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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>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-objFunc__tso-c-usr-sizing-ObjFun-ovw" id = "toc_rg" title = "">Overview</a></li><li><a href = "#tso-c-usr-sizing-objFunc__tso-c-user-sizing-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>



<div class = "body conbody">
<div class = "section" id = "tso-c-usr-sizing-objFunc__tso-c-usr-sizing-ObjFun-ovw"><h2 class = "title sectiontitle">Overview</h2>

<p>The <code class = "ph codeph">OBJECTIVE FUNCTION</code> is the function, which value can be maximized or
minimized during the optimization. This function depends on the results of the FE analysis.
Therefore, the values of interest must be derived from the FE results to define an objective
function and functional constraints. The results of the FE analysis (total displacement, energy,
etc.) for determining the objective function and functional constraints are called "design
responses." A single value from the design response must be specified for the definition of
the objective function using the command <code class = "ph codeph">DRESP</code> (<code class = "ph codeph">DESIGN
RESPONSE</code>).</p>
<table class = "table" id = "tso-c-usr-sizing-objFunc__table_sizing_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_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"><p>VOLUME</p></td>
<td class = "entry"><p>Volume 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>
<tr class = "row">
<td class = "entry"><span class = "ph uicontrol">Frequency response</span></td>
<td class = "entry"><span class = "ph uicontrol">Description</span></td>
</tr>
<tr class = "row">
<td class = "entry"><p>FS_ACCEL_X</p>
                      <p>FS_ACCEL_Y</p>
                      <p>FS_ACCEL_Z</p></td>
<td class = "entry"><p>Acceleration for frequency response</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>FS_PHASE_X</p>
                      <p>FS_PHASE_Y</p>
                      <p>FS_PHASE_Z</p></td>
<td class = "entry"><p>Phase for frequency response</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>FS_DISP_ABS</p>
                      <p>FS_DISP_X_ABS</p>
                      <p>FS_DISP_Y_ABS</p>
                      <p>FS_DISP_Z_ABS</p></td>
<td class = "entry"><p>Amplitude for frequency response</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>FS_VELOCITY_X</p>
                      <p>FS_VELOCITY_Y</p>
                      <p>FS_VELOCITY_Z</p></td>
<td class = "entry"><p>Velocity for frequency response</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>FS_COMP</p>
                      <p>FS_DBA_PRESSURE</p>
                      <p>FS_DB_PRESSURE</p>
                      <p>FS_PRESSURE</p>
                      <p>FS_RMS_PRESSURE</p></td>
<td class = "entry"><p>Dynamic compliance for frequency response</p>
                      <p>Sound Pressure Level [dBA] for frequency response</p>
                      <p>Sound Pressure Level [dB] for frequency response</p>
                      <p>Instantaneous Sound Pressure [Pa] for frequency response</p>
                      <p>Effective Sound Pressure(RMS)[Pa] for frequency response</p></td>
</tr>

<tr class = "row">
<td class = "entry"><span class = "ph uicontrol">Analysis independent</span></td>
<td class = "entry"><span class = "ph uicontrol">Description</span></td>
</tr>
<tr class = "row">
<td class = "entry"><p>VOLUME</p></td>
<td class = "entry"><p>Volume design response</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">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>


<div class = "section" id = "tso-c-usr-sizing-objFunc__tso-c-user-sizing-ObjFun-MinMax"><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">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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