Document Zbl 1423.74730

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Methods Appl. Mech. Eng.</a> <a href="/?q=in%3A432802" title="Articles in this Issue">294, 359-383 (2015)</a>. </div> <div class="abstract">Summary: This paper addresses extended shape optimization problems where structural supports, i.e., Dirichlet boundaries and free boundaries are simultaneously optimized. Unlike traditional FEM, the weighted B-spline finite cell method (FCM) is applied as structural analysis tool and combined with the level-set function (LSF) to take into account Dirichlet boundary condition (DBC) automatically through penalization of the displacement field. The proposed shape optimization method achieves a comprehensive integration of fixed grid, B-spline shape function and level-set function. As both the structure and Dirichlet boundaries are described in the form of LSF, any modification of Dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables. Meanwhile, the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells. Stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of Dirichlet boundaries.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7055041">Cited in <strong>15</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74P05" title="MSC2020">74P05</a> </td> <td class="space"> Compliance or weight optimization in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49Q10" title="MSC2020">49Q10</a> </td> <td class="space"> Optimization of shapes other than minimal surfaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D07" title="MSC2020">65D07</a> </td> <td class="space"> Numerical computation using splines </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65N30" title="MSC2020">65N30</a> </td> <td class="space"> Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74S05" title="MSC2020">74S05</a> </td> <td class="space"> Finite element methods applied to problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74S10" title="MSC2020">74S10</a> </td> <td class="space"> Finite volume methods applied to problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C90" title="MSC2020">90C90</a> </td> <td class="space"> Applications of mathematical programming </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ashape+optimization+of+support+boundary">shape optimization of support boundary</a>; <a href="/?q=ut%3ADirichlet+boundary+condition">Dirichlet boundary condition</a>; <a href="/?q=ut%3Afinite+cell+method">finite cell method</a>; <a href="/?q=ut%3Aweighting+function">weighting function</a>; <a href="/?q=ut%3Afixed+grid">fixed grid</a>; <a href="/?q=ut%3Alevel-set+function">level-set function</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11037">BOSS-Quattro</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1423.74730" data-ciurl="/ci/07055041" data-biburl="/bibtex/07055041.bib" data-amsurl="/amsrefs/07055041.bib" data-xmlurl="/xml/07055041.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07055041.pdf" title="Zbl 1423.74730 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.cma.2015.06.012" aria-label="DOI for “Shape optimization of Dirichlet boundaries based on weighted B-spline finite cell method and level-set function”" title="10.1016/j.cma.2015.06.012">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Haslinger, J.; Makinen, R. 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