Convergence of a solution algorithm typically means your model satisfies equilibrium and compatibility for the current applied loads and any nonlinear response. But there are pathological cases where the algorithm converges while the model remains in a state that violates equilibrium or compatibility. A simple case (brought to my attention by Chen Fei) involves a … Continue reading Pathological Convergence
Tag: Force-based element
Apples and Oranges
Good articles on finite element formulations combine accessible theory with reproducible examples. One such article, Alemdar and White (2005), balances theory and examples for distributed plasticity frame element formulations quite well. I never did more than skim the article and give indirect, second hand citations over the years. So, when I recently rolled up my sleeves … Continue reading Apples and Oranges
Getting the Digits
In a recent post, I pointed out that the LobattoBeamIntegration class uses only ten, instead of 16, significant figures for the locations and weights of the integration points. Those six missing digits made for a perfectly fine demonstration of how to use the isclose function for verification. But, in the bigger picture, omitting six significant … Continue reading Getting the Digits
Is It Close Enough?
The locations and weights for Gauss-Lobatto beam integration, the de facto beam integration for force-based elements, are hard-coded in the OpenSees source code. For most cases in the LobattoBeamIntegration class, the locations and weights are written to only ten significant figures instead of 16 or more. Although I am certain that leaving six sig-figs on … Continue reading Is It Close Enough?
Beam With Hinges Interior Redux
When it was but a wee blog, I wrote a post expressing second thoughts on how I presented the elastic interior of the beamWithHinges element in Scott and Fenves (2006). The post had a lot of words, but no figures or examples. So, let's try again. Consider a simple span comprised of one beamWithHinges element, … Continue reading Beam With Hinges Interior Redux
Could Not Invert Element Flexibility
Due to inversion of section stiffness to flexibility, then inversion of element flexibility to stiffness, the force-based frame element implementation in OpenSees is finicky, to say the least. A common error message spawned from the force-based element is "could not invert flexibility..." You will see the same message many times, but, ultimately, you will get … Continue reading Could Not Invert Element Flexibility
Shutting Off the Containment Unit
If you've used OpenSees--even if you're a geotech--you've used the force-based element. When Remo implemented the force-based element, it was the only material nonlinear frame element available in OpenSees (G3 at the time); thus, the original name nonlinearBeamColumn. Only after a standard displacement-based frame element (dispBeamColumn) was added did we change the name from nonlinearBeamColumn … Continue reading Shutting Off the Containment Unit
Pruning OpenSees
Most OpenSees pull requests add to the code base. Often incremental and sometimes innovative, the new additions keep OpenSees moving forward, offering something for everyone. But it's rare that we remove code. Although it would be great to purge OpenSees of Concrete23 and all its unused variations, to prune code in frequently used OpenSees classes … Continue reading Pruning OpenSees
Force-Based Element Moment Release
The common approach to adding a moment release at the end of a force-based frame element is to define an extra node then use the equalDOF command to constrain all but the released rotational DOFs. Although this approach is cumbersome, it is fine as long as the element lies within a global plane (X-Y, Y-Z, … Continue reading Force-Based Element Moment Release
A Nod to Backward Compatibility
I didn't want to do it, but I imagined an OpenSees user somewhere out there converting OpenSees Tcl scripts to OpenSeesPy--either manually line by line or using a converter script--and ending up with lines of code that look something like this: ops.section('Fiber',5) ops.patch(...) ops.layer(...) # tag I J secI lpI secJ lpJ E A I … Continue reading A Nod to Backward Compatibility