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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> Objective Function</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">The objective function describes the optimization target.
In general, one scalar value (sometimes combined from other scalars)
is to be maximized or minimized.</span>

</p>
<ul><li><a href = "#tso-c-usr-beadOpt-beadObjectiveFunction__tso-c-user-BeadOpt-ObjFun-MinMax" id = "toc_rg" title = "">Differences in Objective Target Formulation</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 = "The objective function defines the values to be maximized or minimized during optimization. This function might depend on analysis results, geometric values or combinations of those." href = "tso-m-usr-terms-objfunc-sb.htm#tso-m-usr-terms-objfunc-sb">Objective Function</a></td></tr><tr><td><a title = "Most design responses are only available for certain analysis types. Others are independent of the analysis type because they are directly linked to the geometry of the FE-model. Each design response represents one scalar value which can be extracted from the model information (like the volume) or from the FE-results." href = "tso-m-usr-terms-dresps-sb.htm#tso-m-usr-terms-dresps-sb">Design Responses</a></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 the objective function of the optimization." href = "../TsoCmdMap/tso-r-cmd-objFunc.htm#tso-r-cmd-objFunc">OBJ_FUNC</a></td></tr></table></td></tr></table>




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<p>Bead optimization is mostly used to maximize stiffness of a structure or improve the dynamical properties of a shell structure. As already noted,
<span class = "ph">Tosca Structure.bead</span>
has two different optimization approaches (see <a class = "xref" href = "tso-c-usr-beadOptTask-diffBeadOptAlgos.htm#tso-c-usr-beadOptTask-diffBeadOptAlgos" title = "The user might choose between two bead optimization algorithms in Tosca Structure.bead. The algorithms have different ways to find the solution and their differences will be discussed in this chapter.">Differences between Bead Optimization Algorithms</a>).
The possible design responses in the objective function are  one of the major differences that becomes obvious by looking at the following table.</p>

