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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>About the Symmetric Plate Example</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 = "shortdesc">This example shows a sensitivity-based topology optimization using the Kreisselmeier-Steinhauser criterion.<p>This page discusses: </p><ul><li><a href = "#tso-c-example-topo-sensTopoPlate__cs-AbouttheModel" id = "toc_rg" title = "">About the Model</a></li><li><a href = "#tso-c-example-topo-sensTopoPlate__cs-ProcedureSummary" id = "toc_rg" title = "">Procedure Summary</a></li></ul>
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<div class = "section" id = "tso-c-example-topo-sensTopoPlate__cs-AbouttheModel"><h2 class = "title sectiontitle">About the Model</h2>
<p>The definition of the optimization problem is done using the definition of a variable (design
                response variable) which contains the first natural frequency. This definition is
                referenced in the objective function. By maximizing the first natural eigenfrequency
                is the danger that the modes might switch; that is, that the original first
                eigenfrequency becomes greater than the original second. This can be avoided by the
                Kreisselmeier-Steinhauser criterion that creates a weighting of the eigenfrequencies
                causing the lowest eigenfrequency to stay the lowest.</p>

<p>For the optimization of the first natural frequency, a symmetric plate is generated in the
                FE-preprocessor. The plate is fixed at the corners and fixed in z-direction in the
                middle. The center node is attached to a mass element.<br/><img class = "image" src = "../TsoExampleImages/sensTopoPlateModel.png"/><br/></p>
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<div class = "section" id = "tso-c-example-topo-sensTopoPlate__cs-ProcedureSummary"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Procedure Summary</h2>

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<td class = "entry">Model:</td>
<td class = "entry">plate_sym_freq.ext</td>
</tr>
<tr class = "row">
<td class = "entry">Design Area:</td>
<td class = "entry">All elements</td>
</tr>
<tr class = "row">
<td class = "entry">Objective:</td>
<td class = "entry">Maximize first eigenfrequency (using the Kreisselmeier-Steinhauser criterion)</td>
</tr>
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<td class = "entry">Constraint:</td>
<td class = "entry">Relative volume of 30 % (less or equal constraint)</td>
</tr>
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<td class = "entry">Settings:</td>
<td class = "entry">Filter radius 25 mm</td>
</tr>
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