Limit Analysis by Direct Method of Variation

by Toshio Mura,
Seng-Lip Lee,
Robert H. Bryant,
Walid H. Rimawi,

Serial Information: Journal of the Engineering Mechanics Division, 1967, Vol. 93, Issue 5, Pg. 67-78

Document Type: Journal Paper


Two functionals for the limit analysis of perfectly plastic solids by variational method are presented, one for the lower bound solution and the other for the upper bound solution. The stationary value of these functionals are equal to the safety factor. The variation of these functionals with respect to their arguments, subject to auxiliary constraint conditions, leads to the lower and upper bounds on the safety factor. It is further shown that the method of analysis can be extended to problems expressed in terms of generalized stresses and strain rates. The method is then applied to a cylindrical sandwich shell for which a numerical example is given to illustrate the procedure of analysis. The results are compared with the corresponding collapse loads based on Tresca's sandwich yield condition.

Subject Headings: Limit analysis | Plastic analysis | Safety | Stress analysis | Stress strain relations | Failure loads | Solid mechanics | Strain rates

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