# A course of mathematical analysis, Part I (International by Anisim Fedorovich Bermant

By Anisim Fedorovich Bermant

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Additional info for A course of mathematical analysis, Part I (International series of monographs on pure and applied mathematics;vol.44)

Sample text

7) 1J ii~. (s. 1) and 1J represents the displacements at a certain point where u~. perpendicular to the load direction i 1J q, 1J lying on a passing through s. 9) + 1)!. 7) can be used to find the two dimensional fundamental displacements as follows [u~. r. r . 2). Note that the displacements are zero at q (depending on the direction of the load). The second class of fundamental solutions adopted corresponds to half-space problems. In this case the Kelvin region is subdivided by an infinite horizontal plane as Q* + and its lower part is considered r*.

Consequently. Alternatively. 2) and can be used to justify the passage from 3-D to 2-D by integrating the former with respect to x 3 (s) • Thus, consider the following alternative expression for displacements in the 3-D case ~'L (s, q) 1J u~. - ;;~. 7) 1J ii~. (s. 1) and 1J represents the displacements at a certain point where u~. perpendicular to the load direction i 1J q, 1J lying on a passing through s. 9) + 1)!. 7) can be used to find the two dimensional fundamental displacements as follows [u~.

The problem of formulating physical relations describing the actual behaviour of a material during plastic flow is a very complex one. This complexity is due to the non-linearity and irreversibility of the deformation processes and to a number of phenomena which occur only after the material becomes plastic. The yield characteristics of many materials, for instance, are modified by the rate of straining, with the resistance to deformation increasing markedly with the speed of loading (viscous effect).