What is your structural analysis model not telling you? Ramaseshan Kannan
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What is your structural analysis model not telling you?
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What is your structural analysis model not telling you?
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What is your structural analysis model not telling you?
Questions
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What is your structural analysis model not telling you?
Questions I
Why do ill-conditioning warnings arise?
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What is your structural analysis model not telling you?
Questions I I
Why do ill-conditioning warnings arise? How can Model stability analysis help us debug errors that lead to ill-conditioning?
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What is your structural analysis model not telling you?
Ill-Conditioning
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What is your structural analysis model not telling you?
Ill-Conditioning I
All FE computation done in ‘finite precision’ arithmetic real number ≈ significand × baseexponent
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What is your structural analysis model not telling you?
Ill-Conditioning I
All FE computation done in ‘finite precision’ arithmetic real number ≈ significand × baseexponent
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What is your structural analysis model not telling you?
Ill-Conditioning
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What is your structural analysis model not telling you?
Ill-Conditioning
k + k2 −k2 K = 1 −k2 k1
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What is your structural analysis model not telling you?
Ill-Conditioning
k1 + k2 −k2 K = −k2 k1 f1 k1 + k2 −k2 u1 = f2 −k2 k1 u2
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What is your structural analysis model not telling you?
Ill-Conditioning
k1 + k2 −k2 K = −k2 k1 f1 k1 + k2 −k2 u1 = f2 −k2 k1 u2 −1 u1 k + k2 −k2 f1 = 1 u2 −k2 k1 f2
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What is your structural analysis model not telling you?
Ill-Conditioning
With k1 = k2 = 10
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What is your structural analysis model not telling you?
Ill-Conditioning
With k1 = k2 = 10
20 −10 K = −10 10
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What is your structural analysis model not telling you?
Ill-Conditioning
With k1 = k2 = 10
20 −10 K = −10 10 1 1 − 10 −1 5 K = 1 1 − 10 10
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What is your structural analysis model not telling you?
Ill-Conditioning
With k1 = 0.001 and k2 = 10
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What is your structural analysis model not telling you?
Ill-Conditioning
With k1 = 0.001 and k2 = 10
10 −10 K = −10 10.0001
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What is your structural analysis model not telling you?
Ill-Conditioning
With k1 = 0.001 and k2 = 10
10 −10 K = −10 10.0001 10 −10 K ' −10 10
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What is your structural analysis model not telling you?
Ill-Conditioning
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What is your structural analysis model not telling you?
Ill-Conditioning I
Accuracy of solution depends on the ‘conditioning’ of K.
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What is your structural analysis model not telling you?
Ill-Conditioning I
I
Accuracy of solution depends on the ‘conditioning’ of K. Given by the condition number κ(K ) of the matrix κ(K ) =
λn λ1
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What is your structural analysis model not telling you?
Ill-Conditioning I
I
Accuracy of solution depends on the ‘conditioning’ of K. Given by the condition number κ(K ) of the matrix κ(K ) =
I
λn λ1
Bounded by 1 and ∞ (numerically 1016 !)
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What is your structural analysis model not telling you?
Ill-Conditioning I
I
Accuracy of solution depends on the ‘conditioning’ of K. Given by the condition number κ(K ) of the matrix κ(K ) =
I I
λn λ1
Bounded by 1 and ∞ (numerically 1016 !) Rule of thumb for solution accuracy: Number of digits of accuracy ≈ 16 − log10 κ(K )
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What is your structural analysis model not telling you?
Analysis types I I I I
Static: Ku = f . P-∆: Ku1 = f1 and (K + Kg (u1 ))u2 = f2 . Dynamic: Ku = λMu. Buckling: Ku1 = f1 and Kv = λKg (u1 )v .
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I
Idealization
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I I
Idealization Discretization
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I I
Idealization Discretization
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I I
Idealization Discretization
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I I
Idealization Discretization
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I I I
Idealization Discretization Erroneous modelling
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What is your structural analysis model not telling you?
Large Îş? Could be indicative of errors I I I
Idealization Discretization Erroneous modelling
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What is your structural analysis model not telling you?
Intuition and heuristics
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What is your structural analysis model not telling you?
Intuition and heuristics I
Traditionally: hunt for zero pivots
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What is your structural analysis model not telling you?
Intuition and heuristics I I
Traditionally: hunt for zero pivots Look for unrestrained elements
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What is your structural analysis model not telling you?
Intuition and heuristics I I I
Traditionally: hunt for zero pivots Look for unrestrained elements Run modal analysis
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What is your structural analysis model not telling you?
Intuition and heuristics I I I
Traditionally: hunt for zero pivots Look for unrestrained elements Run modal analysis
Only for singularities – not ill-conditioning!
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What is your structural analysis model not telling you?
Model Stability Analysis
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What is your structural analysis model not telling you?
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What is your structural analysis model not telling you?
Example
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What is your structural analysis model not telling you?
Example
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What is your structural analysis model not telling you?
Example Îş1 (K ) = O(1012 ) 1 2 3 4 5 6 7 8
1.001 1.001 1.001 1.001 1.001 1.001 171.788 271.649
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What is your structural analysis model not telling you?
Example
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What is your structural analysis model not telling you?
Example
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What is your structural analysis model not telling you?
Example
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What is your structural analysis model not telling you?
Example After fixing the connectivity, Îş1 (K ) = O(109 )
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What is your structural analysis model not telling you?
Causes of errors In our experience. . . I I I I I
Models imported from BIM or CAD. Releases on beams. Mixing QUAD8s and beams. Nodal connectivity errors. Constraints.
Best to keep Îş(K ) in check while model is being assembled.
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What is your structural analysis model not telling you?
In summary... I I
Necessary to ensure K is well-conditioned. Model Stability Analysis can be used to detect hidden errors that cause ill-conditioning.
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What is your structural analysis model not telling you?
Thank you.
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What is your structural analysis model not telling you?