Combined Loadings

I talked with a graduate student from Mechanical Engineering the other day. The student is learning OpenSees and successfully analyzed a truss. No, not that truss from Example 1.1. After showing me the truss results, the student said something along the lines of “Deflections are fine and OpenSees does a good job, but I really … Continue reading Combined Loadings →

Daisy Chains and Gaffes

When analyzing rigid bodies with multi-point constraints, one potential problem with the Transformation constraint handler is the sequencing of primary and secondary, or retained and constrained, nodes across multiple constraints. Using OpenSees to solve Problem 9.39 from J.C. Smith’s Structural Analysis is a perfect opportunity to show how defining constraints in series, i.e., daisy chaining the constraints, can knock … Continue reading Daisy Chains and Gaffes →

Bring Your Own Matrix

Getting a stiffness matrix out of OpenSees is straightforward using printA(). But what about getting a stiffness matrix into OpenSees? This is the situation I faced recently testing BennySparse with linear systems from the SuiteSparse Matrix Collection. I had no way of building an OpenSees model that could recreate those matrices. After some trial and error, I found that … Continue reading Bring Your Own Matrix →

Choose Your Own Topology

I've been working on a sparse linear equation solver. Not anything new, just implementing the methods presented by Timothy Davis in Direct Methods for Sparse Linear Systems. Why? Because I want to learn how sparse matrix solvers work. So for the sake of discussion, let's call my solver BennySparse. Aside from implementing a standalone sparse … Continue reading Choose Your Own Topology →

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 →

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 →

Invertible Does Not Mean Stable

That you can invert a stiffness matrix does not tell you everything about the numerical stability of a structural model built in OpenSees or any other finite element software. In fact, no finite element software actually forms the inverse of the stiffness matrix, but let's go with the misleading terminology anyway. Consider the beam shown … Continue reading Invertible Does Not Mean Stable →

No Reaction

As the old mantra goes, "you can displace without deforming, but you can't deform without displacing". Other than a post here and there on particle dynamics, the examples on this site deal with element deformation (or strain), which requires nodal displacement. But what about examples with elements that undergo only rigid body displacement with no … Continue reading No Reaction →

The Good, the Not So Bad, and the Full General

Just like shopping for a new refrigerator, picking a linear equation solver in OpenSees (via the system command) can lead to paralysis of choice. And while you can consult Consumer Reports for the pros and cons of refrigerators A, B, and C, the only way to figure out the pros and cons of OpenSees solvers … Continue reading The Good, the Not So Bad, and the Full General →

A Load at a Fixed DOF

If you apply a nodal load in the direction of a fixed DOF, will you get a reaction? The answer depends on which structural analysis software you use. Let's see what happens in OpenSees with a minimal working example. All we need is one fixed node and an applied load, P. This is one of … Continue reading A Load at a Fixed DOF →