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-<h1>1D Meshing Hypotheses</h1>\r
-\r
-<ul type="disc" class="whs1">\r
- \r
- <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "\r
- class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#arithmetic_1D"><span \r
- style="font-weight: bold;"><B>Arithmetic 1D</B></span></a></p></li>\r
- \r
- <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "\r
- class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Average_length"><span \r
- style="font-weight: bold;"><B>Average Length</B></span></a></p></li>\r
- \r
- <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "\r
- class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#deflection_1D"><span \r
- style="font-weight: bold;"><B>Deflection 1D </B></span></a></p></li>\r
- \r
- <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "\r
- class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Number_of_elements"><span \r
- style="font-weight: bold;"><B>Number of segments</B></span></a></p></li>\r
- \r
- <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "\r
- class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#start_and_end_length"><span \r
- style="font-weight: bold;"><B>Start and end length</B></span></a></p></li>\r
- \r
- <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "\r
- class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#automatic_length"><span \r
- style="font-weight: bold;"><B>Automatic Length</B></span></a></p></li>\r
-</ul>\r
-\r
-<h3><a name=arithmetic_1D>Arithmetic 1D hypothesis</a></h3>\r
-\r
-<p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows \r
- to split edges into segments with a length that changes in arithmetic \r
- progression (Lk = Lk-1 + d) beginning from a given starting length and \r
- up to a given end length.</p>\r
-\r
-<p> </p>\r
-\r
-<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>\r
-\r
-<p> </p>\r
-\r
-<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> \r
- a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining \r
- Arithmetic 1D hypothesis</a> operation. </p>\r
-\r
-<h3><a name=deflection_1D>Deflection 1D hypothesis</a></h3>\r
-\r
-<p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can \r
- be applied for meshing curvilinear edges composing your geometrical object. \r
- It uses only one parameter: the value of deflection. </p>\r
-\r
-<p>A geometrical edge is divided into equal segments. The maximum distance \r
- between a point on the edge within a segment and the line connecting the \r
- ends of the segment should not exceed the specified value of deflection \r
- . Then mesh nodes are constructed at end segment locations and 1D mesh \r
- elements are constructed on segments.</p>\r
-\r
-<p> </p>\r
-\r
-<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>\r
-\r
-<p> </p>\r
-\r
-<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> \r
- a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining \r
- Deflection 1D hypothesis</a> operation. </p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs9"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs10"></p>\r
-\r
-<h3><a name=Average_length>Average Length hypothesis</a></h3>\r
-\r
-<p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can \r
- be applied for meshing of edges composing your geometrical object. Definition \r
- of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span> \r
- of segments, which will split these edges. The points on the edges generated \r
- by these segments will represent nodes of your mesh. Later these nodes \r
- will be used for meshing of the faces abutting to these edges.</p>\r
-\r
-<p> </p>\r
-\r
-<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>\r
-\r
-<p> </p>\r
-\r
-<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> \r
- a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining \r
- Average Length hypothesis</a> operation. </p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs12"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs13"></p>\r
-\r
-<h3><a name=Number_of_elements>Number of segments hypothesis</a> </h3>\r
-\r
-<p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis \r
- can be applied for meshing of edges composing your geometrical object. \r
- Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span> \r
- of segments, which will split these edges. In other words your edges will \r
- be split into a definite number of segments with approximately the same \r
- length. The points on the edges generated by these segments will represent \r
- nodes of your mesh. Later these nodes will be used for meshing of the \r
