Users:Form Finding/Discussion of the Prestress State
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| − | The main value in the ''URS'' is the prestress state. If the prestress don't match to the given problem there are no physical solution. So it can be seen, that the problem of finding the right prestress state is the main difficulty in the ''URS''. For a lot of sufaces an isotropic prestress state (σ<sub>11</sub> = σ<sub>22</sub> and σ<sub>12</sub>=0) is valid. But there are surfaces were an isotropic prestress state don't fit to the physics. The most popular kind of surface were an isotropic prestress state don't lead to a solution is the ''Chinese Hat'' (see figure below). | + | The main value in the ''URS'' is the prestress state. If the prestress don't match to the given problem there are no physical solution. So it can be seen, that the problem of finding the right prestress state is the main difficulty in the ''URS''. For a lot of sufaces an isotropic prestress state (σ<sub>11</sub> = σ<sub>22</sub> and σ<sub>12</sub>=0) is valid. But there are surfaces were an isotropic prestress state don't fit to the physics. The most popular kind of surface were an isotropic prestress state don't lead to a solution is the ''Chinese Hat'' (see figure below<ref name="Ish95">Ishii, K.: Membrane structures in Japan, SPS Publishing Company, Tokyo, 1995</ref>). |
[[File:Chinese hat.jpg|400px|up|Chinese hat]] | [[File:Chinese hat.jpg|400px|up|Chinese hat]] | ||
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In figure below the definition of the stress dircetion of the chinese hat are shown. | In figure below the definition of the stress dircetion of the chinese hat are shown. | ||
Revision as of 10:04, 3 September 2010
The main value in the URS is the prestress state. If the prestress don't match to the given problem there are no physical solution. So it can be seen, that the problem of finding the right prestress state is the main difficulty in the URS. For a lot of sufaces an isotropic prestress state (σ11 = σ22 and σ12=0) is valid. But there are surfaces were an isotropic prestress state don't fit to the physics. The most popular kind of surface were an isotropic prestress state don't lead to a solution is the Chinese Hat (see figure below[1]).
In figure below the definition of the stress dircetion of the chinese hat are shown.
By using an isotropic stess state the nono physical solution for the Chinese Hat can be seen in Figure below.
To enable the form finding to find the physical solution for such kind of structures, the possibility of stress adaption is used. By controlling the element distortion an adaption of the prestress in each Gauss point is possible. Herein the element distortion is controlled w.r.t. the principal stretch of an element (see figure below).
In the distortion control scheme a maximum allowable configuration is defined. That means, the initial configuration a maximum of displacement is allowed with a maximum deformation gradient Fmax. This configuration is the maximum allowable. During the form finding process the actual configuration is compared with the maximum allowable one. If the distortion is too much, the prestress will be modified in that way, that the maximum of distortion is kept in the allowable values. With this control scheme the Chinese Hat is possible to control and to get a physical meaningful solution (see figur below). But it should be noticed, that the final stress state isn't identical to the choosen one. Due to the choice of λ_max the stress is more or less different to the choosen one.
References
- ↑ Ishii, K.: Membrane structures in Japan, SPS Publishing Company, Tokyo, 1995
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