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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>DEF_TYPE = OPER</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">With <code class = "ph codeph">DEF_TYPE=OPER</code> the design response is the difference between two design responses of the same type for the same <span class = "ph">load case</span>(s) or a weighted combination of several displacement responses.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-r-cmd-dresp-operDefType__tso-r-cmd-dresp-operDefType-combDrespSens" id = "toc_rg" title = "">Combination of Design Responses for the Sensitivity-Based Algorithms</a></li><li><a href = "#tso-r-cmd-dresp-operDefType__tso-r-cmd-dresp-operDefType-combDrespCtrl" id = "toc_rg" title = "">Combination of Design Responses for the Controller-Based Algorithm for Shape Optimization</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body refbody">
<div class = "section" id = "tso-r-cmd-dresp-operDefType__tso-r-cmd-dresp-operDefType-combDrespSens"><h2 class = "title sectiontitle">Combination of Design Responses for the Sensitivity-Based Algorithms</h2>


<table class = "table" id = "tso-r-cmd-dresp-operDefType__aa1164865"><caption/><colgroup><col/><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VAR_OPER</span></p></td>
<td class = "entry" colspan = "2"><p>Operator linking the variables <code class = "ph codeph">VAR_A</code> to <code class = "ph codeph">VAR_D</code>.</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operators with 2 operands:</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= SUB</p></td>
<td class = "entry"><p>General case: subtraction.</p>
  <p>Special case: where <code class = "ph codeph">VAR_A</code> and <code class = "ph codeph">VAR_B</code> are both of <code class = "ph codeph">TYPE=DISP_ABS</code> this operator is evaluated as follows:
  <table class = "table" id = "tso-r-cmd-dresp-operDefType__table_C0A1619CF1934290AB5B77091E3E1BD4"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
        <tr class = "row">
          <td class = "entry">
            <p>
              <span class = "ph inlineequation">
                <math altimg-valign = "5" altimg-height = "19" altimg-width = "197" class = "- topic/foreign ">
                  <mrow class = "- topic/foreign ">
                    <mtext class = "- topic/foreign ">DRESP=</mtext>
                    <mo class = "- topic/foreign ">Δ</mo>
                    <mi class = "- topic/foreign ">u</mi>
                    <mo class = "- topic/foreign ">=</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">l</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">def</mtext>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">−</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">l</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">ini</mtext>
                      </mrow>
                    </msub>
                  </mrow>
                </math>
              </span>
            </p>
            <p>
              with
              <span class = "ph inlineequation">
                <math altimg-valign = "10" altimg-height = "35" altimg-width = "528" class = "- topic/foreign ">
                  <mrow class = "- topic/foreign ">
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">l</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">def</mtext>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">=</mo>
                    <msqrt class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <msup class = "- topic/foreign ">
                          <mrow class = "- topic/foreign ">
                            <mo class = "- topic/foreign ">(</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">x</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mtext class = "- topic/foreign ">pos</mtext>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">+</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">u</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">x</mi>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">)</mo>
                          </mrow>
                          <mrow class = "- topic/foreign ">
                            <mn class = "- topic/foreign ">2</mn>
                          </mrow>
                        </msup>
                        <mo class = "- topic/foreign ">+</mo>
                        <msup class = "- topic/foreign ">
                          <mrow class = "- topic/foreign ">
                            <mo class = "- topic/foreign ">(</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">y</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mtext class = "- topic/foreign ">pos</mtext>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">+</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">u</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">y</mi>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">)</mo>
                          </mrow>
                          <mrow class = "- topic/foreign ">
                            <mn class = "- topic/foreign ">2</mn>
                          </mrow>
                        </msup>
                        <mo class = "- topic/foreign ">+</mo>
                        <msup class = "- topic/foreign ">
                          <mrow class = "- topic/foreign ">
                            <mo class = "- topic/foreign ">(</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">z</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mtext class = "- topic/foreign ">pos</mtext>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">+</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">u</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">z</mi>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">)</mo>
                          </mrow>
                          <mrow class = "- topic/foreign ">
                            <mn class = "- topic/foreign ">2</mn>
                          </mrow>
                        </msup>
                      </mrow>
                    </msqrt>
                  </mrow>
                </math>
              </span>
              as deformed length
            </p>
            <p>
              and
              <span class = "ph inlineequation">
                <math altimg-valign = "10" altimg-height = "35" altimg-width = "341" class = "- topic/foreign ">
                  <mrow class = "- topic/foreign ">
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">l</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">ini</mtext>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">=</mo>
                    <msqrt class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <msup class = "- topic/foreign ">
                          <mrow class = "- topic/foreign ">
                            <mo class = "- topic/foreign ">(</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">x</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mtext class = "- topic/foreign ">pos</mtext>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">)</mo>
                          </mrow>
                          <mrow class = "- topic/foreign ">
                            <mn class = "- topic/foreign ">2</mn>
