Numerical Method for Lower-Bound Solution of the Rigid-Plastic Limit Analysis Problem
Publication: Journal of Engineering Mechanics
Volume 127, Issue 11
Abstract
This paper describes a numerical method to determine the lower-bound solution of limit load of a rigid–perfectly plastic body obeying the von Mises yield criterion. The idea of this method is to construct a smoothed linear stress field that satisfies the yield criterion everywhere in the body. Applying the similar stress recovery techniques as superconvergent patch recovery and recovery by equilibrium in patch in the elastic finite-element analysis, the nodal stresses are obtained from those stresses at the integration points from an iterative process of upper-bound limit analysis. Then, the improved stress fields and lower-bound solutions can be derived by ensuring all the nodal stresses within the yield surface. The convergence of this method is guaranteed. The validity of the proposed method is demonstrated with some numerical examples. The computational results show that more reliable lower-bound solutions can be obtained by using this method, especially for problems with strain singularity.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ainsworth, R. A., Ruggles, M. B., and Takahashi, Y. ( 1992). “Flaw assessment procedure for high-temperature reactor components.” J. Pressure Vessel Technol., 114(2), 166–170.
2.
Andersen, K. D., Christiansen, E., and Overton, M. L. ( 1998). “Computing limit loads by minimizing a sum of norms.” J. Sci. Comp., 19(3), 1046–1062.
3.
Belytschko, T., and Hodge, P. G. (1970). “Plane stress limit analysis by finite elements.”J. Engrg. Mech. Div., ASCE, 96(6), 931–943.
4.
Boroomand, B., and Zienkiewicz, O. C. ( 1997). “Recovery by equilibrium in patches (REP).” Int. J. Numer. Methods in Engrg., 40, 137–164.
5.
Chen, H. F., Liu, Y. H., Cen, Z. Z., and Xu, B. Y. ( 1998). “Numerical analysis of limit load and reference stress of defective pipelines under multi-loading systems.” Int. J. Pressure Vessel Piping, 75, 105–114.
6.
Ewing, D. J. F., and Hill, R. ( 1967). “The plastic constraint of V-notched tension bars.” J. Mech. Phys. Solids, 15, 115–124.
7.
Hinton, E., and Huang, H. C. ( 1986). “A family of quadrilateral Mindlin plate elements with substitute shear strain fields.” Comp. and Struct., 23(3), 409–431.
8.
Huh, H., and Yang, W. H. ( 1991). “A general algorithm for limit solutions of plane stress problems.” Int. J. Solids and Struct., 28(6), 727–738.
9.
Hung, N. D. ( 1976). “Direct limit analysis via rigid-plastic finite elements.” Comput. Methods Appl. Mech. Engrg., 8, 81–116.
10.
Hutula, D. N. ( 1976). “Finite element analysis of two-dimensional plane structures.” Limit analysis using finite elements, ASME, New York, 35–52.
11.
Liu, Y. H., Cen, Z. Z., and Xu, B. Y. ( 1995). “A numerical method for plastic limit analysis of 3-D structures.” Int. J. Solids and Struct., 32(12), 1645–1658.
12.
Mackenzie, D., and Boyle, J. T. ( 1993). “A method of estimating limit loads by iterative analysis. I—Simple examples.” Int. J. Pressure Vessel Piping, 53, 77–95.
13.
Seshadri, R., and Fernando, C. P. D. ( 1992). “Limit loads of mechanical components and structures using the Gloss r-node method.” J. Pressure Vessel Technol., 114, 201–208.
14.
Wiberg, N. E., and Abulwahab, F. ( 1993). “Patch recovery based on superconvergent derivatives and equilibrium.” Int. J. Numer. Methods in Engrg., 36, 2703–2724.
15.
Yang, W. H. ( 1982). “A variational principle and an algorithm for limit analysis of beams and plates.” Comp. Methods Appl. Mech. Engrg., 33, 575–582.
16.
Zhang, Y. G., and Lu, M. W. ( 1995). “An algorithm for plastic limit analysis.” Comput. Methods Appl. Mech. Engrg., 126, 333–341.
17.
Zhang, Y. G., Zhang, P., and Xue, W. M. ( 1994). “Limit analysis considering initial constant loadings and proportional loadings.” Computational Mech., 14, 229–233.
18.
Zienkiewicz, O. C., and Zhu, J. Z. ( 1992). “The superconvergent patch recovery and a posteriori error estimators. Part 1: The recovery technique.” Int. J. Numer. Methods in Engrg., 33, 1331–1364.
Information & Authors
Information
Published In
History
Received: Apr 28, 2000
Published online: Nov 1, 2001
Published in print: Nov 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.