1. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Section 8: Mesh Quality

2. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information SimLab generates mesh that can be used for different analysis types such as stress analysis, NVH analysis to name a few. Mesh of each of these analysis should meet certain quality criteria. It is also important to understand the definition of the quality measures clearly. Mesh Quality

3. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Mesh Quality

4. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Compute Computes the minimum and the maximum values of the quality measures for the elements present in the body. Supports computation of multiple quality types. Display Shows the elements that have failed the qualities measures of the quality type selected. Mesh Quality – Compute, Display

5. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Mesh Quality – Clean Up, Bar Chart Clean Up Automatic clean up of a particular quality type can be done based on the quality measure specified. Bar Chart Plots a bar chart for the quality measure selected.

6. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Tri – Quality measures 1.Aspect Ratio 2.Edge Length 3.Interior Angle 4.Stretch 5.Skew 6.Element Face Angle 7.Area 8.Mid-Node Offset : Distance 9.Mid-Node Offset : Ratio

7. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information The Aspect Ratio (AR) of a TRI element is defined as the largest of 3 / 2(L/h ), where L is the length of the edge and h is the height of the node opposite to this edge. The scale factor 3 / 2 is to make the AR for an equilateral triangle equal to 1. Tri - Aspect Ratio

8. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information 1.Edge Length 1.Minimum and maximum length of the element edge. Interior Angle The min and max interior angle is calculated based on angle formed by the edges at each vertex of the Tri. Tri – Edge Length, Interior Angle

9. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Stretch of a TRI element is 12 (R / L-Max). Where R is the radius of the inscribed circle and L-Max is the longest edge of the TRI element. The scale factor 12 is to make Stretch for an equilateral triangle equal to 1. Tri - Strecth

10. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Skew The skew angle of a TRI3 element is the difference between 90 degrees and the minimum of three angles  1,  2,  3. These angles are defined, for the TRI element, as the smallest of the angles created when a line drawn from a node to the midpoint of the opposing side intersects a line connecting the midpoints of the adjacent two sides. The skew angle has a range from 0 degrees for a perfect triangle to 90 degrees for a collapsed triangle. Skew = 90 – Min ( 1,  2,  3 ) Element Face Angle 1.Element Face Angle is the angle between two TRI elements along the common edge. Area 1.Area of the TRI element. Tri – Skew, Element Face Angle, Area

11. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Tri – Mid node distance, Ratio 1.Mid-Node Offset : Distance 1.It is the offset distance of mid node from the mid position of the corresponding element edge. For example, let N1-N2 be an higher order element edge with mid node M1 and MP be the mid position of the element edge N1-N2. Here, "d" represents the Mid-Node Offset distance. 1.Mid-Node Offset : Ratio 1.It is the ratio between offset distance of mid node from the mid position of the corresponding element edge to element edge length. If EL denote the length of the element edge N1-N2, then d / El represents the Mid-Node Offset ratio.

12. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Quad – Quality measures 1.Aspect Ratio 2.Edge Length 3.Interior Angle 4.Warpage 5.Skew 6.Area 7.Mid-Node Offset : Distance 8.Mid-Node Offset : Ratio

13. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Aspect Ratio The aspect ratio of a QUAD element is the ratio of longest edge to shortest edge. Edge Length 1.Minimum and maximum length of the element edge. Interior Angle The min and max interior angle is calculated based on angle formed by the edges at each node of the QUAD element. Quad – Aspect Ratio, Edge Length, Interior Angle

14. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Quad – Warpage The warpage of QUAD element is calculated by splitting the QUAD into two TRIs and finding the angle between the two planes, which the TRIs form. The QUAD is then split again, this time using the opposite corners and forming the second set of TRIs. The angle between the two planes is the warp angle of the element. The aspect ratio of QUAD element is the ratio of longest edge to shortest edge.

15. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Quad - Skew The skew angle of a QUAD element is calculated by finding the minimum angle between two lines joining opposite mid-sides of the element. Ninety degrees minus the minimum angle is skew. Area 1.Area of the QUAD element. Quad – Skew, Area

16. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Quad – Mid node distance, Ratio 1.Mid-Node Offset : Distance 1.It is the offset distance of mid node from the mid position of the corresponding element edge. For example, let N1-N2 be an higher order element edge with mid node M1 and MP be the mid position of the element edge N1-N2. Here, "d" represents the Mid-Node Offset distance. 1.Mid-Node Offset : Ratio 1.It is the ratio between offset distance of mid node from the mid position of the corresponding element edge to element edge length. If EL denote the length of the element edge N1-N2, then d / El represents the Mid-Node Offset ratio.

17. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Tet – Quality measures 1.Stretch 2.Collapse Ratio 3.Tet Collapse 4.Skew 5.Aspect Ratio 6.Distortion 7.Jacobian 8.Interior Angle 9.Volume 10.Fluid - Aspect Ratio

18. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Stretch of a TET is R/L-Max). Where R is the radius of the inscribed sphere and L-Max is the longest edge of the TET. Tet – Stretch

19. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Collapse ratio Collapse ratio is the ratio between the smallest of h from each node to the longest edge of the tetrahedron. Where h is the perpendicular distance from a node to the opposite face. Collapse Ratio = h(smallest) / L(longest). Tet – Collapse Ratio, Tet Collapse Tet Collapse Tet Collapse of a TET element is minimum of (h)/(1.24 . Where h is the perpendicular distance from a node to the opposite face of the TET and A is the area of the opposite face.

20. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Tet – Skew, Aspect Ratio Skew Skew ness is the ratio between the volume of the TET element to the volume of the perfect TET element. Volume of perfect TET Element is the volume of an equilateral TET element with the same circumradius as the element. Aspect Ratio Aspect Ratio for a TET is the maximum of (h)/(1.24  Where h is the perpendicular distance from a node to the opposite face of the TET and A is the area of the opposite face.

21. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Distortion Distortion is the ratio between the smallest determinant of the Jacobian matrix at corner and mid points of Tet10 to the volume of the Tet Jacobian Jacobian is the ratio between the smallest determinant of the Jacobian matrix to largest determinant of Jacobian matrix at gauss points. Tet – Distortion, Jacobian

22. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Interior Angle Interior Angle is the angle between the edges of a triangular face of TET. Minimum and maximum value of interior angle for each TET element is calculated by considering all the four triangular faces of the TET element. Volume Volume of the TET element. Fluid - Aspect Ratio Fluid - Aspect Ratio is the ratio of the volume of the circumscribed sphere of the tetrahedron to volume of tetrahedron, normalised to the equilateral tetrahedron. Tet – Interior Angle, Tet Collapse

23. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Hex – Quality measures 1.Aspect Ratio 2.Warpage 3.Skew 4.Interior Angle 5.Volume

24. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Aspect Ratio Aspect ratio of a HEX element is defined as the ratio of the longest edge to its shortest edge Warping The face warpage of a HEX element is defined as the maximum warpage among its six faces. Each face is treated as a QUAD element. Skew The face skew angle of a HEX element is defined as the maximum skew angle among its six faces. Each face is treated as a QUAD element. Interior Angle Interior Angle is the angle between the edges of a rectangular face of HEX. Minimum and maximum value of the interior angel of each HEX element is calculated by considering all the six faces of the HEX element. Volume Volume of the HEX element. Hex - Aspect Ratio, Warping, Skew, Interior Angle, Volume

25. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Wedge – Quality measures 1.Aspect Ratio 2.Warpage 3.Skew 4.Volume

26. Copyright © 2010 Altair Engineering, Inc. All rights reserved.Altair Proprietary and Confidential Information Warp Angle The face warpage of a WEDGE element is defined as the maximum warpage among the three quadrilateral faces, each treated as a QUAD element. Aspect Ratio Aspect ratio of a HEX element is defined as the ratio of the longest edge to its shortest edge Skew The skew angle of a WEDGE element is defined as the maximum skew angle among its three quadrilateral faces and two triangular faces. Each quadrilateral face is treated as a QUAD element and each triangular face as a TRI element. Volume Volume of the WEDGE element. Wedge – Warp Angle Aspect Ratio, Skew, Volume