                          </mrow>
                        </msup>
                        <mo class = "- topic/foreign ">+</mo>
                        <msup class = "- topic/foreign ">
                          <mrow class = "- topic/foreign ">
                            <mo class = "- topic/foreign ">(</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">y</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mtext class = "- topic/foreign ">pos</mtext>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">)</mo>
                          </mrow>
                          <mrow class = "- topic/foreign ">
                            <mn class = "- topic/foreign ">2</mn>
                          </mrow>
                        </msup>
                        <mo class = "- topic/foreign ">+</mo>
                        <msup class = "- topic/foreign ">
                          <mrow class = "- topic/foreign ">
                            <mo class = "- topic/foreign ">(</mo>
                            <mo class = "- topic/foreign ">Δ</mo>
                            <msub class = "- topic/foreign ">
                              <mrow class = "- topic/foreign ">
                                <mi class = "- topic/foreign ">z</mi>
                              </mrow>
                              <mrow class = "- topic/foreign ">
                                <mtext class = "- topic/foreign ">pos</mtext>
                              </mrow>
                            </msub>
                            <mo class = "- topic/foreign ">)</mo>
                          </mrow>
                          <mrow class = "- topic/foreign ">
                            <mn class = "- topic/foreign ">2</mn>
                          </mrow>
                        </msup>
                      </mrow>
                    </msqrt>
                  </mrow>
                </math>
              </span>
              as initial length.
            </p>
            <p>
              Thereby <span class = "ph inlineequation">
                <math altimg-valign = "8" altimg-height = "22" altimg-width = "223" class = "- topic/foreign ">
                  <mrow class = "- topic/foreign ">
                    <mo class = "- topic/foreign ">Δ</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">n</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">pos</mtext>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">=</mo>
                    <mo class = "- topic/foreign ">Δ</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">n</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">pos</mtext>
                        <mn class = "- topic/foreign ">1</mn>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">−</mo>
                    <mo class = "- topic/foreign ">Δ</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">n</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mtext class = "- topic/foreign ">pos</mtext>
                        <mn class = "- topic/foreign ">2</mn>
                      </mrow>
                    </msub>
                  </mrow>
                </math>
              </span>, for n = x,y,z and
              <span class = "ph inlineequation">
                <math altimg-valign = "4" altimg-height = "18" altimg-width = "176" class = "- topic/foreign ">
                  <mrow class = "- topic/foreign ">
                    <mo class = "- topic/foreign ">Δ</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">u</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">n</mi>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">=</mo>
                    <mo class = "- topic/foreign ">Δ</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">u</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">n</mi>
                        <mn class = "- topic/foreign ">1</mn>
                      </mrow>
                    </msub>
                    <mo class = "- topic/foreign ">−</mo>
                    <mo class = "- topic/foreign ">Δ</mo>
                    <msub class = "- topic/foreign ">
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">u</mi>
                      </mrow>
                      <mrow class = "- topic/foreign ">
                        <mi class = "- topic/foreign ">n</mi>
                        <mn class = "- topic/foreign ">2</mn>
                      </mrow>
                    </msub>
                  </mrow>
                </math>
              </span>, for n = x,y,z, where pos1 and pos2
              are the coordinates of the nodes and u the displacements. The DRESP can
              also be negative and gives the stretch between two nodes (that is, the difference
              between the two notes in deformed and undeformed configuration). 
            </p>
          </td>
        </tr>
      </tbody></table>
  </p>
</td>
<td class = "entry"><p>A - B</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= SUB_ABS</p></td>
<td class = "entry"><p>General case: absolute value of the subtraction.</p>
                      <p>Spacial cases: where <code class = "ph codeph">VAR_A</code> and <code class = "ph codeph">VAR_B</code> are both of equal <code class = "ph codeph">TYPE=DISP_ABS</code>, <code class = "ph codeph">TYPE=ROT_ABS</code>, <code class = "ph codeph">TYPE=REACTION_FORCE_ABS</code>, <code class = "ph codeph">TYPE=REACTION_MOMENT_ABS</code>, <code class = "ph codeph">TYPE=INTERNAL_FORCE_ABS</code> or <code class = "ph codeph">TYPE=INTERNAL_MOMENT_ABS</code> this operator is evaluated as follows:
</p><p><span class = "ph inlineequation">
                        <math altimg-width = "434" altimg-height = "33" altimg-valign = "9" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">Δ</mo><mi class = "- topic/foreign ">Q</mi><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi><mi class = "- topic/foreign ">A</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi><mi class = "- topic/foreign ">B</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi><mi class = "- topic/foreign ">A</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi><mi class = "- topic/foreign ">B</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi><mi class = "- topic/foreign ">A</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi><mi class = "- topic/foreign ">B</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math>
                      </span>
</p>
                        <p>Here, Q is the symbolic representation of nodal displacements, rotations, internal and reaction forces and moments.
</p>
</td>
<td class = "entry"><p>| A - B |</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= ADD_ABS</p></td>
<td class = "entry"><p>Addition of absolute values.</p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "31" altimg-width = "75" class = "- topic/foreign "><mrow class = "- topic/foreign "><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">B</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operators with up to 2500 operands:</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= COMBINE</p></td>
<td class = "entry"><p>Weighted sum of up to 2500 variables.</p></td>
<td class = "entry"><p>Var1*w1 + Var2*w2 +...</p></td>
</tr>

