Hallo,
es gibt hin und wieder bei Stressberechnungen die Fehlermeldung, dass kein genaues Ergebnis im betreffenden Lastfall erreicht wurde, durch Iteration.
Was genau passiert da technisch im Hintergrund?
Iteration
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Bschwe
- Beiträge: 3
- Registriert: Mo 13. Nov 2023, 05:49
Re: Iteration
Typically these types of programs determines a residual, the difference between the external energy vector and the internal energy vector, for each loadstep. Theoretically the system reaches equilibrium when the difference of these equals zero. Another method is to study the change in displacement between two load steps, where equilibrium is reached when the change in displacement equals zero.
Due to various reasons, the convergence of this residual can never reach exactly 0 because the program uses a "linear" approximation in each step (newton rhapson, arc-length method, picard etc...). Hence why a tolerance has to be defined (default is 0.1%) when the equilibrium is "good enough".
When the calculations cant converge, perhaps because of poor boundary conditions, or geometrically nonlinear nonsense, the program will keep iterating until the maximum amount of allowed iterations has been reached, and will subsequently warn the user that the residual never reached the defined tolerance, so the results shouldn't be blindly trusted as the system is techniqually not in the defined window of equilbrium.
Due to various reasons, the convergence of this residual can never reach exactly 0 because the program uses a "linear" approximation in each step (newton rhapson, arc-length method, picard etc...). Hence why a tolerance has to be defined (default is 0.1%) when the equilibrium is "good enough".
When the calculations cant converge, perhaps because of poor boundary conditions, or geometrically nonlinear nonsense, the program will keep iterating until the maximum amount of allowed iterations has been reached, and will subsequently warn the user that the residual never reached the defined tolerance, so the results shouldn't be blindly trusted as the system is techniqually not in the defined window of equilbrium.