ISSN:
1573-2703
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Technology
Notes:
Conclusion In the foregoing sections a series of solutions of the problem of plastic plane strain have been found, all of which are of the following form: the Cartesian coordinates x and y of the physical plane are trigonometrical functions of θ, the direction of the major principal stress, multiplied by a power of s, a quantity directly connected with the isotropic stress. If the boundary condition can be described in the same form, the boundary value problem can be solved. In sec. 4 this was done for a special sort of boundary condition. There the shape of the boundary was arbitrary, but the surface traction was a constant normal pressure. The analytical method seems very suitable for the determination of the stresses in the plastic region around a hole. The method may also be applicable to other sorts of plasticity problems, but this is beyond the scope of the present paper. The possibilities are limited in the first place by the requirement that along the boundary the functions θ and s are continuous and further that there exists a one-to-one relation between the points (θ, s) and (x, y) of the boundary. One conclusion of practical importance to be drawn from sec. 3 is that the plastic stress distribution around a hole of general shape, and loaded by an arbitrary surface traction, will tend to circular symmetry at a great distance from the hole. An example of this behaviour is shown in fig. 8.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01540589
