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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>Differences between Shape Algorithms</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">
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The user might choose between two shape optimization algorithms in 
<span class = "ph">Tosca Structure.shape</span>. 
The algorithms have different ways to find the solution and their differences will be discussed in this chapter.      
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<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-shape-optTaskDiff__tso-c-usr-shape-optTaskDiff-ctrl" id = "toc_rg" title = "">SHAPE_CONTROLLER</a></li><li><a href = "#tso-c-usr-shape-optTaskDiff__tso-c-usr-shape-optTaskDiff-sens" id = "toc_rg" title = "">SHAPE_SENS</a></li></ul>
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<p>The algorithm used for the controller-based shape optimization is based on an optimality criteria. 
Usually an optimality criteria is based on a set of rules that guide to a more optimal solution if certain prerequisites are fulfilled.
This leads to fast specialized algorithms typically usable for one class of problems with the drawback that they are not applicable if the prerequisites are not fulfilled. 
For more information about the optimality criteria used with the controller-based shape optimization, see 
<a class = "xref" href = "tso-c-usr-shape-optTaskCtrl.htm#tso-c-usr-shape-optTaskCtrl" title = "The theoretical background of the controller-based shape optimization approach is briefly discussed.">Controller-Based Shape Optimization</a>.</p>

<div class = "section" id = "tso-c-usr-shape-optTaskDiff__tso-c-usr-shape-optTaskDiff-ctrl"><h2 class = "title sectiontitle">SHAPE_CONTROLLER</h2>

<p>The controller-based shape optimization approach is very robust and reliable in removing stress
                peaks that lie in the design area. On the other hand, this includes that stress
                peaks outside the design area are in general not attackable.
                
                One drawback is that by default only stress-based design responses can be used.
                These can be used as objectives only and not even as constraints. <ul class = "ul">
                    <li class = "li">for standard problems (stress minimization and volume constraint)</li>
                    <li class = "li">just volume constraint feasible</li>
                    <li class = "li">only one constraint for each task</li>
                    <li class = "li">manufacturing restrictions are possible</li>
                    <li class = "li">just about 15 iterations necessary</li>
                    <li class = "li">homogenization of stress distribution by adding material at points of high
                        stress and removing material at points of low stress</li>
                </ul>
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<div class = "section" id = "tso-c-usr-shape-optTaskDiff__tso-c-usr-shape-optTaskDiff-sens"><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">SHAPE_SENS</h2>

<p>The sensitivity approach is much more flexible in terms of what should be optimized, that is,
                what design responses are usable in the objective function and in constraints.
                Typically, this higher flexibility is bought with longer run times. <span class = "ph">Tosca</span> specific disadvantages of the sensitivity-based approach compared to the
                controller-based approach cover the number of usable element types and the number of
                supported manufacturing constraints. <ul class = "ul">
                    <li class = "li">extended problems (combination of different design response)</li>
                    <li class = "li">up to 45 iterations, sometimes more</li>
                    <li class = "li">uses sensitivities (derivatives) of design responses</li>
                    <li class = "li">more types of design responses feasible (displacements, volume, reaction
                        forces etc.)</li>
                    <li class = "li">possible to define several constraints for one task</li>
                    <li class = "li">possible to solve problems with long range effects</li>
                    <li class = "li">manufacturing restrictions not implemented correctly yet</li>
                </ul>
            </p>
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