<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= KSO</p></td>
<td class = "entry"><p>Kreisselmeier-Steinhauser operator. It can be used only for combination of frequency (<code class = "ph codeph">DYN_FREQ</code>) design responses.</p></td>
<td class = "entry"><p>

<span class = "ph inlineequation">
  <math altimg-valign = "11" altimg-height = "33" altimg-width = "137" class = "- topic/foreign ">
    <mfenced open = "" close = "" separators = " " class = "- topic/foreign ">
      <mrow class = "- topic/foreign ">
        <mo class = "- topic/foreign ">-</mo>
        <mfrac class = "- topic/foreign ">
          <mrow class = "- topic/foreign ">
            <mn class = "- topic/foreign ">1</mn>
          </mrow>
          <mrow class = "- topic/foreign ">
            <mi class = "- topic/foreign ">k</mi>
          </mrow>
        </mfrac>
        <mo class = "- topic/foreign ">ln</mo>
        <mfenced open = "(" close = ")" separators = "" class = "- topic/foreign ">
          <munder class = "- topic/foreign ">
            <mo class = "- topic/foreign ">∑</mo>
            <mrow class = "- topic/foreign ">
              <mi class = "- topic/foreign ">j</mi>
            </mrow>
          </munder>
          <msup class = "- topic/foreign ">
            <mrow class = "- topic/foreign ">
              <mi class = "- topic/foreign ">e</mi>
            </mrow>
            <mrow class = "- topic/foreign ">
              <mo class = "- topic/foreign ">−</mo>
              <mi class = "- topic/foreign ">k</mi>
              <msub class = "- topic/foreign ">
                <mrow class = "- topic/foreign ">
                  <mi class = "- topic/foreign ">f</mi>
                </mrow>
                <mrow class = "- topic/foreign ">
                  <mi class = "- topic/foreign ">j</mi>
                </mrow>
              </msub>
            </mrow>
          </msup>
        </mfenced>

      </mrow>
    </mfenced>
  </math>
</span>

</p></td>
</tr>
<tr class = "row">
<td class = "entry" colspan = "4"><p>Specifying the operands for <code class = "ph codeph">SUB</code> and <code class = "ph codeph">SUB_ABS</code> with their <code class = "ph codeph">ID_NAME</code>:</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VAR_A</span></p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_a&gt;</var></p></td>
<td class = "entry"/>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VAR_B</span></p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_b&gt;</var></p></td>
<td class = "entry"/>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry" colspan = "4"><p>Specification of operands for <code class = "ph codeph">COMBINE</code> with their <code class = "ph codeph">ID_NAME </code> (can be specified several times):</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>VARIABLE</p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id&gt;</var>,<code class = "ph codeph">&lt;weight&gt; </code></p></td>
<td class = "entry"><p>Only displacements and rotations, modal eigenfrequencies, or reaction forces and internal forces
                  are allowed. </p><p>if the weight parameter is not specified it is assumed to be 1.</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry" colspan = "4"><p>Specification of operands for <code class = "ph codeph">KSO</code> with their <code class = "ph codeph">ID_NAME </code> (can be specified several times):</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>VARIABLE</p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id&gt;</var></p></td>
<td class = "entry"><p>Only frequency (<code class = "ph codeph">DYN_FREQ</code>) design responses are allowed. </p></td>
<td class = "entry"/>
</tr>
</tbody></table>

