Users:Structural Optimization/Response Functions/SurfaceCurvature
(→Estimation of nodal curvature) |
(→Estimation of nodal curvature) |
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[[ File:curv_ks_sketch.png |500px | center |Sketch of curvature estimation in 1D ]] | [[ File:curv_ks_sketch.png |500px | center |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 '' | + | 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 v''i'' is the access vector to the ith node. |
[[ File:curv_ks_formula.png |300px | center | ]] | [[ File:curv_ks_formula.png |300px | center | ]] | ||
Revision as of 11:52, 21 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.
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