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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>General Information about Combined Terms</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">Combination of values derived from model properties or analysis
results could be done getting the maximum or minimum value within a number
of <span class = "ph">load cases</span>
or a number of group entities or creating response combinations like
relative values, differences or mean values. </span>

</p>

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<div class = "body conbody">
<p>In <span class = "ph">Tosca Structure</span>
combination of values can be performed in several ways:</p>
<ol class = "ol">
<li class = "li">The simplest way to combine terms is using a weighted sum for the objective
function, or using a <code class = "ph codeph">MINMAX</code> formulation with the different
weighting of the design responses. See <a class = "xref" href = "tso-m-usr-terms-objfunc-sb.htm" 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.">Objective Function</a> for more
information.</li>
<li class = "li">Combining terms might also be done using an operator - a special design
response (<code class = "ph codeph">DRESP</code>)
of the <code class = "ph codeph">DEF_TYPE = OPER</code>. This should only be done with
caution to avoid meaningless optimization tasks. You must also be aware
of the difference in the way sensitivity and controller-based algorithms
handle the operator.  Note that for weighted sums you might as well use
the formulations used in <a class = "xref" href = "tso-m-usr-terms-objfunc-sb.htm" 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.">Objective Function</a>.</li>
<li class = "li">Values of one type from several <span class = "ph">load cases</span>
can be combined directly using <span class = "ph">load case</span>
selection and weighting for the design response (command <code class = "ph codeph">DRESP</code>,
item <code class = "ph codeph">LC_SET</code>).</li>
<li class = "li"> Values of one type at several locations (nodes, elements) in the
model can in general be combined directly using group operations for
the design response (<code class = "ph codeph">DRESP</code>
item <code class = "ph codeph">GROUP_OPER</code>).</li>
</ol>
<p>If several of these possibilities to combine values are applied, <span class = "ph">Tosca Structure</span>
operates as follows: </p>
<ol class = "ol">
<li class = "li">The value over all entities of the group for one <span class = "ph">load case</span>
is calculated. This means that a loop over all entities of the group
is executed and then the value of the inner loop is calculated with the
operator specified in the <code class = "ph codeph">GROUP_OPER</code> parameter. If the operator
is not defined by the user, a default one will be used.</li>
<li class = "li">This value (already combined for the group entities) is calculated
for the different <span class = "ph">load cases</span>
specified in the <code class = "ph codeph">LC_SET</code> parameter. If no <code class = "ph codeph">LC_SET</code>
parameter is present, then all <span class = "ph">load cases</span>
and substeps (frequencies) will be used to determine the value.</li>
<li class = "li">Combination of design responses by operators is applied next.</li>
<li class = "li">Finally, the combination of design responses in the objective function
is applied.</li>
</ol>
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