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# Nonpositive Jacobian Errors or Distorted Elements

Solution problems can occur when very long, skinny tetrahedral elements are created by the solid mesher. For linear stress analysis, these elements have near zero or negative volume (due to round off) that cause solution difficulty such as Jacobian is negative or poor precision results (in the Results environment, use Results Contours Voltage and Current Current Flux Precision.)

With nonlinear stress analysis, distorted elements can give warning messages such as ** Warning: distorted element 2456 in part 2: maintaining its integrity.

Take a look at the Solid Mesh Statistics shown below. (From the FEA Editor environment, go to Mesh Mesh View Mesh Results and look at the Part information. For the last solid mesh generated, the solid mesh statistics are also in the .XLG file.) After the general recap, columns of numbers are given for each of the statistic lines. From left to right, these represent the Tetrahedral (4-node) elements, Pyramid (5-node), Wedge (6-node), and Brick (8-node) elements. The Jacobian problem occurs when the Max. length ratio is relatively large. This usually occurs for the 4-node elements.

 Mesh type Mix of bricks, wedges, pyramids and tetrahedra Watertight Yes Mesh has microholes No Total nodes 966 Volume 136.799506 in^3 Total elements 1511
 Tetrahedra Pyramids Wedges Bricks Elements 744 384 140 243 Volume % 10.96 12.33 9.31 67.38 Max. length ratio 105.2 44.6 5.4 2.3 Avg. length ratio 5.9 4.1 3 1.5 Avg. aspect ratio 1.3 1.4 1.2 1 Unconstrained aspect ratio 3.1 3.2 1.3 1.1

In the example above, 243 brick elements were built, 140 wedge elements, 384 pyramid elements, and 744 tetrahedral elements were created. For the maximum length ratio, the brick elements were 2.3, and the tetrahedral elements were 105.2.

In general, there is no guide line for what the maximum acceptable length ratio can be. Each model is different, so a value of 10000 may be acceptable in some cases, where as some models may have problems with much lower numbers.

There are a couple of options to reduce the problem of the length ratio. If the part was not meshed with the mircrohole option activated, consider using it. This will remove the sliver elements with large length ratios. (See the page The Effects of Microholes within a Solid Mesh for a discussion.) In the FEA Editor environment, select the part or parts to re-mesh, right-click, and choose Created Solid Mesh Options Allow microholes. Then create the solid mesh and run the analysis with the better mesh. (The solid mesh dialog can also be accessed from Mesh Mesh Create Solid Mesh. Parts to be meshed need to be selected first.)

The next option is to re-create the solid mesh with the maximum aspect ratio set. The goal is to reduce the value until the solid mesh either fails to create a complete mesh or the solid mesh engine does not reach the ratio you specified. So, you could run the solid mesh engine and cut the aspect ratio in half (50, 25, and so on), until you reach the limit. In the FEA Editor environment, select the part or parts to re-mesh, right-click, and chooseCAD Mesh OptionsCreate Solid Mesh Quality. (See Controlling the Aspect Ratio on the page Solid for a description of the input.) Then create the solid mesh and run the analysis with the better mesh.

Be sure to check the log file after each solid mesh generation. If the solid mesh engine was unable to completely fill the volume with the parameters you specified, there will be an error message. The following is a partial listing of a log file.

 TYPE OF OPERATION: Meshing only surface defined by part 4 Generating bricks, wedges, pyramids and tetrahedra elements Keeping maximum aspect ratio below 10.0   ERROR NUMBER 300: Cannot continue meshing solid; yet, solid is unfilled.   FINAL STATISTICS: Still have: 4 nodes; 6 lines; 4 triangles Elements built (4,5,6,8 noded): 1953 (1153, 482, 73, 245 )

Finally, if the model is not located near the origin, then round-off errors in the nodal coordinates can create distorted elements. If the model is located entirely with coordinates in the thousands, then another solution would be to move the CAD model closer to the origin. (Ideally, the model should be centered at the origin.) This requires that the entire model be imported and re-meshed.

If the Jacobian problem still occurs, then the surface mesh must be changed to get a different solid mesh.