<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html
  SYSTEM "about:legacy-compat">
<html xmlns:mml = "http://www.w3.org/1998/Math/MathML" lang = "en"><head><meta charset = "UTF-8"/><meta name = "copyright" content = "(C) Copyright 2020"/><meta name = "DC.rights.owner" content = "(C) Copyright 2020"/><meta name = "DC.type" content = "concept"/><meta name = "abstract" content = "This section reviews useful options and possibilities regarding nonlinearities in topology optimization."/><meta name = "description" content = "This section reviews useful options and possibilities regarding nonlinearities in topology optimization."/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-c-user-TopOpt-NonLin-ReviewOptions"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Review of Available Options and Possibilities</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script></head><body onLoad = "highlightSearchTerms();" id = "tso-c-user-TopOpt-NonLin-ReviewOptions">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Review of Available Options and Possibilities</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">This section reviews useful options and possibilities regarding nonlinearities in
               topology optimization.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-General" id = "toc_rg" title = "">General Information for Topology Optimization</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca" id = "toc_rg" title = ""><span class = "ph">Tosca Structure</span> Options</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Solver" id = "toc_rg" title = "">Solver Settings: <span class = "ph">Abaqus</span></a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">

<div class = "section" id = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-General"><h2 class = "title sectiontitle">General Information for Topology Optimization</h2>

<ul class = "ul">
<li class = "li"> Since the design variables for topology optimization are the elemental pseudo densities, the
                         elemental stiffness is changes during the optimization process. This can
                         lead to larger deformations and strains compared to the initial simulation.
                         Therefore, the material laws need to be defined for all material states,
                         especially plasticity laws. Continuous material laws such as Johnson-Cook
                         are preferred for nonlinear optimizations since they are defined for all
                         strain values.</li>
<li class = "li"> As the structure softens during the optimization, the recommendation is to adapt applied loads
                         in such a manner that they are reasonable for the final, softer structure
                         with less material, for example 20% of the original material. Otherwise,
                         too much plastic deformation occurs.</li>
<li class = "li"> If possible, convert loading to prescribed displacements to improve the robustness of the optimization.</li>
</ul>
</div>

  
<div class = "section" id = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca"><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"><span class = "ph">Tosca Structure</span> Options</h2>

