STAC

Stochastic Analysis Computation

Deterministic Process:

PROCESSINPUT OUTPUT

f(input) = outputf(X) = Y

X = 5 Y = 12.5

INPUT

Stochastic Process:

PROCESS OUTPUT

f(P(Inputs)) = P(Outputs)

X = P(x,s) Y = P(f(P(x,s)))

Input

Who makes the dirty job?

•It is necessary to write 100000 of input data files to have a confident variable distribution.•Send to run the program 100000 times•Read and gather the results 100000 times

Process Output

STAC

•Allows to define a probabilistic low for the input variables.•Allows to execute the batch file as many times as necessary.•Gather the most important results to be analyzed.

Kx, Ky

φ

Conductivity: Standard variation µ = 2.1E11 s = 2.1E10

φ: Standard variation µ = 100 s = 10

PROCESS :CALTEP 2000

INPUT :

OUTPUT :φ 12

Kx, Ky

φ

Define INPUT variables in SCAT:

Open the input data file

Define INPUT variables in SCAT:

Select the variable

Define INPUT variables in SCAT:

Define the Probabilistic Function

Define INPUT variables in SCAT:

Define the Probabilistic Function

Define INPUT variables in SCAT:

Define the Probabilistic Function

Define INPUT variables in SCAT:

Define the Probabilistic Function to a block variable

Define INPUT variables in SCAT:

Define the Probabilistic Function to a block variable

Define OUTPUT variables in SCAT:

Define PROCESS in SCAT:

Define the working space

Define OUTPUT variables in SCAT:

Define the batch file

Define PROCESS in SCAT:

Define some initial variable correlation

Define PROCESS in SCAT:

The GiDButton

Executing PROCESS in SCAT:

Analyzing results in SCAT:

Mobile Mean of the input variable

Analyzing results in SCAT:

Mobile Mean of the output variable

Analyzing results in SCAT:

Simple statistics of the input variable

Analyzing results in SCAT:

Simple statistics of the input variable

Analyzing results in SCAT:

Simple statistics of the input variable

Objective

Analyse the behaviour of imperfectcilyndrical shells under impact situations.

Analyse the influence of the materials in the impact problem.

Problem Definition:

300 BST rotation freeElement

330 nodes.

Impact velocity: 30 m/s Radius = 0,1 mHeight = 0,46 mThickness = 0,003 m

Constant Kinetic Energy

Geometrical imperfection:

Wrra += 0

k

ly

L

xkt

L

xitW cossencos 21

πξπξ +=

423

1.01.0

1.01.0

22

11

===

==

==

lki

ξξ

ξξ

σµσµ

Amplifyed distorsion

Computed Displacements

Imperfect Imperfect cylindercylinderdisplacementdisplacement

Perfect Perfect cylindercylinderdisplacementdisplacement

Deformed Mesh

Steel Scatter

Perfect

Imperfect

Aluminium Scatter

Perfect

Imperfect

Ant-Hill Plot for Steel Results

Imperfect

Perfectvs

Var1 =Var2 =Var3 =Radial Displacement.

1ξ2ξ

Ant-Hill Plot for Steel Results

Imperfect

Perfectvs

Mean = 0.1197Stnd. Dev.= 0.001573

Mean = 0.1006Stnd. Dev.= 0.0002145

2 Stnd. Dev. Volume

Mahalanobis distancefor Steel Results

Imperfect Perfectto ImperfectPerfect to

Ant-Hill Plot for AluminiumResults

Imperfect

Perfectvs

Var1 =Var2 =Var3 =Radial Displacement.

1ξ2ξ

Ant-Hill Plot for AluminiumResults

Imperfect

Perfectvs

Mean = 0.1232Stnd. Dev.= 0.002233

Mean = 0.1135Stnd. Dev.= 0.000444

2 Stnd. Dev. Volume

Mahalanobis distancefor Aluminium Results

Imperfect Perfectto ImperfectPerfect to

Conclusions

Is evident that the imperfect cylinder has more distortion in the impact than the perfect.

The aluminum has more distortion than the steel.

But… what if the collision is between a steel cylinder against aluminum cylinder.

Ant-Hill Plot for Perfect Steeland Perfect Aluminium Results

Perfect Steel

PerfectAluminium

vs

Mahalanobis distance for PerfectSteel and Perfect Aluminium Results

Steel Aluminiumto SteelAluminium to

Ant-Hill Plot for Imperfect Steeland Imperfect Aluminium Results

Imperfect Steel

ImperfectAluminium

vs

Ant-Hill Plot for Imperfect Steel and Imperfect Aluminium Results

Imperfect Steel

Imperfect Aluminium

vs

2 Std. Desv. Volume

Mahalanobis distance for Imperfect Steel and Imperfect Aluminium Results

Steel Aluminiumto SteelAluminium to

Conclusions

The material used to build the cylinders is relevant ONLY when the end quality of the geometry is close to the nominal shape.

In the presence of geometry uncertainty the difference in materials becomes less relevant.

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