<!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN"> <html> <head> <title>Arithmetic 1D</title> <meta http-equiv="content-type" content="text/html; charset=windows-1252"> <meta name="generator" content="RoboHelp by eHelp Corporation www.ehelp.com"> <link rel="stylesheet" href="../default_ns.css"><script type="text/javascript" language="JavaScript" title="WebHelpSplitCss"> <!-- if (navigator.appName !="Netscape") { document.write("<link rel='stylesheet' href='../default.css'>");} //--> </script> <style type="text/css"> <!-- ul.whs1 { list-style:disc; } p.whs2 { background-color:Transparent; color:#000000; font-weight:bold; } p.whs3 { margin-left:40px; } img_whs4 { border:none; width:332px; height:238px; float:none; border-style:none; } img_whs5 { border:none; width:309px; height:316px; float:none; border-style:none; } p.whs6 { margin-left:0px; } img_whs7 { border:none; width:332px; height:212px; float:none; border-style:none; } img_whs8 { border:none; width:267px; height:339px; float:none; 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addButton("show",BTN_TEXT,"Show","","","","",0,0,"","",""); } if (window.writeBtnStyle) writeBtnStyle(); if (window.writeIntopicBar) writeIntopicBar(1); if (window.setRelStartPage) { setRelStartPage("../smesh.htm"); autoSync(1); sendSyncInfo(); sendAveInfoOut(); } } else if (window.gbIE4) document.location.reload(); //--> </script> <h1>1D Meshing Hypotheses</h1> <ul type="disc" class="whs1"> <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ " class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#arithmetic_1D"><span style="font-weight: bold;"><B>Arithmetic 1D</B></span></a></p></li> <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ " class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Average_length"><span style="font-weight: bold;"><B>Average Length</B></span></a></p></li> <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ " class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#deflection_1D"><span style="font-weight: bold;"><B>Deflection 1D </B></span></a></p></li> <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ " class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Number_of_elements"><span style="font-weight: bold;"><B>Number of segments</B></span></a></p></li> <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ " class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#start_and_end_length"><span style="font-weight: bold;"><B>Start and end length</B></span></a></p></li> <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ " class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#automatic_length"><span style="font-weight: bold;"><B>Automatic Length</B></span></a></p></li> </ul> <h3><a name=arithmetic_1D>Arithmetic 1D hypothesis</a></h3> <p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows to split edges into segments with a length that changes in arithmetic progression (Lk = Lk-1 + d) beginning from a given starting length and up to a given end length.</p> <p> </p> <p class="whs3"><img src="../pics/a-arithmetic1d.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> <img src="../pics/b-ithmetic1d.png" x-maintain-ratio="TRUE" width="309px" height="316px" border="0" class="img_whs5"></p> <p> </p> <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining Arithmetic 1D hypothesis</a> operation. </p> <h3><a name=deflection_1D>Deflection 1D hypothesis</a></h3> <p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can be applied for meshing curvilinear edges composing your geometrical object. It uses only one parameter: the value of deflection. </p> <p>A geometrical edge is divided into equal segments. The maximum distance between a point on the edge within a segment and the line connecting the ends of the segment should not exceed the specified value of deflection . Then mesh nodes are constructed at end segment locations and 1D mesh elements are constructed on segments.</p> <p> </p> <p class="whs3"><img src="../pics/a-deflection1d.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> <img src="../pics/b-flection1d.png" x-maintain-ratio="TRUE" width="267px" height="339px" border="0" class="img_whs8"></p> <p> </p> <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining Deflection 1D hypothesis</a> operation. </p> <p> </p> <p class="whs9"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs10"></p> <h3><a name=Average_length>Average Length hypothesis</a></h3> <p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can be applied for meshing of edges composing your geometrical object. Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span> of segments, which will split these edges. The points on the edges generated by these segments will represent nodes of your mesh. Later these nodes will be used for meshing of the faces abutting to these edges.</p> <p> </p> <p class="whs3"><img src="../pics/a-averagelength.