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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>General Information</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3"><table class = "DocHeaderIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">Shape optimization is mostly used at the end of the design
process when the general layout of a component is more or less fixed
and only minor changes and improvements are allowed.</span>

</p>
<ul><li><a href = "#tso-c-usr-shape-genInf__tso-c-usr-shape-genInf-shapesens" id = "toc_rg" title = "">Sensitivity-Based Shape Optimization</a></li></ul>
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr><tr><td><a title = "Design variables for shape optimization are defined when assigning a node group to the design area." href = "tso-c-usr-shape-desArea-desVar.htm#tso-c-usr-shape-desArea-desVar">About Design Variables (DV_SHAPE)</a></td></tr></table></td></tr></table>




<div class = "body conbody">
<p>In the following figure, an example of nonparametric shape optimization is demonstrated. (Pictures by courtesy of Audi AG).</p>
<table class = "table" id = "tso-c-usr-shape-genInf__ae394296"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/tso-c-usr-shape-genInf-shape_intro_combined.jpg" width = "587"/><br/></td>
</tr>
</tbody></table>

<p>
Typically, the objective function is to minimize stress concentrations.
Based on the results of a stress analysis modifications of the surface
geometry of a component are performed until the required stress level
is reached. This process is usually carried out manually by trial-and-error.
</p>
<p>
<span class = "ph">Tosca Structure.shape</span>
allows an automation of this improvement process. The surface geometry
of a given FE model is modified iteratively based on the FE results,
such that the required optimization target is reached. The start model
is taken from an existing design, which should be improved, or from a
previous topology optimization.
</p>
<p>
<span class = "ph">Tosca Structure.shape</span> enables you to perform the following tasks
<ul class = "ul">
<li class = "li">Minimization of the equivalent stress</li>
<li class = "li">Maximization of selected natural frequencies</li>
</ul>
</p>
<p> Under the possible restrictions:
<ul class = "ul">
<li class = "li">Specification of a volume constraint</li>
<li class = "li">Surface-based manufacturing constraints for casting, forging, stamping, extrusion and drilling</li>
<li class = "li">Minimum and maximum member size</li>
<li class = "li">Symmetry constraints</li>
<li class = "li">Specification of design domain restrictions by FE meshes</li>
<li class = "li">Mesh adjustment and mesh smoothing in each optimization cycle</li>
</ul>
</p>
<p>
Additional functionalities like optimization using durability results
are available with <span class = "ph">Tosca Structure.durability</span>.
Functionalities like optimization using nonlinear results or
optimization of contact areas are available with
<span class = "ph">Tosca Structure.nonlinear</span>.
</p>

<div class = "section" id = "tso-c-usr-shape-genInf__tso-c-usr-shape-genInf-shapesens"><h2 class = "title sectiontitle">Sensitivity-Based Shape Optimization</h2>

<p>
Sensitivity-based shape optimization (SHAPE_SENSITIVITY) makes it possible
to define very complex optimization tasks. It has been shown in industrial
size examples that the method is very powerful and attractive for problems with many CONSTRAINTs.
</p>
<p>The typical problems which can be solved by this algorithm are:</p>
<ul class = "ul">
<li class = "li">Minimize volume with stiffness or displacement constraint</li>
<li class = "li">Minimize volume with stress constraint</li>
<li class = "li">Maximize stiffness (linear static) with a volume constraint</li>
<li class = "li">Minimize displacement for critical nodes (linear static) with a volume constraint</li>
<li class = "li">Maximize first eigenvalue (modal) with a volume constraint</li>
<li class = "li">Maximize a certain eigenvalue (using mode tracking)</li>
<li class = "li">Move eigenvalues away from certain frequency (band gap optimization with modal analysis)</li>
</ul>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">
<p>
<ol class = "ol">
<li class = "li">Nonlinear analysis (for example, plasticity, large strains, contacts, etc.) is supported since version R2019x with solver sensitivities (SENS_CALC_MODE=SOLVER).</li>
<li class = "li">Design nodes must be connected to elements which are supported by <span class = "ph">Tosca Structure</span>.
<p>
Supported elements by shape sensitivity, see <a class = "xref" href = "tso-c-usr-shape-desArea-desVar.htm#tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-shapeSensElems-AbqSens">Supported Elements Attached to Shape Sensitivity Design Nodes using SENS_CALC_MODE = SOLVER with Abaqus.</a>
and <a class = "xref" href = "tso-c-usr-shape-desArea-desVar.htm#tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-shapeSensElems">Supported Elements Attached to Shape Sensitivity Design Nodes using SENS_CALC_MODE = TOSCA.</a>.
</p>
</li>
</ol>
</p>
</span></td></tr></table>


<dl class = "dl">

<dt class = "dt dlterm">Analysis Types</dt>
<dd class = "dd">

<table class = "table" id = "tso-c-usr-shape-genInf__analysisTypes"><caption/><colgroup><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><span class = "ph uicontrol">Analysis type</span></td>
<td class = "entry"><span class = "ph uicontrol">Supported</span></td>
</tr>

<tr class = "row">
<td class = "entry">Linear Analysis</td>
<td class = "entry">Yes</td>
</tr>
<tr class = "row">
<td class = "entry">Linear modal (no pre-tension)</td>
<td class = "entry">Yes</td>
</tr>
<tr class = "row">
<td class = "entry">Nonlinear contact only, linear material, linear strains (NLGEOM=NO)</td>
<td class = "entry">Yes</td>
</tr>
<tr class = "row">
<td class = "entry">Nonlinear material (for example, *PLASTICITY)</td>
<td class = "entry">Yes</td>
</tr>
<tr class = "row">
<td class = "entry">Nonlinear strains (NLGEOM=YES)</td>
<td class = "entry">Yes</td>
</tr>
</tbody></table>
</dd>



<dt class = "dt dlterm">Remarks on Boundary Conditions Using Solver Sensitivities SENS_CALC_MODE=SOLVER</dt>
<dd class = "dd">
<p>
<ul class = "ul">
<li class = "li">Prescribed displacements are supported.</li>
<li class = "li">Temperature preloading is allowed, but must stay constant during optimization.</li>
<li class = "li">TEMPERATURE_FILE is not allowed with sensitivity-based shape optimization.</li>
<li class = "li">Forces, surface forces, gravity forces and contact forces on design nodes are supported.</li>
</ul>
</p>
</dd>



<dt class = "dt dlterm">Remarks on Boundary Conditions Using <span class = "ph">Tosca</span> Sensitivities SENS_CALC_MODE=TOSCA</dt>
<dd class = "dd">
<p>
<ul class = "ul">
<li class = "li">Prescribed displacements are supported.</li>
<li class = "li">Temperature preloading and TEMPERATURE_FILE are NOT allowed.</li>
<li class = "li">Forces, surface forces, gravity forces and contact forces on design nodes are NOT supported as well.</li>
</ul>
</p>
</dd>

</dl>

</div>

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