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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>Optimization Task</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">
 In <span class = "ph">Tosca Structure</span>,
a sensitivity-based approach is used for solving sizing problems. This algorithm uses the
sensitivities of the design variables regarding the objective function and the constraints.
<span class = "ph">Tosca Structure</span> uses an algorithm based on the Method of Moving Asymptotes from Krister Svanberg (Sweden).
In one optimization run approximately 10 to 15 iterations are required - much fewer compared
to the sensitivity-based approach for topology optimization. The number of iterations as well
as the CPU-time is independent of the number of shell element thicknesses chosen as design variables.
</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-anaTypes" id = "toc_rg" title = "">Analysis Types </a></li><li><a href = "#tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-nonlin" id = "toc_rg" title = "">Nonlinearities</a></li><li><a href = "#tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-model" id = "toc_rg" title = "">Model</a></li><li><a href = "#tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-objFuncConst" id = "toc_rg" title = "">Allowed Objective Functions and Constraints</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">

<div class = "section" id = "tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-anaTypes"><h2 class = "title sectiontitle">Analysis Types </h2>

<p>
<span class = "ph">Tosca Structure.sizing</span>
supports the responses of linear static (nonconservative forces) and linear
eigenfrequency (not allowed to be prestressed) finite element analysis. Temperature loading
is allowed for 
<span class = "ph">Abaqus</span> and
<span class = "ph">ANSYS®</span>. </p>
</div>


<div class = "section" id = "tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-nonlin"><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">Nonlinearities</h2>

<p>
Contact for <span class = "ph">Abaqus</span>
and <span class = "ph">ANSYS®</span>
is supported in- and outside the design area.
</p>
<p>
All types of constitutive nonlinear modeling are allowed; for example, a nonlinear spring. Geometrical nonlinearities are also supported.
</p>
<p>
<span class = "ph">Tosca Structure.sizing</span>
supports contact for <span class = "ph">Abaqus</span>
and <span class = "ph">ANSYS®</span>.
</p>
<p>
In addition, prescribed displacements are allowed in the CAE model for static sizing
optimization. However, prescribed displacements are not allowed for modal and frequency
response analysis.
</p>

</div>


<div class = "section" id = "tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-model"><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">Model</h2>

<p>
<span class = "ph">Tosca Structure.sizing</span>
supports only single layered shells (admitted for sensitivity-based optimization).
</p>

<p>
In addition, “constant” temperature loading is supported. 
</p>
</div>


<div class = "section" id = "tso-c-usr-sizing-optTask__tso-c-usr-sizing-optTaskOvw-objFuncConst"><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">Allowed Objective Functions and Constraints</h2>

<p>For sizing optimization, a variety of combinations of objective functions and constraints can be selected</p>
<ul class = "ul">
<li class = "li">
Static <span class = "ph">load cases</span>: Stiffness (= compliance), Displacements, Forces</li>
<li class = "li">Modal eigenfrequency <span class = "ph">load cases</span>: Eigenfrequencies</li>
<li class = "li">Frequency response, including vibroacoustic</li>
<li class = "li">Mass</li>
</ul>
<p>
Several constraints and several terms for the objective function for an
arbitrary number of <span class = "ph">load cases</span>
can be specified.
</p>
</div>

</div>

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