</div>

<div class = "section" id = "tso-r-cmd-dresp-operDefType__tso-r-cmd-dresp-operDefType-combDrespCtrl"><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">Combination of Design Responses for the Controller-Based Algorithm for Shape Optimization</h2>

<table class = "table" id = "tso-r-cmd-dresp-operDefType__aa1208743"><caption/><colgroup><col/><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VAR_OPER</span></p></td>
<td class = "entry" colspan = "2"><p>Operator linking the variables<code class = "ph codeph"> VAR_A</code> to <code class = "ph codeph">VAR_D</code>.</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operators with 2 to 4 operands:</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= ADD</p></td>
<td class = "entry"><p>Addition.</p></td>
<td class = "entry"><p>A+B+C+D</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= MULT</p></td>
<td class = "entry"><p>Multiplication.</p></td>
<td class = "entry"><p>A*B*C*D</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= MIN</p></td>
<td class = "entry"><p>Minimum.</p></td>
<td class = "entry"><p>min(A,B,C,D)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= MAX</p></td>
<td class = "entry"><p>Maximum.</p></td>
<td class = "entry"><p>max(A,B,C,D)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operators with 2 operands:</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= SUB</p></td>
<td class = "entry"><p>Subtraction.</p></td>
<td class = "entry"><p>A - B</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DIV</p></td>
<td class = "entry"><p>Division.</p></td>
<td class = "entry"><p>A / B</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operators with 1 operand:</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= ABS</p></td>
<td class = "entry"><p>Absolute value.</p></td>
<td class = "entry"><p>abs(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= SIN</p></td>
<td class = "entry"><p>Sinus.</p></td>
<td class = "entry"><p>sin(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= COS</p></td>
<td class = "entry"><p>Cosine.</p></td>
<td class = "entry"><p>cos(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= CUT_OFF</p></td>
<td class = "entry"><p>Cutoff operator to remove peaks </p><p>(parameters are specified with additional settings).</p></td>
<td class = "entry"><p>max<code class = "ph codeph">(&lt;</code><code class = "ph codeph">CUT_OFF_LOW&gt;</code>,<code class = "ph codeph"> </code>min(A<code class = "ph codeph">,&lt;</code><code class = "ph codeph">CUT_OFF_HIGH&gt;</code>))</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= TAN</p></td>
<td class = "entry"><p>Tangent.</p></td>
<td class = "entry"><p>tan(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= LOG</p></td>
<td class = "entry"><p>Common logarithm. </p></td>
<td class = "entry"><p>log(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= EXP</p></td>
<td class = "entry"><p>Exponential function.</p></td>
<td class = "entry"><p>exp(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= FILTER</p></td>
<td class = "entry"><p>Filter function for vectors used as terms for the controller-based algorithms (parameters are specified with additional settings).</p></td>
<td class = "entry"><p>filter(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= LN</p></td>
<td class = "entry"><p>Nat. logarithm.</p></td>
<td class = "entry"><p>ln(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= NORM</p></td>
<td class = "entry"><p>Norm for vectors (maximum norm) used as terms for the controller-based algorithms.</p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "1" altimg-height = "14" altimg-width = "24" class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">‖</mo><mi class = "- topic/foreign ">A</mi><mo class = "- topic/foreign ">‖</mo></mrow></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= NORM_FIRST</p></td>
<td class = "entry"><p>Norm for vectors (maximum norm) used as terms for the controller-based algorithms, based on the value in first iteration .</p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "1" altimg-height = "14" altimg-width = "24" class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">‖</mo><mi class = "- topic/foreign ">A</mi><mo class = "- topic/foreign ">‖</mo></mrow></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= NPOWER</p></td>
<td class = "entry"><p>N-th power to A (parameter is specified with <code class = "ph codeph">EXPONENT</code> item).</p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "0" altimg-height = "17" altimg-width = "20" class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></msup></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= NROOT</p></td>
<td class = "entry"><p>N-th root (parameter is specified with <code class = "ph codeph">EXPONENT</code> item).</p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "28" altimg-width = "27" class = "- topic/foreign "><mrow class = "- topic/foreign "><mroot class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></mroot></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= SQRT</p></td>
<td class = "entry"><p>Square root.</p></td>
