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Krizek, Michal

An equilibrium finite element method in three-dimensional elasticity. (English) Zbl 0488.73072

Apl. Mat. 27, 46-75 (1982).
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Cited in 1 Review
Cited in 9 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74P99 Optimization problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics

Keywords:

composite tetrahedral equilibrium element; two types of finite approximation; three-dimensional problem; polyhedral domain; Castigliano- Menabrea’s principle; minimum complementary energy; a priori error estimates; existence of strongly regular family of decompositions
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\textit{M. Krizek}, Apl. Mat. 27, 46--75 (1982; Zbl 0488.73072)
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References:

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[2] J. H. Bramble M. Zlámal: Triangular elements in the finite element method. Math. Comp. 24 (1970), 809-820. · Zbl 0226.65073
[3] P. G. Ciarlet P. A. Raviart: General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods. Arch. Rational Mech. Anal. 46 (1972), 177-199. · Zbl 0243.41004
[4] P. G. Ciarlet: The finite element method for elliptic problems. North-Holland publishing company, Amsterdam, New York, Oxford, 1978. · Zbl 0383.65058
[5] G. Duvaut J. L. Lions: Inequalities in mechanics and physics. Springer-Verlag, Berlin, Heidelberg, New York, 1976. · Zbl 0331.35002
[6] B. J. Hartz V. B. Watwood: An equilibrium stress field model for finite element solution of two-dimensional elastostatic problems. Internat. J. Solids and Struct. 4 (1968), 857-873. · Zbl 0164.26201
[7] I. Hlaváček J. Nečas: Mathematical theory of elastic and elasto-plastic bodies. SNTL, Praha, Elsevier, Amsterdam, 1980.
[8] I. Hlaváček: Convergence of an equilibrium finite element model for plane elastostatics. Apl. Mat. 24 (1979), 427-457.
[9] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math. 30 (1978), 103-116. · Zbl 0427.73072
[10] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha, 1967. · Zbl 1225.35003
[11] Энциклопедия элементарной математики - Геометрия книга 4, 5. Hauka, Москва, 1966. · Zbl 0156.18206
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