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This command is used to construct a StaticIntegrator object of type ArcLength. Arc-length methods are used to enable the solution algorithm to pass limit points, such as maximum and minimum loads, and snap-through and snap-back responses. At these limit points, the stability of the numerical system is dependent on whether the analysis is performed under load or displacement control. In structural analysis, these limit points are characteristic of cracking of reinforced concrete and of buckling of shells.
integrator ArcLength $arclength $alpha
(??? is this the correct order, at the workshop Frank had it different)
$arclength |
arclength value |
$alpha |
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SEE FMK
The equilibrium equation can be written in the from:
the arc-length method aims to find the intersection of the above equation with s=constant, where s is the arc-length, defined by:
and
the scaling parameter y is required because the load contribution depends on the adopted scaling between the load and displacement terms.
for the arc-length methods, one should replace the differential form of the equation for ds with an incremental form:
???
where Dl is the fixed 'radius of the desired intersection.
In the arc-length method the load parameter l becomes a variable, adding one to the n displacement variables and equations.
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