Sensitivity Training

Sensitivity of structural response with respect to modeling parameters provides search directions for gradient-based algorithms in reliability analysis, optimization, and system identification. In addition to these applications, stand-alone sensitivity analysis gives useful information about the effect of parameters on the structural response. There are three methods to compute response sensitivity for nonlinear, path-dependent analysis of … Continue reading Sensitivity Training

Every Ending Is a New Beginning

Simulation of structural response to sequential hazards, e.g., fire following earthquake or tsunami following earthquake, is something OpenSees can handle. But suppose you want to look at different tsunami scenarios after a single earthquake. Tsunami loading occurs over a few seconds where the preceding earthquake lasted a minute or two. Do you want to repeat … Continue reading Every Ending Is a New Beginning

OpenSees Fire v2.0

OpenSees modules for thermal loading and thermo-mechanical behavior were developed by Usmani et al in the early 2010s. This was the first foray for OpenSees outside its earthquake engineering comfort zone and highlighted the benefits of an open, collaborative software framework--an opportunity for the research community to share modeling methodologies, develop new applications, and ensure … Continue reading OpenSees Fire v2.0

The Linear Algorithm Strikes Again

This post on the OpenSees message board reminded me of another reason not to use the Linear algorithm, even when you have a linear model. Some elements need that second iteration in order to record all of their response. Not only shellMITC4 mentioned on the message board, but also the beloved forceBeamColumn. If you define … Continue reading The Linear Algorithm Strikes Again

Ordinary Eigenvalues

There are three applications of eigenvalue analysis in structural engineering. Vibration analysis and buckling analysis involve generalized eigenvalue analysis. OpenSees does vibration eigenvalue analysis pretty well, but does not perform buckling eigenvalue analysis--although you might be able to fake the geometric stiffness matrix for simple frame models. The third application of eigenvalue analysis is ordinary … Continue reading Ordinary Eigenvalues

Variations on Modified Newton

Solving residual equilibrium equations at every time step in a response history analysis can make the definition of "Modified Newton" ambiguous. Is it (a) the tangent stiffness at the start of the analysis (the initial stiffness) or (b) the tangent stiffness at the start of each time step? In OpenSees, the Modified Newton algorithm implements … Continue reading Variations on Modified Newton

Most Solvers Can Be Marplots

Have you ever tried to replicate the familiar beam stiffness coefficients $latex 12EI/L^3$, $latex 6EI/L^2$, $latex 4EI/L$, and $latex 2EI/L$ (there's a poem about them here) by imposing unit displacements and rotations at fixed supports? It should be one of the first sanity checks you make when using or developing new structural analysis software. You … Continue reading Most Solvers Can Be Marplots

A Marathon, Not a Sprint

When tasked with developing an OpenSees model for simulating the nonlinear dynamic response of, let's say, a multi-story reinforced concrete frame, you may be tempted to go straight to force-based frame elements with fiber sections comprised of Concrete23 and Steel08 material models. This sprint to the finish line will undoubtedly lead to an analysis that … Continue reading A Marathon, Not a Sprint

One Iteration of a Second Order Analysis

I was recently asked if one Newton iteration of a second order analysis will give the same results as a first order analysis. This is a good question, and the answer depends on what you're after. I will explain the answer using "Benchmark problem Case 2" from Chapter C of the AISC Steel Manual Commentary. … Continue reading One Iteration of a Second Order Analysis

Meshing for Column Loads

For material nonlinear analysis of frame models, you can improve the computed response by using more displacement-based elements or more integration points in a force-based element. The material nonlinearity occurs inside the basic system, also known as the natural system or the kernel. To capture geometric nonlinearity due to large displacements, you have to go … Continue reading Meshing for Column Loads