng., Volume 50 (2001), pp. 435-466 | DOI | Zbl
[16] Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods, Int. J. Numer. Methods Eng., Volume 53 (2002), pp. 2587-2615 | DOI
[17] A stable, meshfree, nodal integration method for nearly incompressible solids, Finite Elem. Anal. Des., Volume 51 (2012), pp. 81-85 | DOI
[18] A comparative study on the performance of meshless approximations and their integration, Comput. Mech., Volume 48 (2011), pp. 121-137 | DOI | MR | Zbl
[19] In-plane/out-of-plane separated representations of updated Lagrangian descriptions of viscoplastic flow models in plate domains, C. R. Méc., Volume 344 (2016), pp. 225-235 | DOI
[20] A new nodal-integration-based finite element method for the numerical simulation of welding processes, Metals, Volume 10 (2020), pp. 1386-1403 | DOI
[21] The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann, Oxford, 2013
[22] A stabilized nodally integrated tetrahedral, Int. J. Numer. Methods Eng., Volume 67 (2006), pp. 841-867 | DOI | MR | Zbl
[23] Meshfree and finite element nodal integration method, Int. J. Numer. Methods Eng., Volume 74 (2008), pp. 416-446 | DOI | MR | Zbl
[24] Reference Analysis Manual, ESI Group, Rungis, France, released: 2020
[25] Direct nodal imposition of surface loads using the divergence theorem, Finite Elem. Anal. Des., Volume 165 (2019), pp. 31-40 | DOI | MR
[26] Applications of a nodal-integration based finite element method to non-linear problems, 14th WCCM and ECCOMAS Congress 2020 (Virtual Congress 2021) (2021)
[27] A new finite element model for welding heat sources, Metall. Trans. B, Volume 15 (1984), pp. 299-305 | DOI
Cité par Sources :
Commentaires - Politique