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      <div class="title_topic2" id="xps10_pagetitle">Solver</div>
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               <p class="para_td">Overview</p>
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               <p class="para_td"> <a class="links" href="javascript:void(0)" onclick="top.openFile('fabricflat/procedure.html');return(false);">How To</a></p>
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               <p class="para_td"> <a class="links" href="javascript:void(0)" onclick="top.openFile('fabricflat/dialog.html');return(false);">Options</a></p>
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               <p class="para_td"> <a class="links" href="javascript:void(0)" onclick="top.openFile('fabricflat/warnings.html');return(false);">Related Topics</a></p>
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      </table><br><p class="para_topic">The <b class="uiTerm">Woven</b> and <b class="uiTerm">Unidirectional Solvers</b> create flat patterns of fibrous materials in which the fibers have an important effect on the forming of the material. Use the woven solver for woven cloth or composite material and assumes that there are fibers aligned in two directions in the material. The unidirectional solver assumes that all fibers align in one direction in the material. For both solvers, it assumes that the fibers do not stretch and that when the materials are deformed the fibers bend but do not change in length.
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                  <p class="para_note_body">Questions of fiber direction and material characteristics are only relevant when applied to non&ndash;developable surfaces. If a surface is developable, it has a unique flat pattern that preserves the length of all paths on the surface and this flat pattern is appropriate whether the material is woven fabric, unidirectional fabric, sheet metal or any other theoretically flexible sheet. Thus, when speaking of distortion when creating a flat pattern, it assumes that non&ndash;developable distortion is implied.</p>
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      <p class="para_topic">In the <b class="uiTerm">Woven Solver</b>, accommodate the distortion by changing the angle between fibers of the two alignments (such as primary and secondary orientations). Another way of looking at this is that when the material distorts it stretches along one bias direction and shrinks along the other bias direction.
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      <div class="title_figure">Woven solver distortions</div>
      <p class="para_topic">In the <b class="uiTerm">Unidirectional Solver</b> it assumes that when the material distorts, neighboring fibers of the material may slide relative to one another to some extent while maintaining the same spacing relative to one another.
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      <div class="title_figure">Unidirectional solver distortions</div>
      <div class="title_division">Mesh</div>
      <p class="para_division">Mesh creation is the key process in the operation of the Fabric Flattener. The mesh represents a fitting of the fabric to the surface. Distortion calculates as the mesh is created. The mesh consists of nodes, edges, and elements. The nodes lie either on the ply or on the extension of the ply a small distance beyond the edge. The nodes connect pair&ndash;wise by edges and the edges are grouped into elements of four edges. The mesh is strictly rectangular; all elements have four edges and the nodes fall into rows in two directions. Rows of nodes in the primary direction simulate representative fibers of the material in the primary direction. For the woven solver, rows in the other direction follow representative fibers in the secondary direction. In the unidirectional solver the mesh representation is the same, however since there are no fibers in the secondary direction, these rows represent imaginary curves across the material that in the undistorted state would be straight parallel lines.</p>
      <div class="title_division">Grid size</div>
      <p class="para_division">Specifying grid sizes in both primary and secondary directions controls the fineness of the mesh created on the ply surface. In general the grid sizes required to produce a reasonable mesh will depend on the size of the ply being flattened, how much curvature it has and how complicated its boundaries are. In most cases, a grid size that will allow between 10 and 100 points along the length or width of the ply is a reasonable initial choice. Examination of the mesh display can help tell if the choice of grid size is appropriate. If the surface has bends or bumps that are small in relation to the grid size or if there are portions of the surface that are not reached by the mesh, a smaller grid size is probably in order.&nbsp;In almost all cases, primary and secondary grid sizes should be equal. Exceptions to this: 1) cases where the ply is long and narrow; or 2) where it is more severely curved in one direction than the other.</p>
      <div class="title_division">Fiber angle</div>
      <p class="para_division">The angles between edges of the mesh represent angles between fibers of a woven material and provide a measure of distortion of the material. For unidirectional materials, the secondary direction does not represent fibers, but the angles provide a measure of the slippage of fibers relative to one another and thus a measure of the distortion of the material. Fiber angles measure from the positive primary direction to the positive secondary direction. For most materials, a right angle is considered normal or no distortion and deviation above or below a right angle indicates the amount of distortion. Since this distortion is generally symmetrical, most materials act the same way when pulled along either bias direction, it is usually more convenient to consider only angles less than or equal to a right angle. Angles greater than a right angle are replaced by their supplement, that is a straight angle (180&deg; or pi ) minus the original angle. This provides a single gradient of distortion from no distortion at a right angle with decreasing angle indicating increasing distortion. </p>
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      <div class="title_figure">Fiber angle</div>
      <p class="para_division">You can think of the Lock angle as a limit either of the material or on the process of creating a flat pattern. From a materials point of view, the lock angle is the fiber angle attained when the material distorts to the maximum possible or to the maximum allowed by design criteria. The flat pattern processor uses the lock angle simply as the angle at which to cease processing locally. Once it reaches the lock angle, no further meshing is done on that particular area of the surface. It is reasonable to set the processing lock angle lower than the actual lock angle of the material. This would increase the probability of getting a complete mesh of the ply and make it possible to visually determine problem areas. However, the processing lock angle should not be set unreasonably low (half the actual material lock angle would be reasonable) because this increases the likelihood of the processor creating degenerate meshes. The lock angle will have no effect on the mesh or flat pattern results unless distortion is sufficient.</p>
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