<table class = "table" id = "tso-c-usr-beadOpt-beadObjectiveFunction__table_bead_sens_dresps"><caption/><colgroup><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><span class = "ph uicontrol">Static analysis</span></td>
<td class = "entry"><span class = "ph uicontrol">Description</span></td>
</tr>
<tr class = "row">
<td class = "entry"><p>CENTER_GRAVITY_X</p>
                      <p>CENTER_GRAVITY_Y</p>
                      <p>CENTER_GRAVITY_Z</p></td>
<td class = "entry"><p>Center of gravity design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>DISP_ABS</p>
                      <p>DISP_X</p>
                      <p>DISP_Y</p>
                      <p>DISP_Z</p>
                      <p>DISP_X_ABS</p>
                      <p>DISP_Y_ABS</p>
                      <p>DISP_Z_ABS</p></td>
<td class = "entry"><p>Displacement design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>ENERGY_STIFF_MEASURE</p></td>
<td class = "entry"><p>Energy stiffness measure design response</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>INERTIA_XX</p>
                      <p>INERTIA_XY</p>
                      <p>INERTIA_XZ</p>
                      <p>INERTIA_YY</p>
                      <p>INERTIA_YZ</p>
                      <p>INERTIA_ZZ</p></td>
<td class = "entry"><p>Moment of inertia design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>INTERNAL_FORCE_ABS</p>
                      <p>INTERNAL_FORCE_X</p>
                      <p>INTERNAL_FORCE_Y</p>
                      <p>INTERNAL_FORCE_Z</p>
                      <p>INTERNAL_FORCE_X_ABS</p>
                      <p>INTERNAL_FORCE_Y_ABS</p>
                      <p>INTERNAL_FORCE_Z_ABS</p></td>
<td class = "entry"><p>Internal force design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>INTERNAL_MOMENT_ABS</p>
                      <p>INTERNAL_MOMENT_X</p>
                      <p>INTERNAL_MOMENT_Y</p>
                      <p>INTERNAL_MOMENT_Z</p>
                      <p>INTERNAL_MOMENT_X_ABS</p>
                      <p>INTERNAL_MOMENT_Y_ABS</p>
                      <p>INTERNAL_MOMENT_Z_ABS</p></td>
<td class = "entry"><p>Internal moment design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>PEMAG</p></td>
<td class = "entry"><p>Plastic strain magnitude**</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>REACTION_FORCE_ABS</p>
                      <p>REACTION_FORCE_X</p>
                      <p>REACTION_FORCE_Y</p>
                      <p>REACTION_FORCE_Z</p>
                      <p>REACTION_FORCE_X_ABS</p>
                      <p>REACTION_FORCE_Y_ABS</p>
                      <p>REACTION_FORCE_Z_ABS</p></td>
<td class = "entry"><p>Reaction force design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>REACTION_MOMENT_ABS</p>
                      <p>REACTION_MOMENT_X</p>
                      <p>REACTION_MOMENT_Y</p>
                      <p>REACTION_MOMENT_Z</p>
                      <p>REACTION_MOMENT_X_ABS</p>
                      <p>REACTION_MOMENT_Y_ABS</p>
                      <p>REACTION_MOMENT_Z_ABS</p></td>
<td class = "entry"><p>Reaction moment design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>ROT_ABS</p>
                      <p>ROT_X</p>
                      <p>ROT_Y</p>
                      <p>ROT_Z</p>
                      <p>ROT_X_ABS</p>
                      <p>ROT_Y_ABS</p>
                      <p>ROT_Z_ABS</p></td>
<td class = "entry"><p>Rotation design responses</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SIG_1</p></td>
<td class = "entry"><p>Maximum principal stress.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SIG_3</p></td>
<td class = "entry"><p>Minimum principal stress.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SIG_MISES</p></td>
<td class = "entry"><p>Von Mises stress design response</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SIG_SENS_MISES</p></td>
<td class = "entry"><p>Von Mises Stress design responses</p>
                      <p><code class = "ph codeph">SIG_SENS_MISES</code> is used for sensitivity calculation.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SIG_SIGNED_MISES</p></td>
<td class = "entry"><p>Signed von Mises stress failure criteria.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SIG_GLINKA_EEQ</p>
	                  <p>SIG_GLINKA_PEEQ</p>
	                  <p>SIG_GLINKA_SEQ</p>
	                  <p>SIG_NEUBER_EEQ</p>
	                  <p>SIG_NEUBER_PEEQ</p>
	                  <p>SIG_NEUBER_SEQ</p></td>
<td class = "entry"><p>Glinka and Neuber formulations for equivalent strain (_EEQ), stress (_SEQ) and plastic strain (_PEEQ) using the plastic correction factor, respectively**.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>STRAIN_ENERGY</p></td>
<td class = "entry"><p>Strain energy design response*</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>WEIGHT</p></td>
<td class = "entry"><p>Weight design response*</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph uicontrol">Modal analysis</span></td>
<td class = "entry"><span class = "ph uicontrol">Description</span></td>
</tr>
<tr class = "row">
<td class = "entry"><p>DYN_FREQ</p>
                      <p>DYN_FREQ_KREISSEL</p></td>
<td class = "entry"><p>Dynamic frequency design response*</p>
                      <p>(Kreisselmeier-Steinhauser formulation)</p></td>
</tr>





</tbody></table>

<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">
<ul class = "ul">
<li class = "li">Only design responses marked with <code class = "ph codeph">*</code> are also allowed in the controller-based algorithm (<code class = "ph codeph">BEAD_CONTROLLER</code>).</li>
<li class = "li">The Gravity / Inertia design response types are only usable if at least one design response of the other types is used in the objective function or constraints.</li>
<li class = "li">Design responses marked with <code class = "ph codeph">**</code> are only allowed using <span class = "ph">Abaqus</span> sensitivities.</li>
</ul>
</span></td></tr></table>
</p>

<div class = "section" id = "tso-c-usr-beadOpt-beadObjectiveFunction__tso-c-user-BeadOpt-ObjFun-MinMax"><h2 class = "title sectiontitle">Differences in Objective Target Formulation</h2>

The objective formulation for the optimization varies depending on the objective target such as minimization/
maximization or a Min-Max/ Max-Min definition. For further details and formulas, 
see <a class = "xref" href = "tso-c-usr-terms-minMaxObjFunc.htm" title = "This section deals with the minimization or maximization of the objective function.">Minimization or Maximization of an Objective Function</a>
and <a class = "xref" href = "tso-c-usr-terms-multidiscObjFunc.htm" title = "This section deals with multidisciplinary objective functions.">Multidisciplinary Objectives (Minmax and Maxmin Formulations)</a>. </div>

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