Meshing of 2-D Cross-Section – Mesh Tool Comparison
Final Project Report
ME 501
Graden Hardy
Patrick Lewis
June 13, 2009
Ira A. Fulton College of Engineering and Technology
Mechanical Engineering Department
Brigham Young University
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Table of Contents:
1. Problem Description 1
2. Model Description 1
2.1 Geometry 1
2.2 Element Type 2
3. Results 2
3.1 Free Mesh – Default 2
3.2 Free Mesh – Smart Size 3
3.3 Free Mesh – Size Controls: Global 4
3.4 Free Mesh – Q-Morph Mesher 5
3.5 Mapped Mesh – Regions 6
4. Discussion 7
4.1 Automatic Vs. Mapped Meshing 7
4.2 “Mesh Tool” 7
4.3 “Mesher Opts” 7
Appendix i
Appendix A – Complete CAD Drawing Of Model ii
Appendix B – Free Mesh Nodal Plots iii
Appendix C – Mapped Mesh Nodal Plot vi
Table of Figures:
Figure 1 - CAD Model of Cross Section 1
Figure 2 - CAD Model of Cross Section 1
Figure 3 - Default Free Mesh Element Plot 2
Figure 4 - Default Free Mesh Element Plot w/Error 3
Figure 5 - Free Mesh Element Plot w/Smart Size Level 4 3
Figure 6 - Free Mesh Element Plot w/Smart Size Level 5 4
Figure 7 - Free Mesh Element Plot w/Size Controls: Global 4
Figure 8 - Free Mesh Element Plot w/Q-Morph Mesher 5
Figure 9 - Regions for Mapped Mesh 6
Figure 10 - Mapped Mesh - Regions Element Plot 6
Figure 11 - "Mesh Tool" Menu 7
Figure 12 - "Mesher Opts" Menu 7
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1. Problem Description
Finite Element Modeling problems faced by Engineers in industry rarely involve simple geometries that are modeled accurately using automatic meshing tools. In order to properly mesh a given shape, the engineer must understand the strengths and weaknesses of different meshing tools available in ANSYS. The purpose of this project was to develop a cross section that would require the use of advanced mesh generation tools and allow for their comparison. The comparison of these tools was accomplished through visual inspection of the resulting element shapes and sizes. A Solid Model representation of the chosen 6061 Aluminum cross-section can be seen in Figure 1.
2. Model Description
In order to define the model used to compare the different meshing tools the Geometry and Element Type that will be applied to the final mesh are given below.
2.1 Geometry
In order to specify the exact geometry of the cross-section a CAD drawing was created using SolidWorks. A view of the geometry related portion of this drawing may be seen in Figure 2. The complete drawing, along with the material information used in the model is included in Appendix A.
2.2 Element Type
For this model the analysis is best accomplished through the use of a 2-D Plane Stress Element. In the ANSYS model the Plane 82 Element (Solid à Quad à 8node – 82) was used.
3. Results
With the geometry of the model specified an ANSYS model was created and 5 Mesh tool options were identified for comparison. In examining the Meshing tools available through ANSYS it was seen that there are two basic tools that are available, Free Mesh and Mapped Mesh. The abilities and limitations of these tools are described below. Within the Free Mesh Tool were found 4 of the 5 options that were explored: Default Mesh, Smart Size, Size Controls: Global, and Q-Morph Mesher. In the Mapped Mesh Tool the use of Regions provided the 5th option used in the comparison. Results from the different Mesh tool options are found below. Nodal Plots created by each of the tools discussed below can be found in Appendix B (Free Mesh) and Appendix C (Mapped Mesh).
3.1 Free Mesh – Default
Tool Description:
No restrictions are placed on the element shape, and no specified pattern is followed. Any model geometry will be meshed, but there is no active control of the shapes or sizes of the elements created in irregularly shaped geometries.
Element Plots:
As a result of the inability to control the element generation, badly shaped elements are often produced. (See Figures 3-4). Figure 3 is the result of free meshing the geometry using the default size setting found within ANSYS. It clearly does not provide a very desirable mesh. ANSYS provided a modeling warning and Figure 4 is a result of the Check Mesh feature within ANSYS. The highlighted element indicates a modeling error. In ANSYS the angle between two adjoining sides of an element can be no greater than 165°, and for the highlighted element the angle is 167.3°. To see the Nodal Plot for the Mesh shown in Figure 3 see Appendix B.
3.2 Free Mesh – Smart Size
Tool Description:
This meshing feature creates initial element sizes for free meshing operations, and gives the mesher a better chance of creating reasonably shaped elements during automatic mesh generation. This enhancement is accomplished through a built in algorithm that first computes an estimated element edge length for all lines in the area or volumes being meshed. These edge lengths are then further refined to account for curvature and proximity of surrounding features in the geometry.
