Minimum Unbalanced Displacement Norm: Difference between revisions

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| style="background:yellow; color:black; width:800px" | '''integrator MinUnbalDispNorm $dlambda11 <$Jd $minLambda $maxLambda>'''
| style="background:yellow; color:black; width:800px" | '''integrator MinUnbalDispNorm $dlambda1 <$Jd $minLambda $maxLambda>'''
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|  style="width:150px" | '''$dlambda11 ''' || first load increment (pseudo-time step) at the first iteration in the next invocation of the [[Analysis Command|analysis]] command.
|  style="width:150px" | '''$dlambda1 ''' || first load increment (pseudo-time step) at the first iteration in the next invocation of the [[Analysis Command|analysis]] command.
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| $Jd || factor relating first load increment at subsequent time steps (optional, default: 1.0)
| '''$Jd''' || factor relating first load increment at subsequent time steps (optional, default: 1.0)
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| $minLambda, $maxLambda || arguments used to bound the load increment (optional, default: $dLambda11 for both)
| '''$minLambda, $maxLambda''' || arguments used to bound the load increment (optional, default: $dLambda1 for both)
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THEORY:
THEORY:


The load increment at iteration i, dLambda1(i), is related to the load increment at (i-1), dLambda1(i-1), and the number of iterations at (i-1), J(i-1), by the following:
The load increment at iteration i, <math>d\lambda_{1,i}</math>, is related to the load increment at (i-1), <math>d\lambda_{1,i-1}</math>, and the number of iterations at (i-1), <math>J_{i-1}</math>, by the following:


:<math>d\lambda_{1,i} = d\lambda_{1,i-1}\frac{J_d}{J_{i-1}}</math>  
:<math>d\lambda_{1,i} = d\lambda_{1,i-1}\frac{J_d}{J_{i-1}}</math>  
In Load Control the time in the domain is set to <math>t + \lambda_{t+1}</math> where,
:<math> \lambda_{t+1} = \max \left ( \lambda_{min},  \min \left ( \lambda_{max},  \frac{\text{numIter}}{\text{lastNumIter}} \lambda_{t} \right ) \right ) </math>


   
   

Latest revision as of 00:52, 31 August 2010



This command is used to construct a StaticIntegrator object of type MinUnbalDispNorm.

integrator MinUnbalDispNorm $dlambda1 <$Jd $minLambda $maxLambda>
$dlambda1 first load increment (pseudo-time step) at the first iteration in the next invocation of the analysis command.
$Jd factor relating first load increment at subsequent time steps (optional, default: 1.0)
$minLambda, $maxLambda arguments used to bound the load increment (optional, default: $dLambda1 for both)


EXAMPLE:


integrator MinUnbalDispNorm 0.1;


THEORY:

The load increment at iteration i, <math>d\lambda_{1,i}</math>, is related to the load increment at (i-1), <math>d\lambda_{1,i-1}</math>, and the number of iterations at (i-1), <math>J_{i-1}</math>, by the following:

<math>d\lambda_{1,i} = d\lambda_{1,i-1}\frac{J_d}{J_{i-1}}</math>


Code Developed by: fmk

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