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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>Guidelines for Optimization of Structures with Nonlinear Behavior</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 presents guidelines to build a more robust optimization setup for topology
            optimization. In addition, these guidelines can help you address issues during the
            optimization run. </span>

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<p>This page discusses: </p><ul><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-VolMassConstr" id = "toc_rg" title = "">Volume/Mass Constraint in the Model</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-VolMassObj" id = "toc_rg" title = "">Minimize Volume/Mass as Objective</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-GeneralGuidelines" id = "toc_rg" title = "">Topology Optimization in the Context of Nonlinear <span class = "ph">Structural Analysis</span>
</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-ManuConstr" id = "toc_rg" title = "">Manufacturing Constraints in the Model</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-Thermal" id = "toc_rg" title = "">Thermal Expansion in the Model</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-Contact" id = "toc_rg" title = "">Contact in the Model</a></li><li><a href = "#tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-StressObj" id = "toc_rg" title = "">Minimize Stress as Objective</a></li></ul>
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-VolMassConstr"><h2 class = "title sectiontitle">Volume/Mass Constraint in the Model</h2>

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<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/NonLinTopOpt_VolumeMass_Constr.png"/><br/></td>
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<p> In cases where volume/mass constraints are in the model, it is important to verify if the
                corresponding constraint values are feasible with respect to the given FE-mesh size.
                For example, if we consider a square plate that is discretized by 9 square elements
                and use a relative volume constraint of 1/9, then we cannot expect a black and white
                solution where some corners of the structure are connected. Set the
                    <code class = "ph codeph">DENSITY_INITIAL = 0.5</code> in cases where very low volume
                constraints (for example 0.05) are used to stabilize the optimization. If the volume
                constraint is not satisfied or there are unconnected regions in the resulting
                optimized structure, follow the given guidelines. Finer meshing of the structure,
                that is, increasing the number of elements appropriate for the volume constraint,
                can overcome these problems. </p>  
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-VolMassObj"><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">Minimize Volume/Mass as Objective</h2>


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<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/NonLinTopOpt_VolumeMass_Obj.png"/><br/></td>
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<p> In cases where volume/mass is used as the objective function, follow the procedure recommendation
    to avoid convergence issues. Check the displacements boundary conditions with
    respect to the third direction if 3D models are used to simulate 2D structures.
    Also, look for unwanted deformations and out of plane buckling. In cases where the
    model uses displacement constraints, define these constraints at load application
    and freeze regions around the displacement constraints. If the above setup does not help
    to satisfy the constraints, then impose additional constraints on the structural
    stiffness to stabilize the optimization. This is required to avoid structures acting
    like compliant mechanisms. If solver convergence issues appear during the
    optimization procedure, set <code class = "ph codeph">DENSITY_LOWER = 0.01</code>. This can help to
    reach convergence, but it aids in the creation of mechanism designs (because it
    increases the unphysical stiffness of holes) which are not favored in most cases. </p>
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-GeneralGuidelines"><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">Topology Optimization in the Context of Nonlinear <span class = "ph">Structural Analysis</span>
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<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/NonLinTopOpt_GeneralGuideLines.png"/><br/></td>
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<p> The above setup is considered to be stable for running topology optimization of structures with
    nonlinear behavior. Even though the settings consume more time for convergence, the
    optimization can converge in the first attempt. The recommendation for the settings
    is: small initial time increment, <code class = "ph codeph">DENSITY_MOVE = 0.1</code>,
    <code class = "ph codeph">DENSITY_UPDATE = CONSERVATIVE</code>, <code class = "ph codeph">DENSITY_INITIAL =
    1.0</code>. If there are still convergence issues on the solver side, check in
    case of <span class = "ph">Abaqus</span> for the above mentioned warnings in the *<code class = "ph codeph">.msg</code> and
    *<code class = "ph codeph">.dat</code> files. If those warnings are found, activate the soft delete
    procedure by adding <code class = "ph codeph">SOFT_DELETE_METHOD = AGGRESSIVE, 0.1</code>,
    <code class = "ph codeph">SOFT_DELETE = &lt;element group&gt;, 0.0</code>. This option offers the
    possibility of removing soft elements that could be distorted during the
    optimization process. Another alternative would be to change
    <code class = "ph codeph">DENSITY_LOWER=0.01</code>. One of the trivial methods of stabilizing a
    nonlinear optimization task is by increasing the frozen domain. If convergence
    issues retain, impose additional constraints on displacement or structural stiffness
    to further stabilize the optimization procedure.</p>
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-ManuConstr"><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">Manufacturing Constraints in the Model</h2>

<p> In cases where the model contains
          manufacturing restrictions:<ul class = "ul">
          <li class = "li"> It is crucial to set the correct origin of the co system and the axis corresponding
            to the restrictions in the parameter file.</li>
          <li class = "li"> In the case of nonlinear problems, if the optimization ends in the solver convergence
            issues, the recommendation to remove the manufacturing constraints and solve the
            convergence issues. After obtaining a converged result, impose the restrictions one
            after the other. </li>
          </ul></p>
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-Thermal"><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">Thermal Expansion in the Model</h2>

<p> For thermal expansion problems, the
          recommendation is to use the <code class = "ph codeph">ENERGY_STIFF_MEASURE</code> design response instead
          of the <code class = "ph codeph">STRAIN_ENERGY</code> design response.</p>
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-Contact"><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">Contact in the Model</h2>

<p> For highly nonlinear contact problems,
          the automatic stabilization technique offered by the <span class = "ph">Abaqus</span> solver is the recommendation. This option helps automatically control rigid body motion
          before the contact closure restrains such motion, which can be activated by
          <code class = "ph codeph">*CONTACT CONTROLS, STABILIZE</code> command. By default, the auto-frozen option
          is activated in <span class = "ph">Tosca Structure</span>, which affects regions with contact, load, and displacement boundary conditions. Hence,
          it is important to deactivate the Auto frozen option <code class = "ph codeph">AUTO_FROZEN=OFF</code> to
          acquire the contact regions as design domain in cases where it is required. Note, this
          setting can lead to solver convergence issues.</p>
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<div class = "section" id = "tso-c-user-TopOpt-NonLin-Guidelines__tso-c-user-TopOpt-NonLin-Guidelines-StressObj"><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">Minimize Stress as Objective</h2>

<p> In cases where stress design
          responses are used to define the objective function, the recommendation is to give
          reference values for the corresponding design responses. If stress design responses are
          used in the model, the recommendation is to use sensitivities calculated by the <span class = "ph">Abaqus</span> solver.</p>
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