Users:Structural Optimization/Response Functions/Stress
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| − | + | The Kreisselmeier-Steinhauser function for the stresses is a global measure of stress in a structure. Stress results are generally very local results but using this responce function, an overall stress indicator is obtained. It can be used as an objective to reduce the overall stress in the structure or as a constraint to limit the stress in the structure to a maximum allowed value. | |
| − | + | The Kreisselmeier-Steinhauser function for the stresses is formulated by | |
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| + | <div style="font-size:150%"> | ||
| + | :: KS = 1/<i>ρ</i> log (<big>∑</big><sub>i</sub> exp (<i>ρ</i> σ<sub>i</sub>/ σ<sub>max</sub> )) | ||
| + | </div> | ||
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| + | with '''<big>∑</big><sub>i</sub>''' a summation over all Gausspoints in the domain and σ<sub>i</sub> the stress in the i-th Gausspoint from a linear or nonlinear analysis. σ<sub>max</sub> is the maximum allowed stress. <i>ρ</i> is a parameter that determines the importance of the largest stresses amongst all σ<sub>i</sub>. The response function requires the ID of a [[Users:General FEM Analysis/Analyses Reference/Static Linear | linear static analysis]] or a [[Users:General FEM Analysis/Analyses Reference/Static Nonlinear | nonlinear static analysis]] specified for parameter 'ANALYSIS'. | ||
| + | |||
| + | (influence of sigma_max) The value of the exponential function becomes infinite very fast, even for reasonable values of the argument. Therefore, the choice of σ<sub>max</sub> is very important. The best results are obtained if the stresses σ<sub>i</sub> are similar to σ<sub>max</sub>. If the stresses in the structure are much smaller than the allowed stress, the value of this response function becomes useless. Since it is in that case a summation of all small values, it will be similar for all structures. | ||
| + | |||
| + | (influence of rho) | ||
| + | |||
| + | (so how to choose the values) | ||
| + | If this response function is used as an objective function, the value of σ<sub>max</sub> should be chosen such that it is close to the real stresses in the structure. Additionally, the value for <i>ρ</i> should not be high to use the global stress results. | ||
| + | If this response function is used as a constraint function, the value of σ<sub>max</sub> should be chosen as the real maximum allowed value. Additionally, the value for <i>ρ</i> should be high enough to localize the largest stress. | ||
Revision as of 10:06, 13 October 2010
General Description
Short Info
The Kreisselmeier-Steinhauser function for the stresses is a global measure of stress in a structure. Stress results are generally very local results but using this responce function, an overall stress indicator is obtained. It can be used as an objective to reduce the overall stress in the structure or as a constraint to limit the stress in the structure to a maximum allowed value.
The Kreisselmeier-Steinhauser function for the stresses is formulated by
- KS = 1/ρ log (∑i exp (ρ σi/ σmax ))
with ∑i a summation over all Gausspoints in the domain and σi the stress in the i-th Gausspoint from a linear or nonlinear analysis. σmax is the maximum allowed stress. ρ is a parameter that determines the importance of the largest stresses amongst all σi. The response function requires the ID of a linear static analysis or a nonlinear static analysis specified for parameter 'ANALYSIS'.
(influence of sigma_max) The value of the exponential function becomes infinite very fast, even for reasonable values of the argument. Therefore, the choice of σmax is very important. The best results are obtained if the stresses σi are similar to σmax. If the stresses in the structure are much smaller than the allowed stress, the value of this response function becomes useless. Since it is in that case a summation of all small values, it will be similar for all structures.
(influence of rho)
(so how to choose the values) If this response function is used as an objective function, the value of σmax should be chosen such that it is close to the real stresses in the structure. Additionally, the value for ρ should not be high to use the global stress results. If this response function is used as a constraint function, the value of σmax should be chosen as the real maximum allowed value. Additionally, the value for ρ should be high enough to localize the largest stress.
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