Document Zbl 0671.73065

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 0671.73065 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">×</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools & Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/0671.73065?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open — the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span> <a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:0671.73065" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span> </span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>  </span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>  </span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>  </span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>  </span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>  </span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>  </span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>  </span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>  </span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>  </span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>  </span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>  </span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>  </span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>  </span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>  </span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>  </span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>  </span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>  </span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a <span class="item">&</span> b </span><span> </span>logical and (default)</a></li> <li><a href="#"><span class="token">a <span class="item">|</span> b </span><span> </span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab   </span><span> </span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>  </span><span> </span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab c<span class="item">"</span></span><span> </span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab c<span class="item">)</span></span><span> </span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki & ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b & au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/bendsoe.martin-philip" title="Author Profile">Bendsøe, Martin Philip</a>; <a href="/authors/kikuchi.noboru" title="Author Profile">Kikuchi, Noboru</a></div> <h2 class="title"> <strong>Generating optimal topologies in structural design using a homogenization method.</strong> <i>(English)</i> <a class="label nowrap" href="/0671.73065">Zbl 0671.73065</a> </h2> <div class="source"> <a href="/serials/64" title="Journal Profile">Comput. Methods Appl. Mech. Eng.</a> <a href="/?q=in%3A170637" title="Articles in this Issue">71, No. 2, 197-224 (1988)</a>. </div> <div class="abstract">Summary: Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, isotropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A4098831">Cited in <strong>7</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A4098831">Cited in <strong>1031</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74P99" title="MSC2020">74P99</a> </td> <td class="space"> Optimization problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74E05" title="MSC2020">74E05</a> </td> <td class="space"> Inhomogeneity in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65K10" title="MSC2020">65K10</a> </td> <td class="space"> Numerical optimization and variational techniques </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74E30" title="MSC2020">74E30</a> </td> <td class="space"> Composite and