Although it has its proper uses, I'm not a fan of the linear algorithm. I'm even less of a fan of modal damping. However, it's totally reasonable to use these two analysis options together--and if you do, watch out! I'll walk you through a recent encounter with this lethal combination, experienced during a live presentation … Continue reading Negative Feedback Loop

# Category: Structural Dynamics

# Get the Accel Out

In OpenSees, a UniformExcitation pattern is functionally equivalent to a regular load pattern, fitting into the framework of a time-varying scalar load factor and constant reference load vector. The scalar load factor is the input ground acceleration, $latex \ddot{u}_g(t)$, while the reference load vector is $latex {\bf P}_{ref}=-{\bf m}{\boldsymbol \iota}$ where $latex {\bf m}$ is … Continue reading Get the Accel Out

# Gimme All Your Modal Damping

The GimmeMCK integrator is one of my more useful contributions to OpenSees. This integrator overcomes the limitations of the printA command and allows you to extract the individual mass, damping, and stiffness matrices, or some linear combination therein, in order to see what's assembled in an OpenSees model or to bootstrap new functionality. While getting … Continue reading Gimme All Your Modal Damping

# More Than You or Eigen Chew

Software does exactly what you tell it to do. But problems arise when you don't know--or assume you know--what instructions you're giving. For example, many people like to use the 'fullGenLapack' eigenvalue solver in OpenSees because it will compute all N eigenpairs (eigenvalue with corresponding eigenvector) for a model whereas the default eigenvalue solver will … Continue reading More Than You or Eigen Chew

# Much Ado About Damping

I do not remember why I was searching the internet for "damping" a couple weeks ago, but I came across this document on constructing a Rayleigh damping matrix, $latex {\bf C}=\alpha {\bf M}+\beta {\bf K}$, as a linear combination of mass and stiffness matrices. Instead of taking the usual approach of specifying damping ratios for … Continue reading Much Ado About Damping

# Initial Conditions

There are a couple ways to set initial conditions for nodal displacements and velocities in OpenSees. If you look at the end of this post, you'll see the hard way to do it: set initial displacements as single point (sp) constraints in a load pattern, do one analysis step, then remove the load pattern prior … Continue reading Initial Conditions

# OpenSeesaw

A moderately frequent OpenSees question is what happens to a structural model when you apply a rotational ground motion as a uniform excitation. Sure, rotational masses will receive effective earthquake forces, but what about dynamic DOFs that are orthogonal to the rotational ground excitation, i.e., with a "moment arm"? And if there is a moment … Continue reading OpenSeesaw

# Interpolation of Ground Acceleration

There was a question on GitHub a few months about whether or not OpenSees uses linear interpolation when the analysis time step is smaller than the time step (digitization) of an input ground acceleration. This is a good question as I've used other software that does not interpolate and instead uses the acceleration of the … Continue reading Interpolation of Ground Acceleration

# The Little IDA

In Fundamentals of Structural Mechanics, Hjelmstad solves a "little" one-dimensional Boundary Value Problem (BVP) for linear-elasticity before moving on to the three-dimensional BVP, which is full of mathematical difficulties. Hjelmstad's reasoning is sound. "Some of these difficulties are of great importance, while others are simply a nuisance. Reducing the issue to its simplest case helps … Continue reading The Little IDA

# Multiple-Support Excitation

Structural systems typically have different ground accelerations at supports separated by long distances. These systems can be a single structure such as a long span bridge or multiple structures in a region. While most OpenSees analyses use uniform excitation with effective earthquake forces applied to the dynamic DOFs of the model, the framework also accommodates … Continue reading Multiple-Support Excitation