A generalization of the upper bound method with particular reference to the problem of a ploughing indenter

Journal of Applied Mechanics, Transactions ASME

Volumn 56, Issue 1, 1989, Pages 10-14

  Azarkhin, A ^a   Richmond, O ^a  

^a ALCOA TECHNICAL CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - ALGORITHMS; SURFACES - ELASTOPLASTICITY; WEAR OF MATERIALS;

ELASTIC CONTACTS; SURFACE ASPERITY ANALYSIS; SURFACE PLOUGHING; UNCONSTRAINED FUNCTIONAL FORMULATION;

FRICTION;

EID: 0024621595     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3176029     Document Type: Article

References (22)

1. Abildgaard, T., 1984, “Prediction of the Force Components Acting on a Ploughing Cone by Means of Three-Dimensional Upper Bound Theory,” Advanced Technology of Plasticity, vol. 1, pp. 121-126.
2. Avitzur, B., Huang, C. K., and Zhu, Y. D., 1984, “A Friction Model Based on the Upper Bound Approach to the Ridge and Sublayer Deformation,” Wear, Vol. 95, pp. 59-77.
3. Bowden, F. P., and Tabor, D., 1950, The Friction and Lubrication of Solids, Part I, Clarendon Press, Oxford.
4. Bracken, J., and McCormic, G. P., 1968, “Selected Applications of Non-Linear Programming,” J. Wiley and Sons, New York.
5. Brent, R. P., 1971, “Algorithms for Finding Zeros and Extremes of Functions without Calculation Derivatives,” Stanford University, Technical Report CS-71-198.
6. DeVathire, M., Delamare, F., and Felder, E., 1981, “An Upper Bound Model of Ploughing by a Pyramidal Indenter,” Wear, Vol. 66, pp. 51-64.
7. Drucker, D, C, 1954, “Coulomb, Friction, Plasticity, and Limit Loads,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 21, pp. 71-74.
8. Drucker, D. C, Greenberg, H. J., and Prager, W., 1951, “The Safety Factor of an Elastic-Plastic Body in Plane Strain,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 18, pp. 371-378.
9. Drucker, D. C, Prager, W., and Greenberg, H. J., 1952, “Extended Limit Design Theorems for Continuous Media,” Quart. Appl. Math., pp. 381-389.
10. Fletcher, R., and Powell, M. J., 1963, “A Rapidly Convergent Descent Method for Minimization,” Computer, Vol. 6, No. 2, pp. 163-168.
11. Fletcher, R., and Reeves, C. M., 1964, “Function Minimization by Conjugate Gradient,” Computer J., Vol. 7, No. 2, pp. 149-154.
12. Goldstein, A., and Price, J. F., 1967, “An Effective Algorithm for Minimization,” Numer. Math., Vol. 10, pp. 184-189.
13. Gvozdev, A. A., 1938, “The Determination of the Value of the Collapse Load for Statically Indeterminate Systems Undergoing Plastic Deformation,” Proceedings of the Conference on Plastic Deformation, Acad, of Sci. USSR, 1938, Moscow, pp. 19-33 (in Russian), English Translation in Intern. J. Mech. Sci, 1960, Vol. 1, pp. 322-355.
14. Hill, R., 1957, “On the State of Stress in a Plastic-Rigid Body at the Yield Point,” Phil. Mag., Vol. 42, pp. 868-875.
15. Hill, R., “A Note on Estimating the Yield-Point Loads in a Plastic-Rigid Body,” Phil. Mag., Vol. 43, pp. 353-355.
16. Oh, S. I., and Kobayashi, S., 1975, “An Approximate Method for a Three-Dimensional Analysis in Rolling,” Intern. J. Mech. Sci., Vol. 17, pp. 293-305.
17. Prager, W., 1959, An Introduction to Plasticity, Addison-Wesley, Reading, MA.
18. Rabinowicz, E., 1965, Friction and Wear of Materials, John Wiley and Sons, New York.
19. Rowe, J. W., 1977, Principles of Industrial Metal Working Processes, E. Arnold, Ltd., London.
20. Suh, N. P., 1986, Tribophysics, Prentice-Hall, Englewood Cliffs, N.J.
21. Wanheim, T., 1978, “A Model for Friction in Metal Forming Processes,” Ann CIRP, Vol. 27, pp. 189-196.
22. Zienkiewicz, O. C, 1983, The Finite Element Method, 3rd ed., McGraw-Hill Book Company, Ltd., UK.