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A set of hybrid equilibrium finite element models for the analysis of three-dimensional solids. (English) Zbl 0873.73067

Summary: An approach to the formulation of equilibrium elements for the analysis of three-dimensional elasticity problems is presented. This formulation is an extension of the approach proposed earlier for the analysis of two-dimensional elasticity problems. The general aspects of the formulation remain unchanged when applied to the new problem, but new points are considered, namely the way to perform volume integrations for general elements and the techniques used to obtain the self-equilibrated three-dimensional stress approximation functions. The numerical behaviour of such elements is presented and discussed.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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[1] Almeida, Comp. Struct. 40 pp 1043– (1991)
[2] ’Modelos de elementos finitos para a análise elastoplástica’, Ph.D. Thesis, Technical University of Lisbon, 1989.
[3] de Veubeke, AGARDograf 72 pp 165– (1964)
[4] and , ’Equilibrium finite elements and dual analysis in three-dimensional elastostatics’, in and , (eds.), Education, Practice and Promotion of Computational Methods in Engineering, Techno-Press, Seoul, 1995, pp. 955-960.
[5] and , Plasticity in Structural Engineering Fundamentals and Applications, CISM Courses and Lectures 241, Springer, Wien, 1979.
[6] ’Application of the dual analysis principle’, in (ed.), High Speed Computing of Elastic Structures, Université de Liège, 1971, pp. 167-207.
[7] ’A reappraisal of compound equilibrium finite elements’, Proc. 12th Canadian Congress of Applied Mechanics, Carleton Univ., Ottawa, 1989.
[8] de Veubeke, J. Strain Anal. 2 pp 265– (1967)
[9] Robinson, Comp. Methods Appl. Mech. Eng. 2 pp 43– (1973) · Zbl 0252.73054
[10] ’Um modelo de elementos finitos de equilíbrio para elasticidade tridimensional’, M.Sc. Dissertation, Technical University of Lisbon, 1993.
[11] Pian, AIAA J. 2 pp 1333– (1964)
[12] Pian, Int. J. numer. methods eng. 1 pp 3– (1969) · Zbl 0252.73052
[13] Spilker, Int. J. numer. methods eng. 18 pp 445– (1982) · Zbl 0479.73062
[14] Jirousek, Comp. Methods. Appl. Mech. Eng. 12 pp 77– (1977) · Zbl 0366.73065
[15] Jirousek, Comp. Methods. Appl. Mech. Eng. 14 pp 65– (1978) · Zbl 0384.73052
[16] Jirousek, Commun. numer methods eng. 9 pp 837– (1993) · Zbl 0789.73070
[17] and , ’Hybrid-Trefftz boundary integral formulation for simulation of singular stress fields’, Int. J. numer. methods eng., in press.
[18] Airy, Phil. Trans. Royal Soc. London 153 pp 49– (1863)
[19] A treatise on the mathematical theory of elasticity, 4th edn, Cambridge University Press, Cambridge 1927.
[20] Maxwell, Proc. London Math. Soc. 1 pp 58– (1868)
[21] Morera, Rend. Acc. Naz. Lincei 1 (1892)
[22] ’Surface patches and B-spline curves’, in and , (eds.), Computer Aided Geometric Design, Academic Press, New York, 1974.
[23] Sparse Matrix Technology, Academic Press, London, 1984. · Zbl 0536.65019
[24] ’Modelos de elementos finitos para a análise elástica de lajes’, Ph.D. Thesis, Technical University of Lisbon, 1993.
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