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Hybrid equilibrium hexahedral elements and super-elements. (English) Zbl 1132.74043

Summary: Equilibrated solutions, locally satisfying all the equilibrium conditions, may be obtained by using a special case of the hybrid finite element formulation. Unlike simplicial super-elements in two and three dimensions, which are free from spurious kinematic modes, and the quadrilateral super-element with diagonal subdivision, which has exactly one internal spurious kinematic mode, no hexahedral super-element free of external spurious kinematic modes is yet known as far as the author is aware.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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[1] Fraeijs de Veubeke, Upper and lower bounds in matrix structural analysis, AGARDograf 72 pp 165– (1964) · Zbl 0131.22903
[2] Almeida, Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems, Computer Methods in Applied Mechanics and Engineering 195 pp 279– (2006) · Zbl 1086.74041
[3] Ladevèze, Error estimate procedure in the finite element method and applications, SIAM Journal on Numerical Analysis 20 (3) pp 483– (1983)
[4] Pereira OJBA Utilização de Elementos Finitos de Equilíbrio em Refinamento Adaptativo 1996
[5] Pereira, Adaptive methods for hybrid equilibrium finite element models, Computer Methods in Applied Mechanics and Engineering 176 pp 19– (1999) · Zbl 0991.74072
[6] Almeida, An alternative approach to the formulation of hybrid equilibrium finite elements, Computers and Structures 40 pp 1043– (1991)
[7] Almeida, A set of hybrid equilibrium finite element models for the analysis of three-dimensional solids, International Journal for Numerical Methods in Engineering 39 pp 2789– (1996) · Zbl 0873.73067
[8] Fraeijs de Veubeke, B. M. Fraeijs de Veubeke Memorial Volume of Selected Papers pp 569– (1980)
[9] Maunder, Hybrid-equilibrium elements with control of spurious kinematic modes, Computer Assisted Mechanics and Engineering Sciences 4 pp 587– (1997) · Zbl 0969.74589
[10] Kempeneers, Pure equilibrium tetrahedral finite elements and global error estimation by dual analysis, Computer Methods in Applied Mechanics and Engineering (2005)
[11] Pereira, Aplicação de Elementos Finitos de Equilíbrio à Estimação do Erro em Malhas de Elementos Finitos Utilizadas na Análise de Barragens Abóbada, Revista Portuguesa de Engenharia de Estruturas 53 pp 31– (2004)
[12] Watwood, An equilibrium stress field model for finite element solutions of two dimensional elastoplastic problems, International Journal of Solids and Structures 4 pp 857– (1968) · Zbl 0164.26201
[13] Ramsay, Curious convergence with hypo-static hybrid equilibrium models, Communications in Numerical Methods in Engineering 13 pp 541– (1997)
[14] Sander, High Speed Computing of Elastic Structures pp 167– (1971)
[15] Maunder, A general formulation of equilibrium macro-elements with control of spurious kinematic modes, International Journal for Numerical Methods in Engineering 39 pp 3175– (1996) · Zbl 0878.73070
[16] Pissanetzky, Sparse Matrix Technology (1984)
[17] Richardson, The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam, Transactions of the Royal Society of London, Series A 210 pp 307– (1910) · JFM 41.0871.04
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