<td class = "entry"><p>sqrt(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= INT</p></td>
<td class = "entry"><p>Integer.</p></td>
<td class = "entry"><p>int(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= NINT</p></td>
<td class = "entry"><p>Nearest integer number.</p></td>
<td class = "entry"><p>nint(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= SIGN</p></td>
<td class = "entry"><p>Sign function.</p></td>
<td class = "entry"><p>sign(A)</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DELTA_1</p></td>
<td class = "entry"><p>Difference between 2 iterations   A(i) - A(i-1).</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DELTA_2</p></td>
<td class = "entry"><p>Difference between  2 iterations   A(i) - A(i-2).</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DELTA_3</p></td>
<td class = "entry"><p>Difference between  2 iterations   A(i) - A(i-3).</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DELTA_4</p></td>
<td class = "entry"><p>Difference between  2 iterations   A(i) - A(i-4).</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DELTA_5</p></td>
<td class = "entry"><p>Difference between  2 iterations   A(i) - A(i-5).</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= DELTA_6</p></td>
<td class = "entry"><p>Difference between  2 iterations   A(i) - A(i-6).</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operators with up to 10 operands:</p></td>
<td class = "entry"><p>Operands defined by item <code class = "ph codeph">VARIABLE</code>.</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry"><p>= COMBINE</p></td>
<td class = "entry"><p>Weighted addition.</p></td>
<td class = "entry"><p>w1*VAR1 + w2*VAR2 ...</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "3"><p>Specifying the operands with their <code class = "ph codeph">ID_NAME</code>:</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VAR_A</span></p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_a&gt;</var> </p></td>
<td class = "entry"/>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"><p><span class = "ph uicontrol">VAR_B</span></p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_b&gt;</var> </p></td>
<td class = "entry"/>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"><p>VAR_C</p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_c&gt;</var> </p></td>
<td class = "entry"/>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"><p>VAR_D</p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_d&gt;</var><var class = "keyword varname varname"> </var> </p></td>
<td class = "entry"/>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "3"/>
</tr>
<tr class = "row">
<td class = "entry"><p>RADIUS</p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;radius value&gt;</code> </p></td>
<td class = "entry"><p>Real value. </p></td>
<td class = "entry"><p>The radius defines the maximum distance for influencing neighbor nodes.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>EXPONENT</p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;exponent value&gt;</code> </p><p>= <span class = "ph uicontrol">1.0</span></p></td>
<td class = "entry"><p>Real value. </p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"><p>SIGMA</p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;value&gt;</code> </p><p><span class = "ph uicontrol">= 0.2</span></p></td>
<td class = "entry"><p>Real value. </p></td>
<td class = "entry"><p>Sigma defines the reduction of the radius depending on the surface bending.</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "3"><p>Additional settings for <code class = "ph codeph">VAR_OPER = CUT_OFF</code>:</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>CUT_OFF_LOW</p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;value&gt;</code></p></td>
<td class = "entry"><p>Real value. </p></td>
<td class = "entry"><p>Lower bound of the vector value. All values under this value will be treated as zero.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>CUT_OFF_HIGH</p></td>
<td class = "entry"><p>= <code class = "ph codeph">&lt;value&gt;</code></p></td>
<td class = "entry"><p>Real value. </p></td>
<td class = "entry"><p>Upper bound of the vector value. All values higher than this value will be set to the cut off value.</p></td>
</tr>
<tr class = "row">
<td class = "entry"/>
<td class = "entry" colspan = "2"><p>Operands for <code class = "ph codeph">VAR_OPER = COMBINE</code>:</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry"><p>VARIABLE</p></td>
<td class = "entry"><p>= <var class = "keyword varname varname">&lt;var_id_1&gt;</var>, <code class = "ph codeph">&lt;weight1&gt;</code></p><p><span class = "ph uicontrol">= </span><span class = "ph uicontrol">&lt;var_id_1&gt;</span><span class = "ph uicontrol">, </span><span class = "ph uicontrol">&lt;1&gt;</span></p></td>
<td class = "entry"><p><code class = "ph codeph">ID_NAME</code> of variable <code class = "ph codeph">var1</code> with weight factor w1 for combination.</p></td>
<td class = "entry"><p>Up to 10 different variables can be specified.</p></td>
</tr>
</tbody></table>

</div>

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