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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>Controller-Based Bead Optimization</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">The optimality criteria used in the controller-based bead
optimization method is described in this chapter.</span>

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<p>The controller-based bead optimization (BEAD_CONTROLLER) is based upon a special bending hypothesis developed at IPEK at Karlsruhe University. 
It determines the orientation of the maximum bending stress or Differential Stress Tensor (DST) for each point in the design domain. 
The Differential Stress Tensor (DST) is the difference tensor between the stress tensors at the top and at the bottom shell layer. 
The emerging bead flanks are oriented parallel to the DST eigenvectors. 
Special filters are used to generate these beads along the bending trajectories.</p>  
  
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<p> This method has the following advantages:</p>
<ul class = "ul">
<li class = "li">Solver-independent and sensitivity-independent</li>
<li class = "li">mesh-independent</li>
<li class = "li">clear results</li>
<li class = "li">restrictions on the bead form can be included</li>
</ul>

<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"> Bead optimization does NOT always give
better mechanical behavior. The design problem must be suited for bead
optimization, that is:<p><ul class = "ul"><li class = "li">Design area should be mainly in bending or a bending mode. The bead algorithm
will then increase the moment of inertia which leads to a greater stiffness
or eigenfrequency.</li>
<li class = "li">Design area should NOT be in a membrane stress state (see also <a class = "xref" href = "tso-c-usr-beadParamCtrl-beadPenaltyCond.htm#tso-c-usr-beadParamCtrl-beadPenaltyCond" title = "Areas with either low stresses or low bending/membrane stress ratios will be disregarded from the optimization.">Penalty Conditions (BEAD_MIN_STRESS and BEAD_MAX_MEMBRANE)</a>). A bead might in
this case make the structure softer.</li></ul></p></span></td></tr></table>
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