The Linear Matching Method for Limit Loads, Shakedown Limits and Ratchet Limits
The paper describes the application of the Linear Matching Method to the direct evaluation of limits associated with an elastic-perfectly plastic body subjected to cyclic loading. Methods for limit load and shakedown limit are followed by ratchet limits. The method is distinguished from other programming methods by ensuring that equilibrium and compatibility are satisfied at each stage. The method has been extended beyond the range of most other direct methods by including ratchet limits and high temperature material behaviour. Implementation is possible within the user routines of commercial finite element codes. The paper emphasise the theoretical characteristics of the method and discusses significant aspects of convergence, both theoretical and numerical. The application of the method to industrial Life Assessment problems and to geotechnical problems is summarized.
KeywordsResidual Stress Plastic Strain Limit Load Linear Material Geotechnical Problem
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- 12.Chen H.F., Ponter A.R.S. and Ainsworth R.A. (2006), “The Linear Matching Method Applied to the High Temperature Life Assessment of Structures. Part 2. Assessments Beyond Shakedown Involving Changing Residual Stress Fields”, International Journal of Pressure Vessels and Piping, 83, 136–147CrossRefGoogle Scholar
- 13.Fernando C.P.D. and Seshadri R. (1993), “Limit Loads of Framed Structures and Arches Using the Gloss R-Node Method”, Transactions of the ASME, 17, 2, 197–214Google Scholar
- 14.Gokhfeld D.A. and Cherniavsky D.F. (1980), “Limit Analysis of Structures at Thermal Cycling”, Sijthoff & Noordhoff. Alphen an Der Rijn, The NetherlandsGoogle Scholar
- 15.Goodall I.W., Goodman A.M., Chell G.C., Ainsworth R.A., and Williams J.A. (1991), “R5: An Assessment Procedure for the High Temperature Response of Structures”, Nuclear Electric Ltd., Report, Barnwood, GloucesterGoogle Scholar
- 19.Hentz S. (1998) “Finite Element State Solutions, Accuracy of an Iterative Method”, Report, Department of Engineering, University of Leicester and Department de Genie Mecanique, ENS de Cachan, ParisGoogle Scholar
- 20.Koiter W.T. (1960), “General Theorems of Elastic-Plastic Solids”, in Progress in Solid Mechanics, eds. J.N. Sneddon, R. Hill, Vol 1, 167–221Google Scholar
- 21.Marriot D.L., “Evaluation of Deformation or Load Control of Stresses Under Inelastic Conditions Using Elastic Finite Element Stress Analysis”, Proc. ASME PVP Conf., 136, Pittsburgh, 1988Google Scholar
- 23.Ponter A.R.S. (2007), “The Linear Matching Method for the Evaluation of Limit Loads, Shakedown Limits and Related Problems”, Variational Formulations in Mechanics in Theory and Applications, Ed Taroco E., de Souza Neto and Novotny, CIMNE, Barcelona, Spain, 243–262Google Scholar
- 24.Ponter A.R.S. and Boulbibane M. (2003), “Minimum Theorems and the Linear Matching Method for Bodies in a Cyclic State of Creep”, European Journal of Mechanics, A/Solids, 21, 2003, 915–925Google Scholar