Non-Convergence Is Not Structural Collapse

Legend has it that some published research results based on nonlinear dynamic analysis--incremental dynamic analyses, seismic fragility curves, Monte Carlo simulations, etc.--considered a non-convergent OpenSees model to indicate structural collapse or failure. Let's think about this for a minute. Here is the displacement response in two orthogonal directions at the top of a nearly 50 … Continue reading Non-Convergence Is Not Structural Collapse

Verifying Will Never Be Easy

A previous post compared the natural periods computed by OpenSees for a relatively simple one-story, one-bay, elastic frame to published ETABS results. Many easy to make modeling choices (mass distribution, rigid joint offsets, relative stiffness, etc.) led to "incorrect" periods. The "correct" modeling choices gave periods from OpenSees that were very close to ETABS--close enough … Continue reading Verifying Will Never Be Easy

The Stiffness Matrix Isn’t Everything

After several deliveries of graduate level courses in linear and nonlinear structural analysis, I have started to think that we over-emphasize the stiffness matrix in linear structural analysis. And this emphasis can lead to conceptual difficulties in nonlinear structural analysis. The steps to a linear analysis are presented as: Form the stiffness matrixForm the load … Continue reading The Stiffness Matrix Isn’t Everything

Two Paths You Can Go By

I am confident we can use OpenSees to solve every truss, beam, and frame problem from any statics or structural analysis textbook as well as every single degree-of-freedom and rigid shear frame problem from a structural dynamics textbook. We can also solve any reasonable problem from a finite element textbook. My confidence starts to wane … Continue reading Two Paths You Can Go By

Finite Differences

A previous post showed how to compute response sensitivity by the DDM, or direct differentiation method. Comparisons with finite difference calculations verified that the DDM results were correct. In this post, I'll dig a little deeper into finite differences. The advantage of the finite difference method (FDM) is it will work for any model parameter--you … Continue reading Finite Differences