Syllabus by Blogging

Since joining the faculty at Eastchester, I've taught nonlinear structural analysis many times. The course content is shaped by what I learned, and continue to learn, from Frank, Greg, Filip, and Silvia. The blog is another outcropping of what I've learned. So I've integrated many of the posts into the course, which consists of the … Continue reading Syllabus by Blogging →

Heavy as a Chebyshev

Numerical integration, or quadrature, is essential for material nonlinear finite element formulations. Gauss, Gauss-Lobatto, or a plastic hinge approach is all you need for frame elements. And for fiber sections, midpoint integration gets the job done. Besides some highly specialized cases, there's no need to use other types of numerical integration in nonlinear structural analysis. … Continue reading Heavy as a Chebyshev →

How to Cite a Blog Post

How to cite OpenSees was one of the blog's first posts. Several posts have been made since. Most of them non-sense, but there's a couple that have enough technical content to be citation-worthy. Based on its style guide, ASCE treats blog posts like a website where you provide the author, title and publication year of … Continue reading How to Cite a Blog Post →

Its Power and Its Problem

A recent LinkedIn post by the creator of FEA Academy raised an important issue about the difference between an algorithm and an integrator. The image from the post is shown below. In other corners of the FEA world, the algorithm and the integrator are a package deal--the Newton-Raphson method is commonly understood to mean load … Continue reading Its Power and Its Problem →

OpenSees Is Simple

OpenSees, and nonlinear structural analysis in general, is a simple endeavor. It is not complicated. It does not need to be complex. Although this clip from Bull Durham, the best baseball movie of all time, refers to throwing, hitting, and catching the ball, the simplicity translates to nonlinear structural analysis. https://www.youtube.com/watch?v=PhML1WAGkCs You build the model. … Continue reading OpenSees Is Simple →

Stress Resultant Verification

Verifying material nonlinear frame element formulations is pretty difficult. There are only a handful of analytical solutions that do not rely on bilinear uniaxial constitutive response. You're much better off verifying geometric nonlinearity. However, an example based on a relatively straightforward biaxial stress resultant plasticity model has intrigued me over the years. The example, described … Continue reading Stress Resultant Verification →

Did You Pass Your Patch Test?

The patch test is one of the standard "sanity checks" of finite element implementations. To pass a patch test, an irregular mesh of elements must be able to reproduce a constant stress field. Interior nodes of the mesh should also displace according to a linear displacement field. OpenSees is not known so much for its … Continue reading Did You Pass Your Patch Test? →