×

Restraining approach for the spurious kinematic modes in hybrid equilibrium element. (English) Zbl 1311.74127

Summary: The present paper proposes a rigorous approach for the elimination of spurious kinematic modes in hybrid equilibrium elements, for three well known mesh patches. The approach is based on the identification of the dependent equations in the set of inter-element and boundary equilibrium equations of the sides involved in the spurious kinematic mode. Then the kinematic variables related to the dependent equations are reciprocally constrained and, by application of master slave elimination method, the set of inter-element equilibrium equations is reduced to full rank. The elastic solutions produced by means of the proposed approach verify the homogeneous, the inter-element and the boundary equilibrium equations. Hybrid stress formulation is developed in a rigorous mathematical setting. The results of linear elastic analysis obtained by the proposed approach and by classical displacement based method are compared for some structural examples.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Fraeijs de Veubeke, B, Upper and lower bounds in matrix structural analysis, AGARDograf, 72, 165-201, (1964) · Zbl 0131.22903
[2] Fraeijs de Veubeke, B; Zienkiewicz, OC (ed.); Holister, GS (ed.), Displacements and equilibrium models in the finite elements method, (1965), London
[3] Almeida, JPM; Pereira, OJBA, Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems, Comput Methods Appl Mech Eng, 195, 279-296, (2006) · Zbl 1086.74041
[4] Ladeveze, P; Leguillon, D, Error estimate procedure in the finite element method and applications, SIAM J Numer Anal, 20, 483-509, (1983) · Zbl 0582.65078
[5] Pereira, OJBA; Almeida, JPM; Maunder, EAW, Adaptive methods for hybrid equilibrium finite element models, Comput Methods Appl Mech Eng, 176, 19-39, (1999) · Zbl 0991.74072
[6] Debongniea, JF; Zhongb, HG; Beckersb, P, Dual analysis with general boundary conditions, Comput Methods Appl Mech Eng, 122, 183-192, (1995) · Zbl 0851.73057
[7] Kempeneers, M; Debongnie, JF; Beckers, P, Pure equilibrium tetrahedral finite elements for global error estimation by dual analysis, Int J Numer Methods Eng, 81, 513-536, (2010) · Zbl 1183.74284
[8] Almeida, JPM; Freitas, JAT, An alternative approach to the formulation of hybrid equilibrium finite elements, Comput Struct, 40, 1043-1047, (1991)
[9] Almeida, JPM; Pereira, OJBA, A set of hybrid equilibrium finite element models for the analysis of threedimensional solids, Int J Numer Methods Eng, 39, 2789-2802, (1996) · Zbl 0873.73067
[10] Pian, THH, State-of-the-art development of hybrid/mixed finite element method, Finite Elem Anal Des, 21, 5-20, (1995) · Zbl 0875.73310
[11] Almeida Pereira, OJB, Hybrid equilibrium hexahedral elements and super-elements, Commun Numer Methods Eng, 24, 157-165, (2008) · Zbl 1132.74043
[12] Maunder, EAW; Moitinho de Almeida, JP, A general formulation of equilibrium macro-elements with control of spurious kinematic modes: the exorcism of an old curse, Int J Numer Methods Eng, 39, 3175-3194, (1996) · Zbl 0878.73070
[13] Maunder, EAW; Moitinho de Almeida, JP, Hybrid-equilibrium elements with control of spurious kinematic modes, Comput Assist Mech Eng Sci, 4, 587-605, (1997) · Zbl 0969.74589
[14] Maunder, EAW; Moitinho de Almeida, JP, The stability of stars of triangular equilibrium plate elements, Int J Numer Methods Eng, 77, 922-968, (2009) · Zbl 1183.74294
[15] Maunder, EAW; Moitinho de Almeida, JP, A triangular hybrid equilibrium plate element of general degree, Int J Numer Methods Eng, 63, 315-350, (2005) · Zbl 1140.74555
[16] Moitinho de Almeida, JP; Maunder, EAW, Recovery of equilibrium on star patches using a partition of unity technique, Int J Numer Methods Eng, 79, 1493-1516, (2009) · Zbl 1176.74201
[17] Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. ButterworthHeinemann Press, Oxford · Zbl 0969.74589
[18] Wisniewski, K; Turska, E, Improved four-node Hellinger-Reissner elements based on skew coordinates, Int J Numer Methods Eng, 76, 798-836, (2008) · Zbl 1195.74207
[19] Cook, RD, A plane hybrid element with rotational d.o.f. and adjustable stiffness, Int J Numer Methods Eng, 24, 1499-1508, (1987) · Zbl 0615.73084
[20] Liu, GR; Nguyen-Thoi, T; Lam, KY, A novel alpha finite element method (afem) for exact solution to mechanics problems using triangular and tetrahedral elements, Comput Methods Appl Mech Eng, 197, 3883-3897, (2008) · Zbl 1194.74433
[21] Timoshenko S, Goodier JN (1951) Theory of elasticity. McGraw-Hill, New York, p 83 · Zbl 0045.26402
[22] Howland, RCJ, On the stresses in the neighbourhood of a circular hole in a strip under tension, R Soc Philos Trans Ser A, 229, 49-86, (1930) · JFM 56.1236.04
[23] Alfano, G; Crisfield, MA, Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, Int J Numer Methods Eng, 50, 1701-1736, (2001) · Zbl 1011.74066
[24] Parrinello, F; Failla, B; Borino, G, Cohesive-frictional interface constitutive model, Int J Solids Struct, 46, 2680-2692, (2009) · Zbl 1167.74508
[25] Wilson, EL; Khalvati, M, Finite element for the dynamic analysis of fluidsolid system, Int J Numer Methods Eng, 19, 1657-1668, (1983) · Zbl 0519.76094
[26] Parrinello, F; Borino, G, Lagrangian finite element modelling of damfluid interaction: accurate absorbing boundary conditions, Comput Struct, 85, 932-943, (2007)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.