- faces abutting to these edges.</p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs6">You can set the type of distribution for this \r
- hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span> \r
- dialog bog : </p>\r
-\r
-<p class="whs6"> </p>\r
-\r
-<p class="whs6"><span style="font-weight: bold;"><B>Equidistant \r
- Distribution</B></span> - all segments will have the same length, you define \r
- only the <span style="font-weight: bold;"><B>Number of Segments</B></span>.</p>\r
-\r
-<p class="whs6"> </p>\r
-\r
-<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>\r
-\r
-<p> </p>\r
-\r
-<p class="whs9">Scale Distribution - <span style="font-weight: normal;">each \r
- next segment differs from the previous according to the formula:</span> \r
- A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i \r
- </span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is \r
- a</span> Scale Factor. </p>\r
-\r
-<p class="whs12"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs15">\</p>\r
-\r
-<p class="whs9"> </p>\r
-\r
-<p class="whs9">Distribution with Table Density - <span style="font-weight: normal;">you \r
- input a number of pairs</span> t - F(t),<span style="font-weight: normal;"> \r
- where </span>t<span style="font-weight: normal;"> ranges from 0 to 1,</span> \r
- <span style="font-weight: normal;">and \r
- the module computes the formula, which will rule the change of length \r
- of segments and shows the curve in the plot. You can select the </span>Conversion \r
- mode<span style="font-weight: normal;"> from </span>Exponent<span style="font-weight: normal;"> \r
- and </span>Cut negative<span style="font-weight: normal;">. </span></p>\r
-\r
-<p class="whs9"> </p>\r
-\r
-<p class="whs12"><img src="../pics/distributionwithtabledensity.png" x-maintain-ratio="TRUE" width="368px" height="760px" border="0" class="img_whs16"></p>\r
-\r
-<p class="whs9"> </p>\r
-\r
-<p class="whs9">Distribution with Analytic Density - <span \r
- style="font-weight: normal;">you input the formula, which will rule the \r
- change of length of segments and the module shows the curve in the plot.</span></p>\r
-\r
-<h3 class="whs17"><img src="../pics/distributionwithanalyticdensity.png" x-maintain-ratio="TRUE" width="365px" height="605px" border="0" class="img_whs18"></h3>\r
-\r
-<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> \r
- a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining \r
- Number of Segments hypothesis</a> operation. </p>\r
-\r
-<h3> </h3>\r
-\r
-<h3><a name=start_and_end_length>Start and End Length hypothesis.</a></h3>\r
-\r
-<p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis \r
- allows to divide a geometrical edge into segments so that the first and \r
- the last segments have a specified length. The length of each but the \r
- first segment differs from length of the previous one by a constant factor. \r
- Then mesh nodes are constructed at segment ends location and 1D mesh elements \r
- are constructed on them.</p>\r
-\r
-<p> </p>\r
-\r
-<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>\r
-\r
-<p class="whs6"> </p>\r
-\r
-<p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span> \r
- a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining \r
- Start and End Length hypothesis</a> \r
- operation. </p>\r
-\r
-<p class="whs6"> </p>\r
-\r
-<h3><a name=automatic_length>Automatic Length</a></h3>\r
-\r
-<p>This hypothesis is automatically applied when you select <span style="font-weight: bold;"><B>Assign \r
- a set of hypotheses</B></span> option in Create Mesh menu. </p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs3"><img src="../pics/automaticlength.png" x-maintain-ratio="TRUE" width="205px" height="175px" border="0" class="img_whs20"> </p>\r
-\r
-<p> </p>\r
-\r
-<p>The dialog box prompts you to define the quality of the future mesh \r
- by only one parameter, which is <span style="font-weight: bold;"><B>Fineness</B></span>, \r
- ranging from 0 (coarse mesh, low number of elements) to 1 (extremely fine \r
- mesh, great number of elements). Compare one and the same object (sphere) \r
- meshed with minimum and maximum value of this parameter. </p>\r
-\r
-<p> </p>\r
-\r
-<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>\r
-\r
-<p> </p>\r
-\r
-<p> </p>\r
-\r
-<p> </p>\r
-\r
-<p> </p>\r
-\r
-<script type="text/javascript" language="javascript1.2">\r
-<!--\r
-if (window.writeIntopicBar)\r
- writeIntopicBar(0);\r
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-</html>\r
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+</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);
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