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ArcLength Class Reference#include <ArcLength.h>
Inheritance diagram for ArcLength::
List of all members.
Detailed Description
ArcLength is a subclass of StaticIntegrator, it is used to when performing a static analysis on the FE\_Model using an arc length method. In the arc length method implemented by this class, the following constraint equation is added to equation~\ref{staticFormTaylor} of the StaticIntegrator class:
\begin{equation} \Delta U_n^T \Delta U_n + \alpha^2 \Delta \lambda_n^2 = \Delta s^2 \end{equation}
where
this equation cannot be added directly into equation~\ref{staticFormTaylor} to produce a linear system of 
unknowns. To add this equation we make some assumptions ala Yang (REF), which in so doing allows us to solve a system of 
unknowns using the method of ??(REF). Rewriting equation~\ref{staticFormTaylor} as
The idea of ?? is to separate this into two equations:
\defUh{\dot{\bf U}} \defUb{\overline{\bf U}}
where now
\begin{equation} \Delta U_n^{(i)} = \Delta \lambda_n^{(i)} \Delta Uh_n^{(i)} + \Delta Ub_n^{(i)} \label{splitForm} \end{equation}
We now rewrite the constraint equation based on two conditions:
\begin{enumerate} \item {\bf 
}: assuming 
, i.e. the system is in equilibrium at the start of the iteration, the following is obtained
The question now is whether {\bf +} or {\bf -} should be used. In this class, 
from the previous iteration 
is used, if it was positive {\bf +} is assumed, otherwise {\bf -}. This may change. There are other ideas: ?(REF) number of negatives on diagonal of decomposed matrix, ...
\item {\bf 
}
assuming the constraint equation was solved at 
, i.e. 
, this reduces to
substituting for 
using equation~\ref{splitForm} this can be expressed as:
which is a quadratic in 
, which can be solved for two roots. The root chosen is the one which will keep a positive angle between the incremental displacement before and after this step.
\end{enumerate}
Definition at line 173 of file ArcLength.h.
Constructor & Destructor Documentation
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ArcLength::ArcLength (
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double arcLength,
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double alpha = 1.0 )
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ArcLength::~ArcLength (
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)
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Invokes the destructor on the Vector objects created in {domainChanged()}.
Definition at line 60 of file ArcLength.cpp. |
Member Function Documentation
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void ArcLength::Print (
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ostream & s,
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int flag = 0 ) [virtual]
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The object sends to 
its type, the current value of 
, and 
.
Reimplemented from Integrator.
Definition at line 339 of file ArcLength.cpp. |
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int ArcLength::domainChanged (
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void ) [virtual]
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int ArcLength::newStep (
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void ) [virtual]
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int ArcLength::sendSelf (
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int commitTag,
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Channel & theChannel ) [virtual]
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int ArcLength::update (
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const Vector & deltaU ) [virtual]
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The documentation for this class was generated from the following files:
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Copyright
, 
, 
, 
. To form 
, {formUnbalance()} is invoked on the object, and the 
vector is obtained from the linearSOE. This is 
and 
and updates the model with 
.
and 
. Returns 
if successful, a warning message is printed, 
is returned if {theChannel} fails to receive the 
and invokes {sendVector()} on {theChannel}. Returns 
should be equal to 
and updates the model with 
in the