mixture properties </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49M99" title="MSC2020">49M99</a> </td> <td class="space"> Numerical methods in optimal control </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AOptimal+shape+design">Optimal shape design</a>; <a href="/?q=ut%3Aoptimal+distribution+in+space">optimal distribution in space</a>; <a href="/?q=ut%3Aanisotropic+material">anisotropic material</a>; <a href="/?q=ut%3Ainfimum+of+periodically+distributed+small+holes">infimum of periodically distributed small holes</a>; <a href="/?q=ut%3Ahomogeneous%2C+isotropic+material">homogeneous, isotropic material</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 0671.73065" data-ciurl="/ci/04098831" data-biburl="/bibtex/04098831.bib" data-amsurl="/amsrefs/04098831.bib" data-xmlurl="/xml/04098831.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/04098831.pdf" title="Zbl 0671.73065 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/10.1016/0045-7825(88)90086-2" aria-label="DOI for “Generating optimal topologies in structural design using a homogenization method”" title="10.1016/0045-7825(88)90086-2">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://hdl.handle.net/2027.42/27079" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Haftka, R. T.; Gandhi, R. V., Structural shape optimization—A survey, Comput. Meths. Appl. Mech. Engrg., 57, 91-106 (1986) · <a href="/0578.73080" class="nowrap">Zbl 0578.73080</a></td> </tr><tr> <td>[2]</td> <td class="space">Pironneau, O., Optimal Shape Design for Elliptic Systems (1984), Springer: Springer Berlin · <a href="/0496.93029" class="nowrap">Zbl 0496.93029</a></td> </tr><tr> <td>[3]</td> <td class="space">Schanck, E., An optimization procedure for stress concentration by the finite element technique, Internat. J. Numer. Meths. Engrg., 14, 115-124 (1979) · <a href="/0394.73074" class="nowrap">Zbl 0394.73074</a></td> </tr><tr> <td>[4]</td> <td class="space">Kikuchi, N.; Chung, K. Y.; Torigaki, T.; Taylor, J. E., Adaptive finite element methods for shape optimization of linearly elastic structures, Comput. Meths. Appl. Mech. Engrg., 57, 67-91 (1986) · <a href="/0578.73081" class="nowrap">Zbl 0578.73081</a></td> </tr><tr> <td>[5]</td> <td class="space">Tvergaard, V., (Proceedings IUTAM Symposium on Optimization in Structural Design (1973), Springer: Springer Berlin), also in: · <a href="/0336.73020" class="nowrap">Zbl 0336.73020</a></td> </tr><tr> <td>[6]</td> <td class="space">Botkin, M. E.; Bennett, J. A., Shape optimization of three-dimensional folded-plate structures, AIAA J., 23-11, 1804-1810 (1986)</td> </tr><tr> <td>[7]</td> <td class="space">Braibant, V.; Fleury, C., Shape optimal design using $B- splines$, Comput. Meths. Appl. Mech. Engrg., 44, 247-267 (1984) · <a href="/0525.73104" class="nowrap">Zbl 0525.73104</a></td> </tr><tr> <td>[8]</td> <td class="space">Rodrigues, H., Shape optimal design of elastic bodies using a mixed variational formulation, Comput. Meths. Appl. Mech. Engrg., 69, 29-44 (1988) · <a href="/0629.73079" class="nowrap">Zbl 0629.73079</a></td> </tr><tr> <td>[9]</td> <td class="space">Haug, E. J.; Choi, K. K.; Komkov, V., Design Sensitivity Analysis of Structural Systems (1986), Academic Press: Academic Press New York · <a href="/0618.73106" class="nowrap">Zbl 0618.73106</a></td> </tr><tr> <td>[10]</td> <td class="space">Choi, K. K.; Haug, E. J., Shape design sensitivity analysis of elastic structures, J. Structural Mech., 11, 2, 231-269 (1983)</td> </tr><tr> <td>[11]</td> <td class="space">Choi, K. K.; Seong, K. K., A domain method for shape design sensitivity analysis of built-up structures, Comput. Meths. Appl. Mech. Engrg., 57, 1-16 (1986) · <a