TECHNICAL PAPERS
Jun 1, 1984

Algorithms for Elasto‐Plastic‐Creep Postbuckling

Publication: Journal of Engineering Mechanics
Volume 110, Issue 6

Abstract

This paper considers the development of an improved constrained time stepping scheme which can efficiently and stably handle the pre‐post‐buckling behavior of general structure subject to high temperature environments. Due to the generality of the scheme, the combined influence of elastic‐plastic behavior can be handled in addition to time dependent creep effects. This includes structural problems exhibiting indefinite tangent properties. To illustrate the capability of the procedure, several benchmark problems employing finite element analyses are presented. These demonstrate the numerical efficiency and stability of the scheme. Additionally, the potential influence of complex creep histories on the buckling characteristics is considered.

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References

1.
Bergen, P. G., Horrigmoe, G., Krakeland, B., and Soneide, T. H., “Solution Techniques for Nonlinear Finite Element Problems,” International Journal of Numerical Engineering, Vol. 12, No. 1677, 1978.
2.
Broyden, C. G., “The Convergence of a Class of Double‐Rank Minimization Algorithms, 1: General Considerations,” Journal of Institute of Mathematical Applications, Vol. 6, No. 76, 1970.
3.
Broyden, C. G., “The Convergence of a Class of Double Rank Minimization Algorithms, 2: The New Algorithm,” Journal of Institute of Mathematical Applications, Vol. 6, No. 222, 1970.
4.
Budiansky, B., “Theory of Buckling and Post‐Buckling Behavior of Elastic Structures,” Advances in Applied Mechanics, Vol. 14, Academic Press, New York, 1974.
5.
Crisfield, M. A., “Incremental Iterative Solution Procedures for Nonlinear Structural Analysis,” Int. Conf. on Num. Meth. for Nonlinear Problems, Swansea, Wales, 1980.
6.
Crisfield, M. A., “A Fast Incremental/Iterative Procedure That Handles Snapthrough,” Computers and Structures 13, 1981, pp. 55–62.
7.
Cyr, N. A., and Teter, R. D., “Finite‐Element Elastic‐Plastic Creep Analysis of Two‐Dimensional Continuum with Temperature Dependent Material Properties,” Computers and Structures, Vol. 3, No. 849, 1973.
8.
Fletcher, B., “A New Approach to Variable Metric Algorithms,” Computer Journal, Vol. 13, No. 317, 1970.
9.
Fung, Y. C., “Foundations of Solid Mechanics, Prentice Hall, N.J., 1965.
10.
Goldfarb, D., “A Family of Variable‐Metric Methods Derived by Variational Means,” Mathematical Computation, Vol. 24, No. 23, 1970.
11.
Hutchinson, J. W., “On the Post‐buckling Behavior of Imperfection‐Sensitive Structures in the Plastic Range,” Journal of Applied Mechanics, Vol. 39, No. 155, 1972.
12.
Koiter, W. T., “On Stability of Elastic Equilibrium,” AFFDL‐TR‐70‐25, 1970.
13.
Matthies, H., and Strang, G., “The Solution of Nonlinear Finite Element Equations,” International Journal of Numerical Methods in Engineering, Vol. 14, No. 1612, 1979.
14.
Obrecht, H., “Creep Buckling and Post‐Buckling of Circular Cylindrical Shells Under Axial Compression,” International Journal of Solids Structures, Vol. 13, No. 337, 1977.
15.
Padovan, J., and Tovichakchaikul, S., “Self‐Adaptive Predictor‐Corrector Algorithms for Static Nonlinear Structural Analysis,” Tech. Rep. No. 1, NASA‐Lewis Grant NAG3‐54, 1981, also Computers and Structures, Vol. 15, No. 365, 1982.
16.
Padovan, J., and Tovichakchaikul, S., “On the Solution of Creep Induced Buckling in General Structure,” Computers and Structures, Vol. 15, No. 379, 1982.
17.
Padovan, J., and Tovichakchaikul, S., “On the Solution of Elastic‐Plastic Static and Dynamic Post‐Buckling Collapse of General Structure,” Computers and Structures, Vol. 16, No. 199, 1983.
18.
Rabatnov, Y. N., “Creep Problems in Structural Members,” North Holland, Amsterdam, 1969.
19.
Riks, E., “An Incremental Approach to the Solution of Snapping and Buckling Problems,” International Journal Solids Structures, Vol. 15, No. 529, 1979.
20.
Samuelson, L. A., “Creep Buckling of a Cylindrical Shell Under Non‐Uniform Loads,” International Journal Solids Structures, Vol. 6, No. 91, 1970.
21.
Shanno, D. F., “Conditioning of Quasi Newton‐Methods for Function Minimization,” Mathematical Computation, Vol. 24, No. 647, 1970.
22.
Zienkiewicz, O. C., “The Finite Element Method,” McGraw Hill, New York, N.Y., 1971.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 110Issue 6June 1984
Pages: 911 - 929

History

Published online: Jun 1, 1984
Published in print: Jun 1984

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Authors

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Joseph Padovan
Dept. of Mech. Engrg., The Univ. of Akron, Akron, Ohio 44325
Surapong Tovichakchaikul
Formerly Grad. Student at Univ. of Akron, Currently with IBM, Thailand

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