Shape functions and the accuracy of arch finite elements

AIAA Journal

Volumn 11, Issue 3, 1973, Pages 287-291

  Fried, Isaac ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85003293221     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/3.6742     Document Type: Article

References (28)

1. McLay, R. W., “Completeness and Convergence Properties of Finite Element Displacement Functions- A General Treatment,” AIAA Paper 67-143, New York, 1967.
2. Fried, I., “Discretization and Round-Off Errors in the Finite Element Analysis of Elliptic Boundary Value Problems and Eigenvalue Problems,” PhD. thesis, June 1971, MIT, Cambridge, Mass.
3. Fried, I., “Accuracy of Finite Element Eigenproblems,” Journal of Sound and Vibration, Vol. 18, No. 2, 1971, pp. 289-295.
4. Lynn, P. P. and Dhillon, B. S., “Convergence of Eigenvalue Solutions in Conforming Plate Bending Finite Elements,” International Journal for Numerical Methods in Engineering, Vol. 4, 1972, pp. 217— 234.
5. Synge, J. L., “Triangularization in the Flypercircle Method for Plane Problems,” Proceedings of the Royal Irish Academy, Vol. 54A, 1952, pp. 341-367.
6. Synge, J. L., The Hypercircle in Mathematical Physics, Cambridge University Press, New York, 1957, pp. 209-213.
7. Zlamal, M., “On the Finite Element Method,” Numerische Mathematik, Vol. 12, 1968, pp. 394-409.
8. Flaisler, W. E. and Stricklin, J. A., “Rigid Body Displacement of Curved Elements in the Analysis of Shells by the Matrix Displacement Method,” AIAA Journal, Vol. 5, No. 8, Aug. 1967, pp. 1525-1527.
9. Ashwell, D. G., Sabir, A. B. and Roberts, T. M., “Further Studies in the Application of Curved Finite Elements to Circular Arches,” International Journal of Mechanical Sciences, Vol. 13, 1971, pp. 133— 139.
10. Cantin, G. and Clough, R. W., “A curved Cylindrical Shell Finite Element,” AIAA Journal, Vol. 6, No. 6, June 1968, pp. 1057-1062.
11. Sabir, A. B. and Ashwell, D. G., “A Comparison of Curved Beam Finite Elements when Used in Vibration Problems,” Journal of Sound and Vibration, Vol. 18, No. 4, 1971, pp. 555-563.
12. Fried, I., “Basic Computational Problems in the Finite Element Analysis of Shells,” International Journal of Solids and Structures, Vol. 7, No. 12, 1971, pp. 1705-1715.
13. Ginnini, M. and Miles, G. A., “A curved Element Approximation in the Analysis of Axi-Symmetric Thin Shells,” International Journal for Numerical Methods in Engineering, Vol. 2, No. 3, 1970, pp. 459-476.
14. Cantin, G., “Rigid Body Motions in Curved Finite Elements,” AIAA Journal, Vol. 8, No. 7, July 1970, pp. 1252-1255.
15. Bogner, F. K., Fox, R. L., and Schmit, L. A., “A Cylindrical Shell Discrete Element,” AIAA Journal, Vol. 5, No. 4, April 1967, pp. 745-750.
16. Fried, I., “C and C Bending Finite Elements,” International Journal of Solids and Structures, to be published.
17. Fried, I. and Yang, S. K., “A C°, Nine Degrees of Freedom Plate Bending Element of Quadratic Accuracy,” Quarterly of Applied Mathematics, to be published.
18. Strang, G., “Approximation in the Finite Element Method,” Numerische Mathematik, Vol. 19, 1972, pp. 81-98.
19. Fried, I. and Yang, S. K., “Best Finite Element Distribution Around a Singularity,” AIAA Journal, Vol. 10, No. 9, Sept. 1972, pp. 1244-1245.
20. Olson, M. D. and Lindberg, G. M., “Dynamic Analysis of Shallow Shells with a Doubly Curved Triangular Finite Element,” Journal of Sound and Vibration, Vol. 19, No. 3, 1971, pp. 299-318.
21. Cowper, G. R. and Olson, M. D., “Comparison of Two High-Precision Triangular Finite Elements for Arbitrary Deep Shells,” 3rd Conference on Matrix Methods, Wright-Patterson Air Force Base, Ohio, 19-20, Oct. 1971.
22. Mikhlin, S. G., Variational Methods in Mathematical Physics, Pergamon Press, London, 1964, pp. 230-231.
23. Birkhoff, G., DeBoor, C, Schwartz, B., and Wendrof, B., “Rayleigh Ritz Approximations by Piece-Wise Cubic Polynomials,” SIAM Journal of Numerical Analysis, Vol. 3, pp. 188-203.
24. Fried, I., “Condition of Finite Element Matrices Generated From Non-Uniform Meshes,” AIAA Journal, Vol. 10, No. 2, Feb. 1972, pp. 219-221.
25. Fried, L, “Bounds on the Extremal Eigenvalues of the Finite Element Stiffness and Mass Matrices and Their Spectral Condition Number,” Journal of Sound and Vibration, Vol. 22, No. 4, 1972, pp. 407-418.
26. x Condition Numbers of the Finite Element. Stiffness and Mass Matrices and the Pointwise Convergence of the Method,” Conference on the Mathematics of Finite Elements and Applications, Academic Press, New York, 1972.
27. Zienkiewicz, O. C., Taylor, R. L., and Too, J. M., “Reduced Integration Technique in General Analysis xtf Plates and Shells,” International Journal for Numerical Methods in Engineering, Vol. 3, 1971, pp. 275-290.
28. Clement, P. and Descloux, J., “On the Rigid Displacement Condition,” International Journal for Numerical Methods in Engineering, Vol. 4, 1972, pp. 583-586.