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111 <h1>1D Meshing Hypotheses</h1>
113 <ul type="disc" class="whs1">
115 <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
116 class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#arithmetic_1D"><span
117 style="font-weight: bold;"><B>Arithmetic 1D</B></span></a></p></li>
119 <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
120 class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Average_length"><span
121 style="font-weight: bold;"><B>Average Length</B></span></a></p></li>
123 <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
124 class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#deflection_1D"><span
125 style="font-weight: bold;"><B>Deflection 1D </B></span></a></p></li>
127 <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
128 class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#Number_of_elements"><span
129 style="font-weight: bold;"><B>Number of segments</B></span></a></p></li>
131 <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
132 class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#start_and_end_length"><span
133 style="font-weight: bold;"><B>Start and end length</B></span></a></p></li>
135 <li style="/*begin!kadov{{*/ color: #000000; /*}}end!kadov*/ "
136 class=kadov-p><p class="whs2"><a href="arithmetic_1d.htm#automatic_length"><span
137 style="font-weight: bold;"><B>Automatic Length</B></span></a></p></li>
140 <h3><a name=arithmetic_1D>Arithmetic 1D hypothesis</a></h3>
142 <p><span style="font-weight: bold;"><B>Arithmetic 1D</B></span> hypothesis allows
143 to split edges into segments with a length that changes in arithmetic
144 progression (Lk = Lk-1 + d) beginning from a given starting length and
145 up to a given end length.</p>
149 <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>
153 <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
154 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark">Defining
155 Arithmetic 1D hypothesis</a> operation. </p>
157 <h3><a name=deflection_1D>Deflection 1D hypothesis</a></h3>
159 <p><span style="font-weight: bold;"><B>Deflection ID </B></span>hypothesis can
160 be applied for meshing curvilinear edges composing your geometrical object.
161 It uses only one parameter: the value of deflection. </p>
163 <p>A geometrical edge is divided into equal segments. The maximum distance
164 between a point on the edge within a segment and the line connecting the
165 ends of the segment should not exceed the specified value of deflection
166 . Then mesh nodes are constructed at end segment locations and 1D mesh
167 elements are constructed on segments.</p>
171 <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>
175 <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
176 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining
177 Deflection 1D hypothesis</a> operation. </p>
181 <p class="whs9"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs10"></p>
183 <h3><a name=Average_length>Average Length hypothesis</a></h3>
185 <p><span style="font-weight: bold;"><B>Average Length </B></span>hypothesis can
186 be applied for meshing of edges composing your geometrical object. Definition
187 of this hypothesis consists of setting the <span style="font-weight: bold;"><B>length</B></span>
188 of segments, which will split these edges. The points on the edges generated
189 by these segments will represent nodes of your mesh. Later these nodes
190 will be used for meshing of the faces abutting to these edges.</p>
194 <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>
198 <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
199 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining
200 Average Length hypothesis</a> operation. </p>
204 <p class="whs12"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs13"></p>
206 <h3><a name=Number_of_elements>Number of segments hypothesis</a> </h3>
208 <p><span style="font-weight: bold;"><B>Number of segments </B></span>hypothesis
209 can be applied for meshing of edges composing your geometrical object.
210 Definition of this hypothesis consists of setting the <span style="font-weight: bold;"><B>number</B></span>
211 of segments, which will split these edges. In other words your edges will
212 be split into a definite number of segments with approximately the same
213 length. The points on the edges generated by these segments will represent
214 nodes of your mesh. Later these nodes will be used for meshing of the
215 faces abutting to these edges.</p>
219 <p class="whs6">You can set the type of distribution for this
220 hypothesis in the <span style="font-weight: bold;"><B>Hypothesis Construction</B></span>
223 <p class="whs6"> </p>
225 <p class="whs6"><span style="font-weight: bold;"><B>Equidistant
226 Distribution</B></span> - all segments will have the same length, you define
227 only the <span style="font-weight: bold;"><B>Number of Segments</B></span>.</p>
229 <p class="whs6"> </p>
231 <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>
235 <p class="whs9">Scale Distribution - <span style="font-weight: normal;">each
236 next segment differs from the previous according to the formula:</span>
237 A<span style="vertical-align: Sub;">i+1</span> = A<span style="vertical-align: Sub;">i
238 </span>* k, <span style="font-weight: normal;">where</span> k <span style="font-weight: normal;">is
239 a</span> Scale Factor. </p>
241 <p class="whs12"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs15">\</p>
243 <p class="whs9"> </p>
245 <p class="whs9">Distribution with Table Density - <span style="font-weight: normal;">you
246 input a number of pairs</span> t - F(t),<span style="font-weight: normal;">
247 where </span>t<span style="font-weight: normal;"> ranges from 0 to 1,</span>
248 <span style="font-weight: normal;">and
249 the module computes the formula, which will rule the change of length
250 of segments and shows the curve in the plot. You can select the </span>Conversion
251 mode<span style="font-weight: normal;"> from </span>Exponent<span style="font-weight: normal;">
252 and </span>Cut negative<span style="font-weight: normal;">. </span></p>
254 <p class="whs9"> </p>
256 <p class="whs12"><img src="../pics/distributionwithtabledensity.png" x-maintain-ratio="TRUE" width="368px" height="760px" border="0" class="img_whs16"></p>
258 <p class="whs9"> </p>
260 <p class="whs9">Distribution with Analytic Density - <span
261 style="font-weight: normal;">you input the formula, which will rule the
262 change of length of segments and the module shows the curve in the plot.</span></p>
264 <h3 class="whs17"><img src="../pics/distributionwithanalyticdensity.png" x-maintain-ratio="TRUE" width="365px" height="605px" border="0" class="img_whs18"></h3>
266 <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
267 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark9">Defining
268 Number of Segments hypothesis</a> operation. </p>
272 <h3><a name=start_and_end_length>Start and End Length hypothesis.</a></h3>
274 <p><span style="font-weight: bold;"><B>Start and End Length</B></span> hypothesis
275 allows to divide a geometrical edge into segments so that the first and
276 the last segments have a specified length. The length of each but the
277 first segment differs from length of the previous one by a constant factor.
278 Then mesh nodes are constructed at segment ends location and 1D mesh elements
279 are constructed on them.</p>
283 <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>
285 <p class="whs6"> </p>
287 <p class="whs6"><span style="font-weight: bold;"><B>See Also</B></span>
288 a sample TUI Script of a <a href="../defining_hypotheses_tui.htm#bookmark3">Defining
289 Start and End Length hypothesis</a>
290 operation. </p>
292 <p class="whs6"> </p>
294 <h3><a name=automatic_length>Automatic Length</a></h3>
296 <p>This hypothesis is automatically applied when you select <span style="font-weight: bold;"><B>Assign
297 a set of hypotheses</B></span> option in Create Mesh menu. </p>
301 <p class="whs3"><img src="../pics/automaticlength.png" x-maintain-ratio="TRUE" width="205px" height="175px" border="0" class="img_whs20"> </p>
305 <p>The dialog box prompts you to define the quality of the future mesh
306 by only one parameter, which is <span style="font-weight: bold;"><B>Fineness</B></span>,
307 ranging from 0 (coarse mesh, low number of elements) to 1 (extremely fine
308 mesh, great number of elements). Compare one and the same object (sphere)
309 meshed with minimum and maximum value of this parameter. </p>
313 <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>
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