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2005-11-28 14:57:47 +05:00
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2005-11-28 14:57:47 +05:00
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<h1>1D Meshing Hypotheses</h1>
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<h3>Arithmetic 1D hypothesis</h3>
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<p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows
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to split edges into segments with a length that changes in arithmetic
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progression (Lk = Lk-1 + d) beginning from a given starting length and
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up to a given end length.</p>
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<p> </p>
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<p><img src="../pics/a-arithmetic1d.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs1"> <img src="../pics/b-ithmetic1d.png" x-maintain-ratio="TRUE" width="309px" height="316px" border="0" class="img_whs2"></p>
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<p> </p>
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2004-12-01 15:48:31 +05:00
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2005-11-28 14:57:47 +05:00
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<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining
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Arithmetic 1D hypothesis</a> operation. </p>
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<h3><span style="font-weight: bold;"><B>Deflection</B></span> 1D hypothesis</h3>
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<p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can
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be applied for meshing curvilinear edges composing your geometrical object.
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It uses only one parameter: the value of deflection. </p>
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<p>A geometrical edge is divided into equal segments. The maximum distance
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between a point on the edge within a segment and the line connecting the
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ends of the segment should not exceed the specified value of deflection
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. Then mesh nodes are constructed at end segment locations and 1D mesh
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elements are constructed on segments.</p>
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<p> </p>
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<p><img src="../pics/a-deflection1d.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs4"> <img src="../pics/b-flection1d.png" x-maintain-ratio="TRUE" width="267px" height="339px" border="0" class="img_whs5"></p>
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<p> </p>
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2005-11-28 14:57:47 +05:00
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<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining
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Deflection 1D hypothesis</a> operation. </p>
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<p> </p>
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<p class="whs6"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs7"></p>
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<h3>Average Length hypothesis</h3>
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<p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can
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be applied for meshing of edges composing your geometrical object. Definition
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of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span>
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of segments, which will split these edges. The points on the edges generated
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by these segments will represent nodes of your mesh. Later these nodes
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will be used for meshing of the faces abutting to these edges.</p>
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<p> </p>
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<p><img src="../pics/a-averagelength.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs4"> <img src="../pics/b-erage_length.png" x-maintain-ratio="TRUE" width="252px" height="243px" border="0" class="img_whs8"></p>
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<p> </p>
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<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining
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Average Length hypothesis</a> operation. </p>
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<p> </p>
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<p class="whs9"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs10"></p>
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<h3>Number of segments hypothesis </h3>
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2005-11-28 14:57:47 +05:00
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<p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis
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can be applied for meshing of edges composing your geometrical object.
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Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span>
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of segments, which will split these edges. In other words your edges will
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be split into a definite number of segments with approximately the same
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length. The points on the edges generated by these segments will represent
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nodes of your mesh. Later these nodes will be used for meshing of the
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faces abutting to these edges.</p>
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<p> </p>
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<p class="whs3">You can set the type of distribution for this
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hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span>
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dialog bog : </p>
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<p class="whs3"> </p>
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<p class="whs3"><span style="font-weight: bold;"><B>Equidistant
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Distribution</B></span> - all segments will have the same length</p>
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<p><img src="../pics/a-nbsegments1.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs1"> <img src="../pics/b-mberofsegments.png" x-maintain-ratio="TRUE" width="395px" height="387px" border="0" class="img_whs11"></p>
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<p> </p>
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<p class="whs6">Scale Distribution - <span style="font-weight: normal;">each
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next segment differs from the previous according to the formula:</span>
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A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i
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</span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is</span>
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Scale Factor </p>
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<p class="whs6"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs12">\</p>
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<p class="whs6"> </p>
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<p class="whs6">Distribution with Table Density - <span style="font-weight: normal;">you
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input a number of pairs</span> t - F(t) <span style="font-weight: normal;">and
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the program computes the formula, which will rule the change of length
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of segments.</span></p>
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<p class="whs6"> </p>
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<p class="whs6"><img src="../pics/a-nbsegments3.png" x-maintain-ratio="TRUE" width="333px" height="386px" border="0" class="img_whs13"></p>
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<p class="whs6"> </p>
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<p class="whs6">Distribution with Analytic Density - <span
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style="font-weight: normal;">you input the formula, which will rule the
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change of length of segments</span></p>
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<h3><img src="../pics/a-nbsegments4.png" x-maintain-ratio="TRUE" width="333px" height="285px" border="0" class="img_whs14"></h3>
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<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining
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Number of Segments hypothesis</a> operation. </p>
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<h3> </h3>
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<h3>Start and End Length hypothesis.</h3>
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<p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis
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allows to divide a geometrical edge into segments so that the first and
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the last segments have a specified length. The length of each but the
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first segment differs from length of the previous one by a constant factor.
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Then mesh nodes are constructed at segment ends location and 1D mesh elements
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are constructed on them.</p>
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<p> </p>
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<p><img src="../pics/a-startendlength.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs1"> <img src="../pics/b-art_end_length.png" x-maintain-ratio="TRUE" width="287px" height="305px" border="0" class="img_whs15"></p>
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<p class="whs3"> </p>
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<p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining
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Start and End Length hypothesis</a>
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operation. </p>
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<p> </p>
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2004-12-01 15:48:31 +05:00
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