href="/0591.73112" class="nowrap">Zbl 0591.73112</a></td> </tr><tr> <td>[12]</td> <td class="space">Rousselet, B.; Haug, E. J., Design sensitivity analysis in structural mechanics, III. Effects of shape variation, J. Structural Mech., 10, 3, 273-310 (1983)</td> </tr><tr> <td>[13]</td> <td class="space">Zolesio, J. P., The material derivative (or speed) method for shape optimization, (Haug, E. J.; Cea, J., Optimization of Distributed Parameter Structures (1981), Sijthoff-Noordhoff, Alphen aan den Rijn: Sijthoff-Noordhoff, Alphen aan den Rijn The Netherlands), 1152-1194</td> </tr><tr> <td>[14]</td> <td class="space">Simon, J., Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim., 2, 649-687 (1980) · <a href="/0471.35077" class="nowrap">Zbl 0471.35077</a></td> </tr><tr> <td>[15]</td> <td class="space">Haber, R. B., A new variational approach to structural shape design sensitivity analysis, (Mota Soares, C. A., Computer Aided Optimal Design: Structural and Mechanical Systems (1987), Springer: Springer Berlin), 573-588</td> </tr><tr> <td>[16]</td> <td class="space">Chenais, D., On the existence of a solution in a domain identification problem, J. Math. Anal. Appl., 52, 2, 189-219 (1975) · <a href="/0317.49005" class="nowrap">Zbl 0317.49005</a></td> </tr><tr> <td>[17]</td> <td class="space">Cheng, K. T.; Olhoff, N., An Investigation Concerning Optimal Design of Solid Elastic Plates, Internat. J. Solids and Structures, 16, 3, 305-323 (1981) · <a href="/0457.73079" class="nowrap">Zbl 0457.73079</a></td> </tr><tr> <td>[18]</td> <td class="space">Cheng, K. T.; Olhoff, N., Regularized Formulation for Optimal Design of Axisymmetric Plates, Internat. J. Solids and Structures, 18, 2, 153-170 (1982) · <a href="/0468.73106" class="nowrap">Zbl 0468.73106</a></td> </tr><tr> <td>[19]</td> <td class="space">Cea, J.; Gioan, A.; Michel, J., Quelques Resultat sur l’identification de domaines (1973), Calcolo III-IV</td> </tr><tr> <td>[20]</td> <td class="space">Tartar, L., Estimation de coefficients homogeneises, (Lecture Notes in Mathematics, 704 (1977), Springer: Springer Berlin), 364-373 · <a href="/0443.35061" class="nowrap">Zbl 0443.35061</a></td> </tr><tr> <td>[21]</td> <td class="space">Bendsøe, M. P., Generalized plate models and optimal design, (Eriksen, J. L.; Kinderlehrer, D.; Kohn, R.; Lions, J.-L., Homogenization and effect moduli of materials and media, The IMA Volumes in Mathematics and Its Applications (1986), Springer: Springer Berlin), 1-26 · <a href="/1007.90083" class="nowrap">Zbl 1007.90083</a></td> </tr><tr> <td>[22]</td> <td class="space">Gibiansky, L. V.; Cherkaev, A. V., Design of composite plates of extremal rigidity, (Rept. No. 914 (1984), A.F. Ioffe Physical Technical Institute, Academy of Sciences of the USSR: A.F. Ioffe Physical Technical Institute, Academy of Sciences of the USSR Leningrad), (in Russian) · <a href="/0920.35159" class="nowrap">Zbl 0920.35159</a></td> </tr><tr> <td>[23]</td> <td class="space">Lurie, K. A.; Fedorov, A. V.; Cherkaev, A. V., Regularization of optimal design problems for bars and plates, J. Optim. Theory Appl., 37, 4, 523-543 (1982), Parts I and II · <a href="/0464.73110" class="nowrap">Zbl 0464.73110</a></td> </tr><tr> <td>[24]</td> <td class="space">Rozvany, G. I.N.; Ong, T. G.; Szeto, W. T.; Olhoff, N.; Bendsøe, M. P., Least-weight design of perforated plates, Internat. J. Solids and Structures, 23, 537-550 (1987), (Part II) · <a href="/0606.73106" class="nowrap">Zbl 0606.73106</a></td> </tr><tr> <td>[25]</td> <td class="space">Goodman, J.; Kohn, R. V.; Reyna, L., Numerical study of a relaxed variational problem from optimal design, Comput. Meths. Appl. Mech. Engrg., 57, 107-127 (1986) · <a href="/0591.73119" class="nowrap">Zbl 0591.73119</a></td> </tr><tr> <td>[26]</td> <td class="space">Kohn, R. V.; Strang, G., Optimal design in elasticity and plasticity, Internat. J. Numer. Meths. Engrg., 22, 183-188 (1986) · <a href="/0593.73091" class="nowrap">Zbl 0593.73091</a></td> </tr><tr> <td>[27]</td> <td class="space">Zochowski, A., The design of a two-dimensional domain, Mech. Struct. Mach., 16 (1988), (to appear)</td> </tr><tr> <td>[28]</td> <td class="space">Bensousson, A.; Lions, J.