Mathematics

Plastic Limit Analysis of Plates, Shells and Disks by Gery de Saxce

By Gery de Saxce

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Extra info for Plastic Limit Analysis of Plates, Shells and Disks

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When one of the principal stresses vanishes, say o 3 , the surface reduces to the hexagon obtained by intersecting the prism with the plane o 3 = 0 (fig. 6). The yield condition becomes max[ Io11,Io2t, Io 1 - o21]= o Y. 32) Note finally that because the magnitude of the maximum shear stress is half the (algebraic) difference of the extreme principal stresses, the intermediate principal stress plays no role in Tresca's yield criterion. 6] and fig. 7) that the circular cylinder circumscribed to the considered hexagonal prism was a more exact "yield surface" for most metals.

I. QUINNEY, The Plastic Distortions of Metals, Phil. Trans. Roy. Soc. London, 230 : 323, 1931. 16 2. Fundamental Concepts and Laws. 1. Perfectly plastic solid. We are now able to define a perfectly plastic solid as follows : a solid will be called perfectly plastic if it can undergo unlimited plastic deformations under constant reference stress when it is subjected to a homogeneous state of stress with 6 R = 6y. The value Oy is well defined for each material in a given environment, and is the limiting value that 6 R cannot exceed.

A) and (b) 29 Answer : See fig. 10. 5. 4, but for von Mises' condition only and with reference to cartesian orthogonal axes x, y, z such that/~z = ~/xz = 89 = 0. Answer : Ox-Cy +4Zxy= 5 I O'y (fig. 11). //, ax / //'-[ l:xy ! Fig. 11. References. 1] D. C. DRUCKER, "On uniqueness in the theory of plasticity", Quart. Appl. , 14:35, 1956. 2] D. C. DRUCKER, "On the postulate of stability of material in mechanics of continua", J. de Mecanique, 3 : 235, 1964. 3] R. HILL, "A variational principle of maximum plastic work in classical plasticity", Quant.

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