Displacement Control: Difference between revisions
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If we write the governing finite element equation at <math>t + \Delta t\!</math>as: | If we write the governing finite element equation at <math>t + \Delta t\!</math>as: | ||
:<math> R(U^{t+\Delta t}, \lambda^{t+\Delta t}) = | :<math> R(U^{t+\Delta t}, \lambda^{t+\Delta t}) = \lambda^{t+\Delta t} F^{ext} - F(U^{t+\Delta t}) \!</math> | ||
Revision as of 00:09, 12 March 2010
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This command is used to construct a DisplacementControl integrator object. In an anslysis step with Displacement Control we seek to determine the time step that will result in a displacement increment for a particular degree-of-freedom at a node to be a prescribed value.
| integrator DisplacementControl $node $dof $incr <$numIter $minLambda $maxLambda> |
| $node | node whose response controls solution |
| $dof | degree of freedom at the node, valid options: 1 through ndf at node. |
| $incr | first displacement increment <math>\Delta U_0</math> |
| $numIter | the number of iterations the user would like to occur in the solution algorithm. Optional, default = 1.0. |
| $minLambda | the min stepsize the user will allow. optional, defualt = <math>\Delta U_{min} = \Delta U_0</math> |
| $maxLambda | the max stepsize the user will allow. optional, default = <math>\Delta U_{max} = \Delta U_0</math> |
EXAMPLE:
integrator DisplacementControl 1 2 0.1; # displacement control algorithm seking constant increment of 0.1 at node 1 at 2'nd dof.
THEORY:
If we write the governing finite element equation at <math>t + \Delta t\!</math>as:
- <math> R(U^{t+\Delta t}, \lambda^{t+\Delta t}) = \lambda^{t+\Delta t} F^{ext} - F(U^{t+\Delta t}) \!</math>
where <math>F(U)\!</math> are the internal forces which are a function of the displacements <math>U\!</math>, <math>F^{ext}\!</math> is the set of reference loads and <math>\lambda\!</math> is the load multiplier. This equation represents n equations in <math> n+1</math> unknowns, and so an additional equation is needed to solve the equation.
- <math> K_{t+\Delta t}^{*i} \Delta U_{t+\Delta t}^{i+1} = R_{t+\Delta t}^i</math>
For displacement control we introduce a new constraint equation in which in each analysis step we set to ensure that the displacement increment for the degree-of-freedom <math>\text{dof}</math> at the specified node to be:
- <math> \Delta U_\text{dof} = \text{incr}\!</math>
MORE TO COME:
Code Developed by: fmk