Users:Structural Optimization/Response Functions/SurfaceCurvature
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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.
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.
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.
Via the weighting parameter �ρ the user can control to which extend exceedings of the maximum allowable curvature are weighted.
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