<!DOCTYPE html
  PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

<!--
Copyright (c) 2006 UGS Corp.

All Rights Reserved.

This software and related documentation are proprietary to UGS Corp.
-->
<html>
   <head>
      <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
      <title>Mass Using Curves &amp; Sheets</title>
      <script language="javaScript">
        abridged="false";
        displayConditions=new Array();
      </script>
      <link type="text/css" href="../css/main_styles.css" rel="stylesheet">
   </head>
   <body class="bodydocs" onload="top.pageLoader()" bgcolor="#FFFFFF">
      <div class="title_topic3" id="xps10_pagetitle">Mass Using Curves &amp; Sheets</div>
      <hr noshade="true">
      <p class="para_topic">Mass Using Curves and Sheets analyzes a 3D object which is formed by translating or rotating a closed sequence of curves, or one that is enclosed by or composed of a set of sheet bodies. Example analysis data includes items such as Area, Volume, Moments of Inertia, etc.</p>
      <table cellspacing="3" align="center">
         <tr>
            <th bgcolor="#f4f4f4" colspan="2" rowspan="1" valign="top">
               <p class="para_th">3D Selection Options</p>
            </th>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Rotate About XC</p>
               <p class="para_td">Rotate About YC</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">For a solid body of revolution, the figure must not cross the axis of rotation, although part of that axis may form a boundary of the figure. </p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Project Along ZC</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Enter the distance that the system should project the figure. </p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Bounded by Sheets</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Includes any volume completely enclosed by sheet bodies. You are responsible for ensuring that the volume is completely enclosed, that the sheet bodies are correctly aligned at the edges, and that the face normals are all pointing toward the outside of the enclosed volume. </p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Thin Shell</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Allows any collection of sheet bodies. The sheet bodies themselves are considered as having mass and the density is expressed in terms of mass per unit sheet area. The sheet bodies do not have to enclose a volume or be connected in any way. The mass properties found are of the object formed, by making the sheet bodies of sheet metal or some similar material.</p>
               <p class="para_td">Note that for a correct analysis in a 3D mass property calculation, no sheet can have a sharp bend. Analysis values distort in this situation. You should split the sheet body with the bend at the point of the bend (e.g., break the sheet body at the sharp point) before beginning the analysis.</p>
            </td>
         </tr>
      </table><br><div class="title_division">Rotation or Projection</div>
      <p class="para_division">Select Rotate About XC, Rotate About YC, or Project Along ZC the system will prompt for the density (mass per unit volume). For a figure projected along the ZC axis, the start and end points for the projection must be defined.</p>
      <p class="para_division">Enter the desired tolerance. The tolerance for these options is used as a cordial tolerance in constructing an approximation of the boundary. The smaller the value entered the more accurate the analysis will be and the longer it will take.</p>
      <p class="para_division">Next, select the figure to be analyzed. You must define a boundary and are given two options: Permanent and Temporary.</p>
      <p class="para_division">Use the same conventions for boundary selection as in Area Using Curves.</p>
      <table border="0">
         <tr>
            <td valign="top" align="left"><img align="left" src="../graphics/note.gif" alt="Note" title="Note"></td>
            <td valign="bottom" align="left" width="100%">
               <div class="para_note">
                  <p class="para_note_body">  The distance of the figure from the WCS origin may affect the results. For best results, the WCS origin should be close to the figure being analyzed (or as close as possible for the cases of Rotate About XC or Rotate About YC).</p>
                  <p class="para_note_body"></p>
               </div>
            </td>
         </tr>
      </table>
      <div class="title_division"> Bounded by Sheets and Thin Shell</div>
      <p class="para_division">For Bounded By Sheets and Thin Shell analysis:</p>
      <ul>
         <li>
            <p class="para_item">Enter an accuracy parameter or relative tolerances,</p>
         </li>
         <li>
            <p class="para_item">Specify a density for the volume or shell,</p>
         </li>
         <li>
            <p class="para_item">Select one or more sheet bodies to be analyzed,</p>
         </li>
         <li>
            <p class="para_item">Choose the specific analysis data you want to see.</p>
         </li>
      </ul>
      <div class="title_division">Mass Property Basics</div>
      <div class="title_division">Accuracy, Tolerances and Units</div>
      <p class="para_division">Specify Accuracy Parameter or Relative Tolerances for the mass property computations.</p>
      <p class="para_division">For simple analytic sheet body faces (i.e., planar, cylindrical), the default accuracy value is</p>
      <p class="para_division">If Relative Tolerances are specified, the system iterates on the accuracy values 0.9, 0.99, 0.999, 0.9999, 0.99999, and 0.999999, until successive mass property values are within the specified relative tolerances.</p>
      <p class="para_division">The relative tolerance values are defined by</p>
      <p class="para_division"> <img align="bottom" src="graphics/ana_infoat38.gif" border="0"> 
      </p>
      <p class="para_division">The test value (or estimated relative tolerance) is</p>
      <p align="center"><img align="bottom" src="graphics/ana_infoat37.gif"></p>
      <p class="para_division">where MP(n) is the mass property value for the n-th iteration on the accuracy value.</p>
      <p class="para_division">If a percent relative tolerance of 0.0 is specified, no testing is done for the corresponding mass property value, although all the mass property values are computed using the same accuracy values.</p>
