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Discretization by finite elements of a model parameter dependent problem. (English) Zbl 0446.73066


MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

References:

[1] Babu?ka, I., Aziz, A.K.: Survey lectures on the finite element method. In: The mathematical foundations of the finite element method with applications to partial differential equations (A.K. Aziz, ed.), pp. 5-359. New York: Academic Press 1973
[2] Bercovier, M.: Perturbation of mixed variational problems. Application to mixed finite element methods. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér.12, 211-236 (1978)
[3] Brezzi, F.: On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. Rev. Française Automat. Informat. Recherche Opérationnelle8 R-2, 129-151 (1974) · Zbl 0338.90047
[4] Falk, R., Osborn, J.: Error estimates for mixed methods. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Anal. Numér. (in press 1981)
[5] Fried, I.: Finite element analysis of incompressible material by residual energy balancing. Internat. J. Solids and Structures10, 993-1002 (1974) · Zbl 0281.73045 · doi:10.1016/0020-7683(74)90007-9
[6] Hughes, T.J.R., Cohen, M., Haroun, M.: Reduced and selective integration techniques in the finite element analysis of plates. Nuclear Engrg. Design46, 203-222 (1978) · doi:10.1016/0029-5493(78)90184-X
[7] Hughes, T.J.R., Taylor, R.L., Kanoknukulchai, W.: A simple and efficient finite element for plate bending. Internat. J. Numer. Methods Engrg.11, 1529-1543 (1977) · Zbl 0363.73067 · doi:10.1002/nme.1620111005
[8] Malkus, D.S., Hughes, T.J.R.: Mixed finite element methods-reduced and selective integration techniques: a unification of concepts. Comput. Methods Appl. Mech. Engrg.15, 63-81 (1978) · Zbl 0381.73075 · doi:10.1016/0045-7825(78)90005-1
[9] Pawsey, S.F., Clough, R.W.: Improved numerical integration of thick shell finite elements. Internat. J. Numer. Methods Engrg.3, 545-586 (1971) · Zbl 0248.73035 · doi:10.1002/nme.1620030411
[10] Pugh, E.D.L., Hinton, E., Zienkiewicz, O.C.: A study of quadrilateral plate bending elements with reduced integration. Internat. J. Numer. Methods Engrg.12, 1059-1079 (1978) · Zbl 0377.73065 · doi:10.1002/nme.1620120702
[11] Timoshenko, S.P.: On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philos. Mag. Ser.6, 41, 744-746 (1921) · doi:10.1080/14786442108636264
[12] Zienkiewicz, O.C., Hinton, E.: Reduced integration, function smoothing and non-conformity in finite element analysis (with special reference to thick plates). J. Franklin Inst.302, 443-461 (1976) · Zbl 0351.73099 · doi:10.1016/0016-0032(76)90035-1
[13] Zienkiewicz, O.C., Taylor, R.L., Too, J.M.: Reduced integration techniques in general analysis of plates and shells. Internat. J. Numer. Methods Engrg.5, 275-290 (1971) · Zbl 0253.73048 · doi:10.1002/nme.1620030211
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