Force-Based Beam-Column Integration Options

I like numerical integration because it allows you to do a lot of interesting things with force-based frame elements--so much more than simulating the response of reinforced concrete moment frames. Numerous numerical integration options are available in OpenSees, so in 2011 I wrote and uploaded to the OpenSees wiki a PDF summarizing those options. According … Continue reading Force-Based Beam-Column Integration Options →

The Basics of Frame Element Localization

Those strain softening constitutive models we like to use for concrete can lead to material nonlinearity that isolates, or localizes, in a single element or single integration point of your model. The resulting global response becomes non-objective, non-unique, or mesh-dependent. The objective of this post is to show the localization problem then describe solutions that … Continue reading The Basics of Frame Element Localization →

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 →

Integration Points with Negative Weight

A colleague in Eastchester once told me that faculty have three, maybe four, good ideas over their career. In other words, a faculty member could have over a hundred papers, but there's only three or four underlying concepts. Perhaps it was "two, maybe three", but you get the point. Playing with integration points and weights, … Continue reading Integration Points with Negative Weight →

More Is Not Always Better

I sometimes run across simulations where frame member response is computed using displacement-based beam-column elements with more than two Gauss points per element. These elements require at least two Gauss points to ensure a complete solution and to capture the exact solution for a linear-elastic, prismatic member. While it is well known that you can … Continue reading More Is Not Always Better →

Better Late than Never

Frame finite elements abound in OpenSees, but something very useful has always been missing--a linear-elastic beam element with moment releases. Sure, you can define two nodes at the release location and use the equalDOF command; however, that can be error prone and you're at the mercy of the constraint handler. On the positive side, this … Continue reading Better Late than Never →

A Tale of Two Element Formulations

The question of whether to use the force-based or displacement-based formulation for material nonlinear frame analysis is one that comes up a lot. The answer depends on a few factors, mostly the material and the element length. To get a sense of the basic issues, I will compare the two element formulations with a numerical … Continue reading A Tale of Two Element Formulations →

OpenSees Shells by the Seashore

Other than state-of-the-art material and geometrically nonlinear frame element formulations, it's fair to say OpenSees is not known for its breadth of structural finite elements like quads, bricks, and shells. There are solid elements for geotechnical applications and fluid elements for fluid-structure interaction via the PFEM, but what's the story on shell elements in OpenSees? … Continue reading OpenSees Shells by the Seashore →

Behind the Elastic Interior

If VH1 expanded its list of the top one hit wonders of the 2000s to include journal articles in structural engineering, Scott and Fenves (2006) would be right up there with James Blunt and Gnarls Barkley. Actually, Google Scholar puts the article up there with some pretty nice company. Like all journal articles, there's something … Continue reading Behind the Elastic Interior →