A brief look into how elements are chosen in analysis software, with some parameters involved

1. MESH QUALITY PARAMETERS
&
THEORY BEHIND PENALTY APPROACH
By
SIVA S
M.Tech Machine Design
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2. MESH QUALITY PARARAMETRS
• MESH
• QUALITY OF MESH
• PARAMETRS AFFTECTING MESH
[ACCURACY IN FEA] ∝ [MESH ELEMENT QUALITY]
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3. REASON FOR MESH QUALITY APPROACH
SPRING ELEMENTS
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4. FINNITE ELEMENT PROCEDURE - I 4

5. Terms For Defining Quality Checks On Elements
• SKEWNESS
• ASPECT RATIO
• WARPAGE ANGLE
• TAPER
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6. • SKEWNESS
Minimum angle between vector from each node to the opposing mid-
side and the vector between the 2 adjacent mid-sides at each node of
the element.
Ideal value = 0 (Acceptable < 450 )
• ASPECT RATIO =
Maximum Length Side Of An Element
Minimum Length Side Of The Element
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7. • WARP ANGLE
Angle between the normal to two planes
formed by splitting the quad element along the
diagonals.
Ideal value = 0 (Acceptable < 100 )
• JACOBIAN
It’s the scale factor arising because of the transformation of the coordinate
system
Ideal value = 1.0 (Acceptable > 0.6 )
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8. IMPROVING QAULITY OF POOR ELEMENTS
• MANUAL ADJUSTMENT
• DRAG NODE
• AUTO QUALITY IMPROVEMENT PROGRAMS
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9. What If Elements Aren’t Mannered ?
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10. QUALITY CHECKS FOR TETRA MESHING
• TETRA COLLAPSE:
Ideal Value = 1.0 (Acceptable > 0.1)
Tetra collapse = (h * 1.24) / A
• Volumetric Skew:
Ideal value = 0 (Acceptable < 0.7)
Volumetric Skew =
𝑉𝑖𝑑𝑒𝑎𝑙 − 𝑉𝑎𝑐𝑡𝑢𝑎𝑙
𝑉𝑖𝑑𝑒𝑎𝑙
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11. • Stretch:
Ideal value = 1.0 (Acceptable > 0.2)
Stretch = R * √24 / Lmax
R = Radius of largest possible sphere
inside given tetra element
• Distortion :
Ideal value = 1.0 (Acceptable > 0.5)
Distortion = | J | * VolmLCS / VolmGCS
LCS – Local Coordinate System
GCS – Global Coordinate System
• Jacobian:
Ideal value = 1.0 (Acceptable > 0.5)
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12. Other Checks for Meshing
• Element free edges
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Ex: Duplicate nodes

13. • Duplicate element, nodes
• Shell normal
• Check Mass ( Ma Vs FE Mm )
• Observe type, family and number of elements
• Request your colleague to check the model of elements
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Ex : Shell normal

14. DISCRETIZATION OF STRUCTURES TO ELEMENTS
NODES AT DISCONTINUITIES:
• Geometric
• Load
• Boundary conditions
• Material
Refinishing Mesh:
• To appx. Curved boundary of
structured.
• Places having high stress
gradient.
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15. ELEMENT ASPECT RATIO
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16. EFFECT OF ASPECT RATIO ON ACCURACY OF RESULTS
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17. THEORY BEHIND PENALTY APPROACH
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18. THANK YOU ALL
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