LoadControl

# LoadControl

#include <analysis/integrator/LoadControl.h>

class LoadControl: public StaticIntegrator

MovableObject
Integrator
IncrementalIntegrator
StaticIntegrator

LoadControl is a subclass of StaticIntegrator, it is used to when performing a static analysis on the FE_Model using the load control method. In the load control method, the following constraint equation is added to equation [staticFormTaylor] of the StaticIntegrator class:

\[\lambda_n^{(i)} - \lambda_{n-1} = \delta \lambda_n\]

where $\delta \lambda_n$ depends on $\delta \lambda_{n-1}$, the load increment at the previous time step, $J_{n-1}$, the number of iterations required to achieve convergence in the previous load step, and $Jd$, the desired number of iteraions. $\delta \lambda_n$ is bounded by $\delta \lambda_{min}$ and $\delta \lambda_{max}$. \[\delta \lambda_n = max \left( \delta \lambda_{min}, min \left( \frac{Jd}{J_{n-1}} \delta \lambda_{n-1}, \delta \lambda_{max} \right) \right)\]

Knowing $\lambda_n^{(i)}$ prior to each iteration, the $N+1$ unknowns in equation [staticFormTaylor], is reduced to $N$ unknowns and results in the following equation:

\[\R(\U_{n}) = \lambda_n^{(i)} \P - \f_{R}\left(\U_{n}^{(i)} \right) - \K_n^{(i)} (\U_{n} - \U_{n}^{(i)}) \label{staticFormLoadControl}\]

// Constructors

// Destructor

// Public Methods

// Public Methods for Output

The integer INTEGRATOR_TAGS_LoadControl (defined in $<$classTags.h$>$) is passed to the StaticIntegrator classes constructor. $\delta \lambda_1$ is the load factor used in the first step. The arguments $Jd$, $\delta \lambda_{min}$, and $\delta \lambda_{max}$ are used in the determination of the increment in the load factor at each step.

Does nothing.

int newStep(void);

The object obtains the current value of $\lambda$ from the AnalysisModel object. It increments this by $\delta \lambda_n$.

\[\delta \lambda_n = max \left( \delta \lambda_{min}, min \left( \frac{Jd}{J_{n-1}} \delta \lambda_{n-1}, \delta \lambda_{max} \right) \right)\]

It will then invoke applyLoadDomain(0.0, $\lambda$) on the AnalysisModel object. Returns $0$ if successful. A warning message is printed and a $-1$ is returned if no AnalysisModel is associated with the object.

int update(const Vector &$\Delta U$);

Invoked this causes the object to first increment the DOF_Group displacements with $\Delta U$, by invoking incrDisp($\Delta U)$ on the AnalysisModel, and then to update the domain, by invoking updateDomain() on the AnalysisModel. Returns $0$ if successful, a warning message and a $-1$ is returned if no AnalysisModel is associated with the object.

Sets the value of the load increment in newStep() to be $\delta \lambda$. Returns $0$. int sendSelf(int commitTag, Channel &theChannel);
Places in a vector if size 5 the value of $\delta \lambda_{n-1}$, $Jd$, $J_{n-1}$, $\delta \lambda_{min}$ and $\delta \lambda_{max}$) and then sends the Vector. Returns $0$ if successful, a warning message is printed and a $-1$ is returned if theChannel fails to send the Vector. int recvSelf(int commitTag, Channel &theChannel, FEM_ObjectBroker &theBroker);
Receives in a Vector of size 5 the data that was sent in sendSelf(). Returns $0$ if successful, a warning message is printed, $\delta \lambda$ is set to $0$, and a $-1$ is returned if theChannel fails to receive the Vector.

int Print(OPS_Stream &s, int flag = 0);

The object sends to $s$ its type, the current value of $\lambda$, and $\delta \lambda$.