Buckling of Restrained Plates

The plate buckling analysis in a previous post demonstrated flexural buckling–definitely minimal and definitely necessary if you’re going to tackle more complex cases of plate buckling. Having passed the minimal example, Mark Denavit, a frequent collaborator, suggested I take a look at buckling of plates that are restrained on all four sides. Mark always has good … Continue reading Buckling of Restrained Plates

Minimal Plate Buckling Example

OpenSees is not built to perform linear buckling analysis. But a few years ago, Luigi Caglio shared a workaround described in this post. In the post, the example application is a frame model, but there’s no reason the approach cannot work for shell models. So, here’s a minimal working example. Consider a rectangular steel plate with simple boundary … Continue reading Minimal Plate Buckling Example

The Mechanically Separated Wall

The MVLEM element (and its SFI-MVLEM and E-SFI-MVLEM cousins) has a curious 3D implementation in OpenSees. In plane, the element is a two node link with a fiber section and some rigid beams while out of plane the element is a linear-elastic plate. The mechanics of the in-plane response are separate from the mechanics of … Continue reading The Mechanically Separated Wall

Statically Equivalent Loads

When it comes to numerical integration, OpenSees users either pay too much, or too little, attention. Me? I pay way too much attention to the topic. How else did OpenSees end up with so many integration methods for frame elements? But numerical integration is one of the concepts that users of OpenSees, or any other finite element analysis software, must understand. … Continue reading Statically Equivalent Loads

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

Section Warping Analysis

Loading a ZeroLengthSection element is the easiest approach to compute the moment-curvature and shear force-shear deformation response of fiber sections in OpenSees. However, we cannot do a section warping analysis with a zero length element like we can with non-warping sections--at least not without modifying the ZeroLengthSection element to handle seven DOFs per node. That source code modification is … Continue reading Section Warping Analysis

OpenSees Coming and Going

Years ago, one of those shows like Diners, Drive-Ins, and Dives featured a greasy spoon somewhere in middle America famous for its eggs and fried chicken meal known as the “Coming and Going”–the boundary conditions of a chicken’s life on a single plate. This quarter in Eastchester, I am teaching the introductory undergraduate course in structural analysis and the … Continue reading OpenSees Coming and Going