The Basic Natural Kernel in a Corotating Frame of Reference

Frame elements in OpenSees are formulated in a basic, or natural, system that removes rigid body displacement modes from the element displacement field, leaving only the deformational modes. The basic forces that correspond to the deformational modes depend on the element force-deformation relationship while the remaining local forces are found from rigid body equilibrium. The … Continue reading The Basic Natural Kernel in a Corotating Frame of Reference →

Nonlinear Sections, Elastic Elements

I often make seemingly minor tweaks to OpenSees--tweaks that don't usually make it into the documentation, but that in some cases could be quite useful. For example, did you know that you can create an elasticBeamColumn element by passing a section tag instead of directly specifying material and section properties--E, A, and Iz for 2D, … Continue reading Nonlinear Sections, Elastic Elements →

Shear Verse, Same as the First

In the same vein as a previous post, this post will show a basic comparison of material nonlinear displacement-based and force-based formulations with axial-flexure-shear interaction in frame elements. The timoshenkoBeamColumn element interpolates constant shear deformation along its length, along with constant axial deformation and linear curvature. Two-point Gauss-Legendre integration over the element is sufficient to … Continue reading Shear Verse, Same as the First →

Line Mesh

The DiscretizeMember function, which dates back many years, was recently superseded by the line mesh command, written by Minjie. In addition to creating boundaries for solid meshes, as shown in this post, you can use line meshes to discretize a frame member (2D or 3D) into beam-column elements--just pass the optional element type and arguments … Continue reading Line Mesh →

Repeated Section Modes

If you use a section with linear-elastic response in the displacement-based, force-based, and mixed beam-column elements in OpenSees, you will get the same response from all three elements. TrueFalseIt depends The answer is it depends on the type of "section with elastic response" you use. Also, I wouldn't include "It depends" as a possible answer … Continue reading Repeated Section Modes →

Direct Moment-Curvature

That the force-based frame element and fiber sections are in an open relationship should come as no surprise. The displacement-based and mixed frame elements can use fiber sections and all three element formulations can use stress resultant sections. While this post used a coupled stress resultant plasticity model, you can also use the section aggregator … Continue reading Direct Moment-Curvature →

There’s Three, Actually

The displacement-based and force-based formulations garner a lot of comparisons for simulating nonlinear frame response. My Google Scholar alerts tell me so. And I even wrote a post comparing the two formulations. Doc Ock from Spider-Man: Into the Spider-Verse There is a third formulation--the mixed formulation. Alemdar and White compared three frame element formulations (displacement-based, … Continue reading There’s Three, Actually →

Discretized Members Only

I wrote a DiscretizeMember procedure in Tcl many years ago--I don't know exactly when, definitely after the 1980s and definitely before moving to Eastchester. "Members Only." by The Semi-Frozen Trombone is licensed under CC BY 2.0 After carrying the function around for years, and probably spawning more variations than uniaxial Concrete models, the procedure went … Continue reading Discretized Members Only →

Global Distributed Loads

Distributed loads on frame elements in OpenSees are defined with respect to the local element axes as opposed to global axes. This choice made the implementation easy, but it can give OpenSees users more shadow work, like bagging your own groceries or pumping your own gas. When global distributed loads act on inclined elements, e.g., … Continue reading Global Distributed Loads →

A Vector in the x-z Plane

Three-dimensional frame elements require user input for the local element axes. Although the local $latex x$ axis points from node I to node J, there is no automatic way to define the local $latex y$ and $latex z$ axes, i.e., how the section axes line up with the element. In two-dimensions, this is not an … Continue reading A Vector in the x-z Plane →