-L.; Papanicolaou, G., Asymptotic Analysis for Periodic Structures (1978), North-Holland: North-Holland Amsterdam · <a href="/0404.35001" class="nowrap">Zbl 0404.35001</a></td> </tr><tr> <td>[29]</td> <td class="space">Duvaut, G., Analyse fonctionelle et mecanique des milieux continus. Application a l’etude des materiaux composites elastiques a structure periodique-homogeneisation, (Proceedings 14th IUTAM Congress. Proceedings 14th IUTAM Congress, Delft, The Netherlands, 1976 (1976), North-Holland: North-Holland Amsterdam), 119-132 · <a href="/0373.73002" class="nowrap">Zbl 0373.73002</a></td> </tr><tr> <td>[30]</td> <td class="space">Sanchez-Palencia, E., Non-Homogeneous Media and Vibration Theory, (Lecture Notes in Physics, 127 (1980), Springer: Springer Berlin) · <a href="/0432.70002" class="nowrap">Zbl 0432.70002</a></td> </tr><tr> <td>[31]</td> <td class="space">Murat, F.; Tartar, L., Calcul des variations et homogeneisation, (Les Methodes de l’Homogeneisation: Theorie et Applications en Physique, Coll. de la Dir. des Etudes et Recherches de Electricite de France. Les Methodes de l’Homogeneisation: Theorie et Applications en Physique, Coll. de la Dir. des Etudes et Recherches de Electricite de France, Eyrolles, Paris (1985)), 319-370</td> </tr><tr> <td>[32]</td> <td class="space">Avellaneda, M., Optimal bounds and microgeometries for elastic two-phase composites, SIAM J. Appl. Math., 47, 1216-1228 (1987) · <a href="/0632.73079" class="nowrap">Zbl 0632.73079</a></td> </tr><tr> <td>[33]</td> <td class="space">Francfort, G. A.; Murat, F., Homogenization and optimal bounds in linear elasticity, Arch. Rat. Mech. Anal., 94, 307-334 (1986) · <a href="/0604.73013" class="nowrap">Zbl 0604.73013</a></td> </tr><tr> <td>[34]</td> <td class="space">Kohn, R. V.; Milton, G. W., On bounding the effective conductivity of anisotropic composites, (Eriksen, J. L.; Kinderlehrer, D.; Kohn, R.; Lions, J.-L., Homogenization and Effective Moduli of Materials and Media. Homogenization and Effective Moduli of Materials and Media, The IMA Volumes in Mathematics and Its Applications, 1 (1986), Springer: Springer Berlin), 97-126 · <a href="/0631.73012" class="nowrap">Zbl 0631.73012</a></td> </tr><tr> <td>[35]</td> <td class="space">Lurie, K. A.; Cherkaev, A. V., Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion, (Proc. Roy. Soc. Edinburgh, 99A (1984)), 71-78 · <a href="/0564.73079" class="nowrap">Zbl 0564.73079</a></td> </tr><tr> <td>[36]</td> <td class="space">Kohn, R. V.; Vogelius, M., A new model for thin plates with rapidly varying thickness, Internat. J. Solids and Structures, 29, 4, 333-350 (1984) · <a href="/0532.73055" class="nowrap">Zbl 0532.73055</a></td> </tr><tr> <td>[37]</td> <td class="space">Kohn, R. V.; Vogelius, M., A new model for thin plates with rapidly varying thickness II: A convergence proof, Quart. Appl. Math., 43, 1-22 (1985) · <a href="/0565.73046" class="nowrap">Zbl 0565.73046</a></td> </tr><tr> <td>[38]</td> <td class="space">Kohn, R. V.; Vogelius, M., A new model for thin plates with rapidly varying thickness III: Comparison of different scalings, Quart. Appl. Math., 44, 35-48 (1986) · <a href="/0605.73048" class="nowrap">Zbl 