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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Models for Shape Optimization</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">The basic idea of shape optimization with respect to model requirements is described.
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<p>In shape optimization, the boundaries or surfaces of a component are
modified. At first, the optimizer calculates the new coordinates of
the design nodes on the component surface based on the stress condition
and then adjusts the remaining FE mesh accordingly. The calculation of
the new coordinates of the nodes is not based on geometrical parameters,
but rather on each individual coordinate for the nodes. Generally, every
FE model can serve as a basis for shape optimization.</p>
<p>The mesh must be of such quality that the analysis results from the
FE mesh remain essentially unaffected. To assure this, most FE preprocessors
have checking routines. The user must define an adequate mesh density
for a subsequent optimization, that is, high stress gradients should not
be present within an element.  The mesh density must be set correctly
in order to achieve smooth contours. For example, smooth contours cannot
be expected when a 90 degree curve is meshed by only three elements.
The finer the mesh density, the closer the contour will be to the optimum.
<span class = "ph">Tosca Structure.shape</span>
features an integrated efficient smoothing mesh algorithm. It is capable
of adjusting the FE mesh to the optimized displacement of the design
nodes without remeshing. It is possible that the FE model will collapse
when there is a large optimized displacement of the design nodes due
to a poor mesh. This can be avoided by setting the mesh to an adequate
density.</p>
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