Users:Structural Optimization/Response Functions/SurfaceCurvature

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(Kreisselmeier-Steinhauser weighting)
(General Description)
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Instead of constraining each single nodal curvature, ''Carat++'' provides a technique to control the curvature within bigger element patches. To this purpose a Kreisselmeier-Steinhauser weighting is used.
 
Instead of constraining each single nodal curvature, ''Carat++'' provides a technique to control the curvature within bigger element patches. To this purpose a Kreisselmeier-Steinhauser weighting is used.
  
  [[ File:curv_ks_formula2.png |350px | center | ]]
+
  [[ File:curv_ks_formula2.png |350px | center | KS formulation for one patch ]]
  
 
Via the weighting parameter �ρ the user can control to which extend exceedings of the maximum allowable curvature are weighted.
 
Via the weighting parameter �ρ the user can control to which extend exceedings of the maximum allowable curvature are weighted.

Revision as of 12:30, 21 April 2011


Contents

General Description

Short Info

In the field of structural optimization it is often necessary to apply a constraining of surface curvature in order to maintain manufacturing constraints. To this purpose, Carat++ provides an estimation tool to approximate the mean curvature at a surface node.


Estimation of nodal curvature

The nodal curvature is estimated using the surface normal vector and access vectors to the surrounding nodes. The estimation is based on a local spherical approximation of the geometry (see sketch below). So the radius of curvature r can be computed within the isosceles triangle.

Sketch of curvature estimation in 1D

Having computed this approximated radius of curvature for each surrounding node, the mean curvature of the surface is estimated by a weighted sum over all surrounding nodes i, whereat vi is the access vector to the ith node.

Curv ks formula.png

Kreisselmeier-Steinhauser weighting

Instead of constraining each single nodal curvature, Carat++ provides a technique to control the curvature within bigger element patches. To this purpose a Kreisselmeier-Steinhauser weighting is used.

KS formulation for one patch

Via the weighting parameter �ρ the user can control to which extend exceedings of the maximum allowable curvature are weighted.





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