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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>Initial Values of Density (DENSITY_INITIAL)</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 = "shortdesc">The relative density of each element is the design variable in topology
optimization. In the initial optimization iteration, the design space has a homogenous
material distribution, meaning that each element contains the same
relative material volume.
    
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr></table><table class = "DocTopicsInOtherGuides" id = "table14"><tr><td height = "8px"/></tr><tr><td class = "TopicsTitleNormal">In Other Guides</td></tr><tr><td><a title = "Defines parameters to control optimization." href = "../TsoCmdMap/tso-r-cmd-optParam.htm#tso-r-cmd-optParam">OPT_PARAM</a></td></tr></table></td></tr></table>
  

  

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<p>Initially, all the elements get the density causing the material volume
constraint to be exactly fulfilled if a material volume constraint
is defined for the optimization problem. </p>
<p>When no volume constraint is present in the optimization problem but
the relative material volume is used in the objective function, each
element has an initial relative density of 50%. However, if the constraints
(for example, displacement constraints) require a significantly higher relative
material volume than 50% for being fulfilled and this is known before
the optimization, then the initial relative material volume in the
design space can be set to a larger value (for example, to 90%) using the command
<code class = "ph codeph">DENSITY_INITIAL</code>:</p>
<pre class = "codeblock">
<code class = "ph codeph">OPT_PARAM
 ID_NAME         = opt_params
 OPTIMIZE        = id_of_optimize
 DENSITY_INITIAL = 0.9
END_
</code></pre>
<p>Similarly, if it is known before the optimization that the relative material
volume of significantly less than 50% is required in order to fulfill
the constraints, the initial relative material volume can be set to a
lower value (for example, to 10%):</p>
<pre class = "codeblock">
<code class = "ph codeph">OPT_PARAM
 ID_NAME         = opt_params
 OPTIMIZE        = id_of_optimize
 DENSITY_INITIAL = 0.1
END_
</code></pre>
<p>In both cases, it will lead to lower number of optimization iterations.
</p>

<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><ul class = "ul" id = "tso-c-user-TopOpt-Sett-Sensi-InitDen__ul_26B018945B9848AEA310E2FB09C9E62A">
<li class = "li">The default value of <code class = "ph codeph">DENSITY_INITIAL</code> is 0.5. <code class = "ph codeph">DENSITY_INITIAL</code>
should always be greater than zero and lower than or equal to one.</li><li class = "li">The <code class = "ph codeph">DENSITY_INITIAL</code> parameter can be used to stabilize
nonlinear or contact problems in combination with volume constraints.
Setting a higher material volume in iteration 0 leads to an initially
infeasible volume constraint requiring more optimization iterations.
Nevertheless the higher initial stiffness improves the convergence behavior
of the finite element solver in the first optimization iterations. </li>
<li class = "li">Relative values in constraints always refer to the design response
of the start model for the optimization. In topology optimization, this
start model is the model with eventually adapted element densities, which
may differ from the initial model (for example, when no volume constraint is
present they are set to 50% of the original density). Take this into
account when defining, for example, relative displacement or frequency constraints.
This behavior can be controlled by the user with the parameter <code class = "ph codeph">DENSITY_INITIAL</code>
in the 
<code class = "ph codeph">OPT_PARAM</code>
command.</li>
</ul></span></td></tr></table>
</p>


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