Users:Structural Optimization/Response Functions/SurfaceCurvature

Revision as of 06:55, 26 April 2011

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.