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Automatic Arc Length Control

An automatic arc length control strategy constitutes a very important part of the implementation of any numerical method. The program makes it possible to adaptively adjust the current arc length for a new load step depending on the course of iteration in the previous step by activating option Optimize. The program will then attempt to select a value of arc length that keeps the desired number of iterations in each load step needed for convergence - option Optim. No. of iter. in a single load step.

The next parameter driving the process of iteration is the Ratio load/displacement. This parameter represents a scalar factor, which adjusts the scales of load given by parameter λ and displacement vector u. providing this parameter is sufficiently large the analysis is essentially driven by load increment. Setting this parameter equal to 0 (default setting) we obtain so-called cylindrical ALM and the analysis will be driven by displacement increment. This approach is more stable and recommended by the authors. Nevertheless, the program allows for the optimization of this parameter by activating the option "Optimize". In such a case the current value of this parameter is set equal to the Bergan current stiffness parameter that provides a scalar measure of the degree of nonlinearity. With increasing the degree of nonlinearity this parameter is decreasing. In the vicinity of collapse load, the value of this parameter approaches zero and the solution is driven by displacement increment. This strategy thus supports the use of the cylindrical method having the Ratio load/displacement parameter equal to zero. As for the default setting, this option is turned off.

Arc-length - automatic arc length control

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