Deterioration of a finite element method for arch structures when thickness goes to zero. (English) Zbl 0756.73088

See the preview in Zbl 0734.73076.


74S05 Finite element methods applied to problems in solid mechanics
74K15 Membranes
74K10 Rods (beams, columns, shafts, arches, rings, etc.)


Zbl 0734.73076
Full Text: DOI EuDML


[1] Arnold, D.N. (1981): Discretization by finite elements of a model parameter dependent problem. Numer. Math.37, 405-421 · Zbl 0446.73066
[2] Bernadou, M., Ducatel, Y. (1982): Approximation of general arch problems by straight beam elements. Numer. Math.40, 1-29 · Zbl 0508.73069
[3] Brezis, H. (1983): Analyse fonctionnelle?th?orie et applications. Collection Math?matique appliqu?es pour la Ma?trise. Masson, Paris
[4] Chenais, D., Rousselet, Benedict (1988): Design sensitivity for arch structures. J. Optimization Theory Appl58, 225-239 · Zbl 0631.49015
[5] Ciarlet, P. (1980): The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam · Zbl 0511.65078
[6] Hughes, T.J.R., Taylor, R.L., Kanoknukulchai, W. (1977): A simple and efficient finite element for plate bending. Int. J. Numer. Methods Eng.11, 1529-1543 · Zbl 0363.73067
[7] Kikuchi, F. (1982): Accuracy of some finite element models for arch problems. Comput. Methods Appl. Mech. Eng.35, 315-345 · Zbl 0499.73068
[8] Reedy, B.D. (1988): Convergence of mixed finite element approximations for the shallow arch problem. Numer. Math.53, 687-699 · Zbl 0628.73084
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