Displacement Control: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
{{CommandManualMenu}} | {{CommandManualMenu}} | ||
This command is used to construct a DisplacementControl integrator object. In an | This command is used to construct a DisplacementControl integrator object. In an analysis 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. | ||
{| | {| | ||
| Line 14: | Line 14: | ||
| '''$dof''' || degree of freedom at the node, valid options: 1 through ndf at node. | | '''$dof''' || degree of freedom at the node, valid options: 1 through ndf at node. | ||
|- | |- | ||
| '''$incr''' || first displacement increment <math>\Delta | | '''$incr''' || first displacement increment <math>\Delta U_{\text{dof}}</math> | ||
|- | |- | ||
| '''$numIter''' || the number of iterations the user would like to occur in the solution algorithm. Optional, default = 1.0. | | '''$numIter''' || the number of iterations the user would like to occur in the solution algorithm. Optional, default = 1.0. | ||
| Line 41: | Line 41: | ||
where <math>F(U_{t+\Delta t})\!</math> are the internal forces which are a function of the displacements <math>U_{t+\Delta t}\!</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. | where <math>F(U_{t+\Delta t})\!</math> are the internal forces which are a function of the displacements <math>U_{t+\Delta t}\!</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. Linearizing the equation results in our well known: | ||
:<math> K_{t+\Delta t}^{*i} \Delta U_{t+\Delta t}^{i+1} = | :<math> K_{t+\Delta t}^{*i} \Delta U_{t+\Delta t}^{i+1} = \left ( \lambda^i_{t+\Delta t} + \Delta \lambda^i \right ) F^{ext} - F(U_{t+\Delta t})</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: | 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: | ||
Revision as of 00:18, 12 March 2010
- Command_Manual
- Tcl Commands
- Modeling_Commands
- model
- uniaxialMaterial
- ndMaterial
- frictionModel
- section
- geometricTransf
- element
- node
- sp commands
- mp commands
- timeSeries
- pattern
- mass
- block commands
- region
- rayleigh
- Analysis Commands
- Output Commands
- Misc Commands
- DataBase Commands
This command is used to construct a DisplacementControl integrator object. In an analysis 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_{\text{dof}}</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_{t+\Delta t})\!</math> are the internal forces which are a function of the displacements <math>U_{t+\Delta t}\!</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. Linearizing the equation results in our well known:
- <math> K_{t+\Delta t}^{*i} \Delta U_{t+\Delta t}^{i+1} = \left ( \lambda^i_{t+\Delta t} + \Delta \lambda^i \right ) F^{ext} - F(U_{t+\Delta t})</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