0605.73048</a></td> </tr><tr> <td>[39]</td> <td class="space">Kohn, R. V.; Strang, G., Optimal design and relaxation of variational problems, Comm. Pure Appl. Math., 39, 353-377 (1986), (Part III) · <a href="/0694.49004" class="nowrap">Zbl 0694.49004</a></td> </tr><tr> <td>[40]</td> <td class="space">Bonnetier, E.; Vogelius, M., Relaxation of a compliance functional for a plate optimization problem (1986), University of Maryland: University of Maryland College Park, MD, Preprint · <a href="/0631.73079" class="nowrap">Zbl 0631.73079</a></td> </tr><tr> <td>[41]</td> <td class="space">Bendsøe, M. P., On obtaining a solution to optimization problems for solid, elastic plates by restriction of the design space, J. Structural Mech., 11, 501-521 (1983)</td> </tr><tr> <td>[42]</td> <td class="space">Francu, J., Homogenization of linear elasticity equations, Apl. Mat., 27, 96-117 (1982) · <a href="/0489.73019" class="nowrap">Zbl 0489.73019</a></td> </tr><tr> <td>[43]</td> <td class="space">Josif’jan, G. A.; Oleinik, O. A.; Panasenko, G. P., Asymptotic expansion of a solution of the system of elasticity theory with periodic rapidly oscillating coefficients, Soviet Math. Dokl., 26, 290-294 (1982) · <a href="/0542.35011" class="nowrap">Zbl 0542.35011</a></td> </tr><tr> <td>[44]</td> <td class="space">Bourgat, J. F., Numerical Experiments of the Homogenization Method for Operators with Periodic Coefficients, (Lecture Note in Mathematics, 704 (1977), Springer: Springer Berlin), 330-356 · <a href="/0405.65062" class="nowrap">Zbl 0405.65062</a></td> </tr><tr> <td>[45]</td> <td class="space">Guedes, J. M., Homogenization in linear elasticity theory (1987), University of Michigan: University of Michigan Ann Arbor, MI, Preprint</td> </tr><tr> <td>[46]</td> <td class="space">Cioranescu, D.; Saint Jean Paulin, J., Homogenization in open sets with holes, J. Math. Anal. Appl., 71, 590-607 (1979) · <a href="/0427.35073" class="nowrap">Zbl 0427.35073</a></td> </tr><tr> <td>[47]</td> <td class="space">Olhoff, N.; Taylor, J. E., On structural optimization, J. Appl. Mech., 50, 1134-1151 (1983) · <a href="/0526.73090" class="nowrap">Zbl 0526.73090</a></td> </tr><tr> <td>[48]</td> <td class="space">Kristensen, E. S.; Madsen, N. F., On the optimum shape of fillets in plates subjected to multiple in-plane loading cases, Internat. J. Numer. Meths. Engrg., 10, 1007-1009 (1976) · <a href="/0332.73061" class="nowrap">Zbl 0332.73061</a></td> </tr><tr> <td>[49]</td> <td class="space">Pedersen, P.; Laursen, C. L., Design for minimum stress concentration by finite elements and linear programming, J. Structural Mech., 10, 4, 375-391 (1983)</td> </tr><tr> <td>[50]</td> <td class="space">C.A.M. Soares, H.C. Rodrigues, L.M.O. Faria and E.J. Haug, Optimization of the geometry of shafts using boundary elements, ASME J. Mechanics, Transmissions and Automation in Design 106(2) 199-203.; C.A.M. Soares, H.C. Rodrigues, L.M.O. Faria and E.J. Haug, Optimization of the geometry of shafts using boundary elements, ASME J. Mechanics, Transmissions and Automation in Design 106(2) 199-203.</td> </tr><tr> <td>[51]</td> <td class="space">Rossow, M. P.; Taylor, J. E., A finite element method for the optimal design of variable thickness sheets, AIAA J., 11, 1566-1569 (1973)</td> </tr><tr> <td>[52]</td> <td class="space">Rozvany, G. I.N., Structural layout theory — the present state of knowledge, (Atrek, E.; Gallagher, R. H.; Ragsdell, K. M.; Zienkiewicz, O. C., Directions in Optimum Structural Design (1984), Wiley: Wiley Chichester, U.K), Ch. 7 · <a href="/0356.76048" class="nowrap">Zbl 0356.76048</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

CINXE.COM

Document Zbl 0671.73065 - zbMATH Open