For quadrilateral elements the Smart Size function attempts to set an even number of line divisions around the area so that an all quadrilateral element mesh is possible.
Element Plots:
In order to use this tool the user must specify a mesh size level from 1 (fine mesh) to 10 (coarse mesh). In Figure 5 is found the Element Plot using a mesh size level of 4 (L4), and in Figure 6 is the plot for level 5 (L5). By inspection it can be seen that the L4 mesh is much more acceptable then the (L5) mesh, and that both L4 and L5 meshes are better than the Default mesh.
3.3 Free Mesh – Size Controls: Global
Tool Description:
This mesh control sets the size of the elements to a default size manually specified by the user. It provides a consistent size for all elements in the mesh. It doesn’t use a sizing algorithm, but rather relies on the judgment of the user. Thus, this control requires some knowledge and experimentation on the part of the user in order to come to a suitable final element size.
Element Plot:
As seen below in Figure 7, in this case the free mesh provides a good mesh with no triangular elements though several transition elements. Though no degenerate (triangular) shapes exist here, there is no guarantee that such always occurs. This is a good mesh to begin with when doing an analysis.
3.4 Free Mesh – Q-Morph Mesher
Tool Description:
This mesher generally provides higher quality quadrilateral elements than the alternative and is very effective with boundary sensitive geometries. This tool by default does not remove all triangular elements so the meshing options must be carefully adjusted so as to provide the correct environment for only quadrilateral elements. A triangle element will exist in a mesh if there is an odd number of line divisions on the boundary of the meshed geometry. The smart sizing feature will generally provide an even number of line divisions, so this was enabled in this mesh. It was found that a global element size provision also provided a better mesh in this instance. When these two tools are used together the global element size is used as the default size in the mesh, though this may be overridden for curvature and proximity of features. Q-Morph Mesher is utilized by selecting:
Preprocessor à Meshing à Mesher Opts à Triangle Mesher à Alternate
Quad Mesher à Main
Split poor quality quads à Off
Split poor quality quads must be set to Off in order to ensure that all triangular elements are removed. It is important that the Triangle Mesher be set to Alternate since having the Main mesher enabled will crash ANSYS. These settings provide the mesh as seen below.
Element Plot:
In Figure 8 it can be seen that for a free mesh the Q-Morph Mesher provides a good mesh. There are no triangular elements and few oddly shaped transition elements. The pattern is also quite reasonable.
3.5 Mapped Mesh – Regions
Tool Description:
In a mapped mesh restrictions are placed on the element shape, and a specified pattern is used to control the mesh generation. Generally the geometry of the area or volume being created must be fairly regular. For 2-D Elements the user has the option of choosing between Quadrilateral or Triangular element shapes. In order to incorporate a mapped mesh in a strange or awkward geometry, the geometry must be broken down into basic regular regions.
Node & Element Plots:
As can be seen in Figure 9 the area had to be broken into basic 3-5 sided regions in order to incorporate the mapped mesh. Figure 10 is the result of meshing each region using the Mapped Mesh function on the Mesh Tool. As can be seen this method of meshing provides very nicely shaped elements and a very good pattern.
4. Discussion
4.1 Automatic Vs. Mapped Meshing
Automatic meshing functions have good capabilities for meshing difficult geometries, but are limited in their abilities to provide uniform element shapes and patterns. While triangular shapes can be eliminated from the automatic mesh, transition elements will still result. Mapped meshing tools, although tedious in use, are more powerful and controllable meshing tools.
4.2 “Mesh Tool”
Through experimentation and exploration of the ANSYS tool bars it was discovered that the “Mesh Tool” is the most efficient tool available for rapid mesh creation/control. In this tool bar ANSYS combines most of the other mesh tool menus to allow the user to quickly navigate between different mesh tool settings and options. (See Figure 11) This tool bar is activated by selecting:
Preprocessor à Meshing à Mesh Tool
4.3 “Mesher Opts”
Through the use of the different mesher tools available in ANSYS it was found that the “Mesher Opts” tool is another powerful tool found within the meshing menu. This tool bar allows for more advanced control of the meshing functions, including the Free Meshing functions. (See Figure 12) This tool bar is activated by selecting:
Preprocessor à Meshing à Mesher Opts
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Appendix
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Appendix A – Complete CAD Drawing Of Model
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Appendix B – Free Mesh Nodal Plots
Default:
Smart Size L4:
Smart Size L4:
Size Controls: Global:
Q-Morph Mesher:
Appendix C – Mapped Mesh Nodal Plot
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