      <p class="para_division">If the specified relative tolerance cannot be achieved, a warning message is displayed:</p><pre class="indent">The relative tolerance iterations did not converge. Choose Yes to see the results, including the estimated relative tolerances. Otherwise, select No.</pre><p class="para_division">Data displayed in the Information window is converted to the current units. If you change the unit settings using Analysis&rarr;Units, information will be displayed in the new units.</p>
      <p class="para_division">The system prompts for the density (mass per unit volume for solid bodies bounded by sheets, mass per unit area for thin shells) of the material. The default value is for steel.</p>
      <p class="para_division">Next, select sheet bodies bounding the volume, or sheet bodies for thin shell analysis.</p>
      <p class="para_division">For Bounded by Sheets analysis, the face normals must all be oriented correctly, toward the outside of the volume, to obtain correct results. If this is not the case, go to Modeling&rarr; Edit &rarr; Free Form Feature&rarr; Reverse Normal to reverse the sheet body normals that are not pointing out of the volume.</p>
      <div class="title_division">Choose the Analysis Data...</div>
      <p class="para_division">After you specify the object to be analyzed, the system computes the mass properties to within the specified relative tolerances, and computes additional properties.</p>
      <p class="para_division">Select the data for the system to display. The formulas for determining the analysis data listed in this table are identical to those documented for Mass Using Solids.</p>
      <table cellspacing="3" align="center">
         <tr>
            <th bgcolor="#c0c0c0" colspan="1" rowspan="1" valign="top">
               <p class="para_th">Option</p>
            </th>
            <th bgcolor="#c0c0c0" colspan="1" rowspan="1" valign="top">
               <p class="para_th">Description</p>
            </th>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Area/Volume/Mass</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Obtains the total face area, volume and mass of a 3D object.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Centroid/1st Mom</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Obtains the first moments that serve to define the center of mass.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Moments of Inertia</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Obtains the moment of inertia for certain 3D objects of uniform density about specified axes.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Products of Inertia</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">The Products of Inertia, along with the Moments of Inertia, form the inertia tensor, and are important in rotational dynamics.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Principal Axes/Moments</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">The Principal Axes/Moments are an orthogonal system of three axes through the center of mass such that the three products of inertia relative to the system are all zero.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Radius of Gyration</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Obtains the Radius of Gyration for objects.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Create Cent/Axes</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">For Create Cent/Axes the centroid and principal axes are temporarily displayed when calculated. With this option, you can make permanent objects of the centroid (a point) and/or the principal axes (a coordinate system).</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">List All</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Displays the calculated data for all of the Mass Properties options previously discussed in the Information window.</p>
            </td>
         </tr>
         <tr>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="top">
               <p class="para_td">Relative Errors</p>
            </td>
            <td bgcolor="#f4f4f4" colspan="1" rowspan="1" valign="middle">
               <p class="para_td">Are estimates of the relative tolerances achieved in calculating the mass properties. Often the relative errors are less than the specified relative tolerances, indicating that the mass property values are correct to within tighter tolerances than those specified.</p>
               <p class="para_td">If only a single accuracy value is specified, then +/- Range Errors are given. </p>
            </td>
         </tr>
      </table><br><table border="0">
         <tr>
            <td valign="top" align="left"><img align="left" src="../graphics/note.gif" alt="Note" title="Note"></td>
            <td valign="bottom" align="left" width="100%">
               <div class="para_note">
                  <p class="para_note_body">  For thin shell analysis,in the Area/Volume/Mass option, volume is replaced by area. The volume will always be 0.0.</p>
               </div>
            </td>
         </tr>
      </table>
      <div class="title_division">Assembly Weight Management</div>
      <p class="para_division">For this information, see the Assemblies Help.</p>
      <div class="title_division">Units</div>
      <p class="para_division">Specifies the units in which geometric information is displayed. The following units are available on the Units cascade menu: Lbs-Inches, Lbs-Feet, Grams-Millimeters, Grams-Centimeters, and Kgs-Meters. The label next to the word Units indicates the current units.</p>
      <p class="para_division">The Units menu is available at all times during the session, allowing the current units to be changed at any time. The following Information functions display results in the current units:</p>
      <ul>
         <li>
            <p class="para_item">Object</p>
         </li>
         <li>
            <p class="para_item">Geometric Point</p>
         </li>
         <li>
            <p class="para_item">Geometric Distance</p>
         </li>
         <li>
            <p class="para_item">Geometric Arc Length</p>
         </li>
         <li>
            <p class="para_item">Analysis </p>
         </li>
      </ul>
   </body>
</html>