×

A note on the convergence of finite element approximations for problems formulated in curvilinear coordinate systems. (English) Zbl 0278.73045


MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
Full Text: DOI

References:

[1] Cantin, G.; Clough, R. W., A curved cylindrical-shell finite element, AIAA Journal, 6, No.6, 1057-1062 (1968) · Zbl 0159.27002
[2] Megård, G., Analysis of thin shells using planar and curved finite-elements, (Lich. Techn. Thesis. Lich. Techn. Thesis, Report No. 69-1 (1969), The Norwegian Institute of Technology, The University of Trondheim: The Norwegian Institute of Technology, The University of Trondheim Norway), Division of Structural Mechanics
[3] Argyris, J. H.; Scharpf, D. W., The SHEBA family of shell elements for the matrix displacement method, part I, II, The Aeronautical Journal of the Roy. Aer. Soc., 72, 873-883 (1968)
[4] Dupuis, G.; Göel, J.-J., A curved finite element for thin elastic shells, J. Solids Structures, 6, 1413-1428 (1970) · Zbl 0218.73098
[5] Argyris, J. H.; Lochner, N., On the application of the SHEBA element Computer Methods in Applied Mechanics and Engineering, 1, No. 3, 317-347 (1972)
[6] Argyris, J. H.; Haase, H.; Malejannakis, Natural geometry of surfaces with specific reference to the matrix displacement analysis of shells, (ISD-Report No. 134 (1973), University of Stuttgart) · Zbl 0273.53001
[7] Zienkiewicz, O. C., The finite element method in engineering science (1971), McGraw-Hill: McGraw-Hill London · Zbl 0237.73071
[8] Gowper, G. R.; Olson, M. D., Comparison of two high-precision triangular finite elements for arbitrary deep shells, (3rd Conf. on Matrix Method (Oct. 1971), Wright-Patterson Air Force Base: Wright-Patterson Air Force Base Ohio), 19-20
[9] Synge, J. L., The hypercircle in mathematical physics (1957), Cambridge University Press: Cambridge University Press New York · Zbl 0079.13802
[10] Mclay, R. W., Completeness and convergence properties of finite element displacement functions - a general treatment, AIAA paper, 67-143 (1967), New York
[11] Pian, T. H.H.; Tong, P., The convergence of the finite element method in solving linear elastic problems, International Journal of Solids and Structures, 3, 865-880 (1967) · Zbl 0149.42802
[12] Oliveira, E. R.A., Theoretical foundations of the finite element method, Int. J. Solids Structures, 4, 929-952 (1968) · Zbl 0174.41601
[13] Fried, I., Discretization and round-off error in the finite element analysis of elliptic boundary value problems and eigenvalue problems, (Ph.D. Dissertation (1971), Massachusetts Institute of Technology: Massachusetts Institute of Technology Cambridge)
[14] T. Moan, Forthcoming Lich. Techn. Thesis. Division of Structural Mechanics, The Norwegian Institute of Technology.; T. Moan, Forthcoming Lich. Techn. Thesis. Division of Structural Mechanics, The Norwegian Institute of Technology.
[15] Walz, J. E.; Fulton, R. E.; Cyrus, N. J., Accuracy and convergence of finite element approximations, (Proc. of 2nd Conf. on Matrix Methods in Structural Mechanics (1968), Wright Patterson Air Force Base: Wright Patterson Air Force Base Ohio)
[16] Yamamoto, Y.; Tokuda, N., A note on convergence of finite element solutions, Int. J. Num. Meths. in Engineering, 3, 485-493 (1971) · Zbl 0262.65068
[17] Strang, G., Approximation in the finite element method, Numerische Mathematik, 19, 81-98 (1972) · Zbl 0221.65174
[18] Flügge, W., Stresses in shells (1960), Springer-Verlag · Zbl 0092.41504
[19] Timoshenko, S.; Woinowsky-Krieger, S., Theory of plates and shells (1959), McGraw-Hill: McGraw-Hill New York · Zbl 0114.40801
[20] Donnell, L. H., Stability of thin walled tubes under torsion, N.A.C.A. Techn. Rep. No. 479 (1933), Washington
[21] Koiter, W. T., A consistent first approximation in the general theory of thin elastic shells, (Proc. Symp. on Theory of Thin Elastic Shells. Proc. Symp. on Theory of Thin Elastic Shells, Delft August, 1959 (1960), North-Holland: North-Holland Amsterdam), 12-33 · Zbl 0109.43002
[22] Michlin, S. G.; Smolitskiy, K. L., Approximate methods for the solution of differential and integral equations, (Kalaba, R. E. (1967), Amer. Eisevier Publishing Co. Inc: Amer. Eisevier Publishing Co. Inc New York), trans. from Russian · Zbl 0159.20702
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.