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cmp - fix example for GeneralizedAlpha #24

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12 changes: 7 additions & 5 deletions source/user/manual/analysis/integrator/GeneralizedAlpha.rst
Original file line number Diff line number Diff line change
@@ -1,24 +1,25 @@
.. _GeneralizedAlphaMethod:

Generalized Alpha Method
--------------------------------
------------------------

.. function:: integrator GeneralizedAlpha $alphaM $alphaF <$gamma $beta>

This command is used to construct a Generalized :math:`\alpha` integration object. This is an implicit method that like the HHT method allows for high frequency energy dissipation and second order accuracy, i.e. :math:`\Delta t^2`. Depending on choices of input parameters, the method can be unconditionally stable.
This command is used to define a Generalized :math:`\alpha` integration scheme. This is an implicit method that like the HHT method allows for high frequency energy dissipation and second order accuracy, i.e. :math:`\Delta t^2`. Depending on choices of input parameters, the method can be unconditionally stable.

.. admonition:: Example

1. **Tcl Code**

.. code-block:: tcl

integrator Explicitdifference
integrator GeneralizedAlpha 1.0 1.0

2. **Python Code**

.. code-block:: python

integrator('ExplicitDifference')
model.integrator('GeneralizedAlpha', 1.0, 1.0)

.. note::
* :math:` \alpha_F` and :math:`\alpha_M` are defined differently that in the paper, we use :math:`\alpha_F = (1-\alpha_f)` and :math:`\alpha_M=(1-\gamma_m)` where :math:`\alpha_f` and :math:`\alpha_m` are those used in the paper.
Expand Down Expand Up @@ -92,4 +93,5 @@ and
R_{t+\Delta t}^i = F_{t + \Delta t}^{ext} - F(U_{t + \alpha F \Delta t}^{i-1})^{int} - C \dot U_{t+\alpha F \Delta t}^{i-1} - M \ddot U_{t+ \alpha M \Delta t}^{i-1}


The linear equations are used to solve for :math:`U_{t+\alpha F \Delta t}, \dot U_{t + \alpha F \Delta t} \ddot U_{t+ \alpha M \Delta t}`. Once convergence has been achieved the displacements, velocities and accelerations at time :math:`t + \Delta t` can be computed.
The linear equations are used to solve for :math:`U_{t+\alpha F \Delta t}, \dot U_{t + \alpha F \Delta t} \ddot U_{t+ \alpha M \Delta t}`. Once convergence has been achieved the displacements, velocities and accelerations at time :math:`t + \Delta t` can be computed.

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