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> <img src="../pics/b-erage_length.png" x-maintain-ratio="TRUE" width="252px" height="243px" border="0" class="img_whs11"></p> <p> </p> <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining Average Length hypothesis</a> operation. </p> <p> </p> <p class="whs12"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs13"></p> <h3><a name=Number_of_elements>Number of segments hypothesis</a> </h3> <p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis can be applied for meshing of edges composing your geometrical object. Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span> of segments, which will split these edges. In other words your edges will be split into a definite number of segments with approximately the same length. The points on the edges generated by these segments will represent nodes of your mesh. Later these nodes will be used for meshing of the faces abutting to these edges.</p> <p> </p> <p class="whs6">You can set the type of distribution for this hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span> dialog bog : </p> <p class="whs6"> </p> <p class="whs6"><span style="font-weight: bold;"><B>Equidistant Distribution</B></span> - all segments will have the same length, you define only the <span style="font-weight: bold;"><B>Number of Segments</B></span>.</p> <p class="whs6"> </p> <p class="whs3"><img src="../pics/a-nbsegments1.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> <img src="../pics/b-mberofsegments.png" x-maintain-ratio="TRUE" width="395px" height="387px" border="0" class="img_whs14"></p> <p> </p> <p class="whs9">Scale Distribution - <span style="font-weight: normal;">each next segment differs from the previous according to the formula:</span> A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i </span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is a</span> Scale Factor. </p> <p class="whs12"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs15">\</p> <p class="whs9"> </p> <p class="whs9">Distribution with Table Density - <span style="font-weight: normal;">you input a number of pairs</span> t - F(t),<span style="font-weight: normal;"> where </span>t<span style="font-weight: normal;"> ranges from 0 to 1,</span> <span style="font-weight: normal;">and the module computes the formula, which will rule the change of length of segments and shows the curve in the plot. You can select the </span>Conversion mode<span style="font-weight: normal;"> from </span>Exponent<span style="font-weight: normal;"> and </span>Cut negative<span style="font-weight: normal;">. </span></p> <p class="whs9"> </p> <p class="whs12"><img src="../pics/distributionwithtabledensity.png" x-maintain-ratio="TRUE" width="368px" height="760px" border="0" class="img_whs16"></p> <p class="whs9"> </p> <p class="whs9">Distribution with Analytic Density - <span style="font-weight: normal;">you input the formula, which will rule the change of length of segments and the module shows the curve in the plot.</span></p> <h3 class="whs17"><img src="../pics/distributionwithanalyticdensity.png" x-maintain-ratio="TRUE" width="365px" height="605px" border="0" class="img_whs18"></h3> <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining Number of Segments hypothesis</a> operation. </p> <h3> </h3> <h3><a name=start_and_end_length>Start and End Length hypothesis.</a></h3> <p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis allows to divide a geometrical edge into segments so that the first and the last segments have a specified length. The length of each but the first segment differs from length of the previous one by a constant factor. Then mesh nodes are constructed at segment ends location and 1D mesh elements are constructed on them.</p> <p> </p> <p class="whs3"><img src="../pics/a-startendlength.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> <img src="../pics/b-art_end_length.png" x-maintain-ratio="TRUE" width="287px" height="305px" border="0" class="img_whs19"></p> <p class="whs6"> </p> <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining Start and End Length hypothesis</a> operation. </p> <p class="whs6"> </p> <h3><a name=automatic_length>Automatic Length</a></h3> <p>This hypothesis is automatically applied when you select <span style="font-weight: bold;"><B>Assign a set of hypotheses</B></span> option in Create Mesh menu. </p> <p> </p> <p class="whs3"><img src="../pics/automaticlength.png" x-maintain-ratio="TRUE" width="205px" height="175px" border="0" class="img_whs20"> </p> <p> </p> <p>The dialog box prompts you to define the quality of the future mesh by only one parameter, which is <span style="font-weight: bold;"><B>Fineness</B></span>, ranging from 0 (coarse mesh, low number of elements) to 1 (extremely fine mesh, great number of elements). Compare one and the same object (sphere) meshed with minimum and maximum value of this parameter. </p> <p> </p> <p class="whs3"><img src="../image147.gif" width="195px" height="192px" border="0" class="img_whs21"> <img src="../image148.gif" width="206px" height="195px" border="0" class="img_whs22"></p> <p> </p> <p> </p> <p> </p> <p> </p> <script type="text/javascript" language="javascript1.2"> <!-- if (window.writeIntopicBar) writeIntopicBar(0); //--> </script> </body> </html>