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DESIGN_RESPONSE.html
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DESIGN_RESPONSE.html
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<html><head><link rel="stylesheet" type="text/css" href="style.css"/></head><body> <H2> <BR> *DESIGN RESPONSE </H2> <P> Keyword type: step <P> With *DESIGN RESPONSE one can define the design response functions in a sensitivity analysis. Right now the following design response functions are allowed for TYPE=COORDINATE design variables: <P> <UL> <LI>ALL-DISP: the square root of the sum of the square of the displacements in all nodes of the structure or of a subset if a node set is defined </LI> <LI>x-DISP: the square root of the sum of the square of the x-displacements in all nodes of the structure or of a subset if a node set is defined </LI> <LI>Y-DISP: the square root of the sum of the square of the y-displacements in all nodes of the structure or of a subset if a node set is defined </LI> <LI>Z-DISP: the square root of the sum of the square of the z-displacements in all nodes of the structure or of a subset if a node set is defined </LI> <LI>EIGENFREQUENCY: all eigenfrequencies calculated in a previous *FREQUENCY step (actually the eigenvalues, which are the square of the eigenfrequencies) </LI> <LI>MASS: mass of the total structure or of a subset if an element set is defined </LI> <LI>STRAIN ENERGY: internal energy of the total structure or of a subset if an element set is defined </LI> <LI>STRESS: the maximum von Mises stress of the total structure or of a subset if a node set is defined. The maximum is approximated by the Kreisselmeier-Steinhauser function <P> <P></P> <DIV ALIGN="CENTER" CLASS="mathdisplay"><!-- MATH \begin{equation} f=\frac{1}{\rho} \ln \sum_i e^{\rho \frac{\sigma_{i}}{\bar{\sigma}}}, \end{equation} --> <TABLE CLASS="equation" CELLPADDING="0" WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"> <TD NOWRAP ALIGN="CENTER"><SPAN CLASS="MATH"><IMG WIDTH="125" HEIGHT="52" ALIGN="MIDDLE" BORDER="0" SRC="img2253.png" ALT="$\displaystyle f=\frac{1}{\rho} \ln \sum_i e^{\rho \frac{\sigma_{i}}{\bar{\sigma}}},$"></SPAN></TD> <TD NOWRAP CLASS="eqno" WIDTH="10" ALIGN="RIGHT"> (<SPAN CLASS="arabic">701</SPAN>)</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P> <P> where <SPAN CLASS="MATH"><B><IMG WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img2254.png" ALT="$ \sigma_i$"></B></SPAN> is the von Mises stress in node i, <SPAN CLASS="MATH"><B><IMG WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img33.png" ALT="$ \rho$"></B></SPAN> and <!-- MATH $\bar{\sigma}$ --> <SPAN CLASS="MATH"><B><IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="img2255.png" ALT="$ \bar{\sigma}$"></B></SPAN> are user-defined parameters. The higher <SPAN CLASS="MATH"><B><IMG WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img33.png" ALT="$ \rho$"></B></SPAN> the closer <SPAN CLASS="MATH"><B><IMG WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" SRC="img517.png" ALT="$ f$"></B></SPAN> is to the actual maximum (a value of 10 is recommended; the higher this value, the sharper the turns in the function). <!-- MATH $\bar{\sigma}$ --> <SPAN CLASS="MATH"><B><IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="img2255.png" ALT="$ \bar{\sigma}$"></B></SPAN> is the target stress, it should not be too far away from the actual maximum. <P> </LI> </UL> <P> and for TYPE=ORIENTATION design variables: <P> <UL> <LI>ALL-DISP: the displacements in all nodes. </LI> <LI>EIGENFREQUENCY: all eigenfrequencies (actually the eigenvalues, which are the square of the eigenfrequencies) and eigenmodes calculated in a previous *FREQUENCY step. </LI> <LI>GREEN: the Green functions calculated in a previous *GREEN step. </LI> <LI>MASS: mass of the total structure or of a subset if an element set is defined </LI> <LI>STRAIN ENERGY: internal energy of the total structure or of a subset if an element set is defined </LI> <LI>STRESS: the stresses in all nodes. </LI> </UL> <P> There is one parameter NAME which is compulsary for TYPE=COORDINATE design variables and not used for TYPE=ORIENTATION design variables. It is used for the sake of choosing design responses for the objective and/or constraints in an optimization. It should not be longer than 80 characters. <P> Exactly one *DESIGN RESPONSE keyword is required in a *SENSITIVITY step of type ORIENTATION. This keyword has to be followed by at least one design response function. <P> For a *SENSITIVITY step of type COORDINATE at least one *DESIGN RESPONSE keyword is required. This keyword has to be followed by exactly one design response function. <P> <P><P> <BR> <P> First line: <UL> <LI>*DESIGN RESPONSE. </LI> <LI>specify the parameter NAME and its value for TYPE=COORDINATE design variables. </LI> </UL> <P> Second line: <UL> <LI>an objective function </LI> <LI>an element or node set, if appropriate </LI> <LI><SPAN CLASS="MATH"><B><IMG WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img33.png" ALT="$ \rho$"></B></SPAN> for the Kreisselmeier-Steinhauser function (only for the coordinates as design variables and the stress as target) </LI> <LI><!-- MATH $\bar{\sigma}$ --> <SPAN CLASS="MATH"><B><IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="img2255.png" ALT="$ \bar{\sigma}$"></B></SPAN> for the Kreisselmeier-Steinhauser function (only for the coordinates as design variables and the stress as target) </LI> </UL> Repeat this line if needed. <P> The design response functions STRAIN ENERGY, MASS, ALL-DISP and STRESS require a *STATIC step before the *SENSITIVITY step, the design response function EIGENFREQUENCY requires a *FREQUENCY step immediately preceding the *SENSITIVITY step and the design response function GREEN requires a *GREEN step before the *SENSITIVITY step. Therefore, the {STRAIN ENERGY, MASS, ALL-DISP, STRESS} design response functions, the {EIGENFREQUENCY} design response function and the {GREEN} design response function are mutually exclusive within one and the same *SENSITIVITY step. <P> <PRE>
Example:
*DESIGN RESPONSE
ALL-DISP,N1
</PRE> <P> defines the square root of the sum of the square of the displacements in set N1 to be the design response function. <P> <P><P> <BR> Example files: sensitivity_I. <P> </body></html>