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 110 </script>
 111 <h1>1D Meshing Hypotheses</h1>
 112
 113 <ul type="disc" class="whs1">
 114
 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>
 118
 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>
 122
 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>
 126
 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>
 130
 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>
 134
 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>
 138 </ul>
 139
 140 <h3><a name=arithmetic_1D>Arithmetic 1D hypothesis</a></h3>
 141
 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>
 146
 147 <p>&nbsp;</p>
 148
 149 <p class="whs3"><img src="../pics/a-arithmetic1d.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-ithmetic1d.png" x-maintain-ratio="TRUE" width="309px" height="316px" border="0" class="img_whs5"></p>
 150
 151 <p>&nbsp;</p>
 152
 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. &nbsp;</p>
 156
 157 <h3><a name=deflection_1D>Deflection 1D hypothesis</a></h3>
 158
 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. &nbsp;</p>
 162
 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>
 168
 169 <p>&nbsp;</p>
 170
 171 <p class="whs3"><img src="../pics/a-deflection1d.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-flection1d.png" x-maintain-ratio="TRUE" width="267px" height="339px" border="0" class="img_whs8"></p>
 172
 173 <p>&nbsp;</p>
 174
 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. &nbsp;</p>
 178
 179 <p>&nbsp;</p>
 180
 181 <p class="whs9"><img src="../image41.gif" x-maintain-ratio="TRUE" width="367px" height="224px" align="right" border="0" class="img_whs10"></p>
 182
 183 <h3><a name=Average_length>Average Length hypothesis</a></h3>
 184
 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>
 191
 192 <p>&nbsp;</p>
 193
 194 <p class="whs3"><img src="../pics/a-averagelength.png" x-maintain-ratio="TRUE" width="332px" height="212px" border="0" class="img_whs7"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-erage_length.png" x-maintain-ratio="TRUE" width="252px" height="243px" border="0" class="img_whs11"></p>
 195
 196 <p>&nbsp;</p>
 197
 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. &nbsp;</p>
 201
 202 <p>&nbsp;</p>
 203
 204 <p class="whs12"><img src="../image46.gif" x-maintain-ratio="TRUE" width="431px" height="233px" align="right" border="0" class="img_whs13"></p>
 205
 206 <h3><a name=Number_of_elements>Number of segments hypothesis</a> </h3>
 207
 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>
 216
 217 <p>&nbsp;</p>
 218
 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>
 221  dialog bog : </p>
 222
 223 <p class="whs6">&nbsp;</p>
 224
 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>
 228
 229 <p class="whs6">&nbsp;</p>
 230
 231 <p class="whs3"><img src="../pics/a-nbsegments1.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-mberofsegments.png" x-maintain-ratio="TRUE" width="395px" height="387px" border="0" class="img_whs14"></p>
 232
 233 <p>&nbsp;</p>
 234
 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>
 240
 241 <p class="whs12"><img src="../pics/a-nbsegments2.png" x-maintain-ratio="TRUE" width="332px" height="264px" border="0" class="img_whs15">\</p>
 242
 243 <p class="whs9">&nbsp;</p>
 244
 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  &nbsp;<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>
 253
 254 <p class="whs9">&nbsp;</p>
 255
 256 <p class="whs12"><img src="../pics/distributionwithtabledensity.png" x-maintain-ratio="TRUE" width="368px" height="760px" border="0" class="img_whs16"></p>
 257
 258 <p class="whs9">&nbsp;</p>
 259
 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>
 263
 264 <h3 class="whs17"><img src="../pics/distributionwithanalyticdensity.png" x-maintain-ratio="TRUE" width="365px" height="605px" border="0" class="img_whs18"></h3>
 265
 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. &nbsp;</p>
 269
 270 <h3>&nbsp;</h3>
 271
 272 <h3><a name=start_and_end_length>Start and End Length hypothesis.</a></h3>
 273
 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>
 280
 281 <p>&nbsp;</p>
 282
 283 <p class="whs3"><img src="../pics/a-startendlength.png" x-maintain-ratio="TRUE" width="332px" height="238px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/b-art_end_length.png" x-maintain-ratio="TRUE" width="287px" height="305px" border="0" class="img_whs19"></p>
 284
 285 <p class="whs6">&nbsp;</p>
 286
 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 &nbsp;hypothesis</a>
 290  operation. &nbsp;</p>
 291
 292 <p class="whs6">&nbsp;</p>
 293
 294 <h3><a name=automatic_length>Automatic Length</a></h3>
 295
 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>
 298
 299 <p>&nbsp;</p>
 300
 301 <p class="whs3"><img src="../pics/automaticlength.png" x-maintain-ratio="TRUE" width="205px" height="175px" border="0" class="img_whs20"> </p>
 302
 303 <p>&nbsp;</p>
 304
 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>
 310
 311 <p>&nbsp;</p>
 312
 313 <p class="whs3"><img src="../image147.gif" width="195px" height="192px" border="0" class="img_whs21"> &nbsp;&nbsp;&nbsp;<img src="../image148.gif" width="206px" height="195px" border="0" class="img_whs22"></p>
 314
 315 <p>&nbsp;</p>
 316
 317 <p>&nbsp;</p>
 318
 319 <p>&nbsp;</p>
 320
 321 <p>&nbsp;</p>
 322
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