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

# Category: Structural Dynamics

# 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, $latex {\bf C}=\alpha {\bf M}+\beta {\bf K}$. But instead of taking the usual approach of specifying damping ratios for exactly two frequencies of vibration, the document describes … 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

# That’s a Large Mass

After cutting through all the spam, you'll find some good posts on the OpenSees message board. In one such post, Ahmet Alper Parker asked about the large mass method (LMM) and if it can be implemented in OpenSees. I was not familiar with the LMM, so Ahmet pointed me to this paper. The basic idea … Continue reading That’s a Large Mass

# Absolutely, It’s Relative

One of the most frequently asked OpenSees questions is whether node recorders record absolute or relative displacement (relative to the ground) when a model is subjected to a uniform excitation. There's several approaches to find the answer to this question. One solution is to apply a simple uniform excitation--like a constant ground acceleration--to an SDF … Continue reading Absolutely, It’s Relative

# The Rayleigh Quotient

Eigenvalue analysis wasn't giving me what I wanted the other day. So, to make a long story short, I decided to try Rayleigh's method. I won't go through all the details of Rayleigh's method, but the basic idea is you can obtain a very good approximation of the fundamental frequency of a structural model by … Continue reading The Rayleigh Quotient