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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>Special Remarks on The Sizing Algorithm</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">
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Some remarks on the sizing optimization algorithm are given here.</span>

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<ul><li><a href = "#tso-c-usr-sizing-SpecialRemarks__tso-c-usr-sizing-SpecialRemarks-SemiAnalyticalSensitivity" id = "toc_rg" title = "">SemiAnalytical Sensitivity Calculation </a></li></ul>
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<div class = "section" id = "tso-c-usr-sizing-SpecialRemarks__tso-c-usr-sizing-SpecialRemarks-SemiAnalyticalSensitivity"><h2 class = "title sectiontitle">SemiAnalytical Sensitivity Calculation </h2>

<p>In the context of sizing optimization to obtain the sensitivity of design responses, a 
semianalytical approach is used. It is based on a finite difference of the elemental stiffness and mass matrices.
That means that in addition to the original matrices perturbed matrices must be requested from the solver. This is done by a "matrix-step" (see figure below).</p>

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<p>This matrix step's only purpose is to perturb all pseudo densities to get
   the perturbed matrices - the original matrix is obtained in a usual solver step where also the results of the FE-problem are
   wanted. For situations where matrix step is needed the solver is called twice in each iteration.</p>
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