<p> In <span class = "ph">Tosca Structure</span>, all the following described options are set in the
                    <code class = "ph codeph">OPT_PARAM</code> block of the <code class = "ph codeph">*.par</code> file. </p>
<table class = "table"><caption/><colgroup><col style = "width:50%"/><col style = "width:50%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"> Option: </th>
<th class = "entry" id = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> Description: </th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"> <code class = "ph codeph">DENSITY_MOVE</code></td>
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> This option decides the maximum possible change of the pseudo density values
                                        within each optimization iteration. Smaller values of this
                                        parameter help to overcome convergence issues. But at the
                                        same time, the convergence rate can be slower when compared
                                        to the default settings. The default value is
                                        <code class = "ph codeph">DENSITY_MOVE=0.25</code>. In cases where it is
                                        observed that either the objective function or some of the
                                        constraints are oscillating, the recommendation is to set
                                        <code class = "ph codeph">DENSITY_MOVE=0.1</code>. </td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"> <code class = "ph codeph">DENSITY_UPDATE</code> </td>
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> This option affects the behavior of CSA (Algorithm based on Convex Separable
                                        Approximations). The two available schemes of density update
                                        are <code class = "ph codeph">CONSERVATIVE</code> and
                                        <code class = "ph codeph">NORMAL</code>. Conservative update method is
                                        considered to be more stable. The default is
                                        <code class = "ph codeph">DENSITY_UPDATE=NORMAL</code>. In cases where it is
                                        observed that either the objective function or some of the
                                        constraints are oscillating, the recommendation is
                                        <code class = "ph codeph">DENSITY_UPDATE=CONSERVATIVE</code>. </td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"> <code class = "ph codeph">DENSITY_INITIAL</code> </td>
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> Material properties of design elements are scaled (solid and void properties
                                        are interpolated) based on the pseudo density values.
                                        Different material interpolation schemes like
                                        <code class = "ph codeph">SIMP</code> and <code class = "ph codeph">RAMP</code> are
                                        available in <span class = "ph">Tosca Structure</span>. The initial pseudo density values can be set by the
                                        <code class = "ph codeph">DENSITY_INITIAL</code> option. If one of the
                                        constraints is based on volume design response, then the
                                        initial density is set equal to the value of the volume
                                        constraint by default. In all other cases, the initial
                                        density value is set equal to 0.5. Note, to compare the
                                        DRESP value of <span class = "ph">Tosca Structure</span> with the solver results set <code class = "ph codeph">DENSITY_INITIAL =
                                        1</code> and use the DRESP value from design cycle 0. </td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"><code class = "ph codeph">DENSITY_LOWER</code></td>
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> In topology optimization, the voids are not created by deleting the finite
                                        elements from the mesh, but are simulated scaling the
                                        stiffness of the design elements to a very low value. Zero
                                        elemental stiffness would lead to the loss of positive
                                        definiteness of the global structural stiffness matrix. The
                                        corresponding system of equations would not be solved.
                                        Hence, a minimum value of pseudo density is used within
                                        topology optimization. The default value is
                                        <code class = "ph codeph">DENSITY_LOWER=0.001</code> but can be modified by
                                        the user. </td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"><code class = "ph codeph">SOFT_DELETE_METHOD</code></td>
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> In a topology optimization process, the structure consists of hard (filled)
                                        and soft (void) elements. The soft elements have a
                                        negligible influence on the stiffness of the resulting
                                        structure but they are still relevant for the solution of
                                        the system of equilibrium equations. The soft delete option
                                        activates a procedure that looks for elements that could be
                                        potentially distorted during the optimization procedure
                                        based on the user-defined criteria and deletes them from the
                                        finite element mesh. The deleted elements are reactivated if
                                        required, in case that the force flow changes during the
                                        optimization. Note, this procedure is useful to stabilize
                                        the optimization in the context of nonlinear structural
                                        analysis and helps to overcome solver instabilities. By
                                        default, it is not activated. </td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__1"><code class = "ph codeph">AUTO_FROZEN</code></td>
<td class = "entry" headers = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Tosca__entry__2"> This option is used to keep elements with loaded nodes and boundary
                                        conditions from being optimized. There are four settings
                                        available: <code class = "ph codeph">LOAD</code>, <code class = "ph codeph">SPC</code>,
                                        <code class = "ph codeph">BOTH</code>, and <code class = "ph codeph">OFF</code>.
                                        <code class = "ph codeph">LOAD</code> and <code class = "ph codeph">SPC</code> constrain
                                        elements with loaded nodes or boundary conditions,
                                        respectively, from being optimized, while
                                        <code class = "ph codeph">BOTH</code> simultaneously freezes all elements
                                        with either load and boundary condition. The default setting
                                        is <code class = "ph codeph">AUTO_FROZEN=LOAD</code>. </td>
</tr>
</tbody></table>
</div>


<div class = "section" id = "tso-c-user-TopOpt-NonLin-ReviewOptions__tso-c-user-TopOpt-NonLin-ReviewOptions-Solver"><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">Solver Settings: <span class = "ph">Abaqus</span></h2> 

The <span class = "ph">Abaqus</span> solver gives the possibility to define
settings to improve the convergence for nonlinear
models. See <a class = "xref" href = "tso-c-usr-solver-abaqus-nonlinguide.htm" title = "Features that are supported by Tosca are considered within this section.">Guide for Nonlinear Models</a>. </div>

</div>


</td></tr></table><script type = "text/javascript" src = "../DSDocUI_Bottom34.js">/* */</script></body>
</html>
