Minimal Random Process Example

I know just enough about random vibrations and ground motions to be dangerous. I would like to become less of a liability on these topics, so bear with me on this post. OpenSees has two time series for random processes, both implemented by Terje Haukaas. A DiscretizedRandomProcess uses random variables to construct a time series from filtered unit … Continue reading Minimal Random Process Example →

Damping Is a Sensitive Subject

Dynamic response sensitivity analysis by the direct differentiation method (DDM) works pretty well in OpenSees, minus a couple limitations. First, not all element and material models implement the methods necessary to compute response sensitivity with respect to model parameters. And second, even fewer element and material models implement the methods necessary to compute the sensitivity … Continue reading Damping Is a Sensitive Subject →

A Return to FORM

The structural reliability modules Terje Haukaas implemented in OpenSees comprised one of the last groups of commands to be ported from Tcl to Python. So, performing reliability analysis in OpenSeesPy has been slow to catch on. But the porting is done and there are some slight differences between Tcl and Python. This post shows basic … Continue reading A Return to FORM →

Monte Carlo Simulation with OpenSeesMP

The parallel computing capabilities of OpenSeesSP and OpenSeesMP are easily confused. OpenSeesSP runs your script on a single processor with the other processors awaiting instructions on what to do. OpenSeesSP is ideal for assigning subdomains of a large model to each processor. The main processor, processor 0, directs traffic and solves the governing equations of … Continue reading Monte Carlo Simulation with OpenSeesMP →

The Toy Reliability Problem

In Fundamentals of Structural Mechanics, Hjelmstad uses the "little BVP" to introduce boundary value problems. Chopra uses a two-story rigid shear frame throughout Dynamics of Structures. And in Structural and System Reliability, Der Kiureghian uses a "toy problem" for various types of reliability analyses. The toy reliability problem is defined by two random variables with … Continue reading The Toy Reliability Problem →

Material Testing with White Noise

Pushes, pulls, and cyclic strain histories of increasing magnitude are solid approaches to testing the stress-strain response of material models. But I'm not convinced these tests will hit every code block of a material model implementation. I mean, have you seen all the nested if-statements and uninitialized local variables that went into Concrete23? Although I … Continue reading Material Testing with White Noise →

The Sensitivity Is in the Details

Although the Hardening and Steel01 uniaxial materials can be calibrated to give the same response, the DDM response sensitivity with respect to the same parameter can be different due to how the material models are implemented. Consider the truss model from a previous post on minimal DDM examples. The stress-strain response shows the elastoplastic tangent … Continue reading The Sensitivity Is in the Details →

Minimal DDM Examples

Although it was the subject of my first journal article and has been a welcome diversion since, other than one post, the direct differentiation method (DDM) has not seen much action on the blog. With the DDM, you can compute accurate and efficient derivatives of the structural response with respect to various model and load … Continue reading Minimal DDM Examples →

Monte Carlo Simulation

The uncertainty associated with a finite element analysis is as important, if not more important, than the results of the analysis itself. Thanks to Terje Haukaas, OpenSees has several modules for finite element reliability analysis: FORM, FOSM, SORM, and several other methods to quantify uncertainty. Unfortunately, those methods have not yet made their way into … Continue reading Monte Carlo Simulation →