Its Power and Its Problem

A recent LinkedIn post by the creator of FEA Academy raised an important issue about the difference between an algorithm and an integrator. The image from the post is shown below. In other corners of the FEA world, the algorithm and the integrator are a package deal--the Newton-Raphson method is commonly understood to mean load … Continue reading Its Power and Its Problem →

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 →

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 →

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 →

Better than Ideal Conditions

In simulating the nonlinear response of structural models, the Newton-Raphson algorithm converges quadratically as the iterations approach equilibrium at a time step. Quadratic convergence means the error at the current iteration is less than some constant times the square of the error at the previous iteration, e.g., the error is on the order of $latex … Continue reading Better than Ideal Conditions →

Incompetence, Not Malice

"Never attribute to malice that which can be explained by incompetence" is a form of Hanlan's razor, an aphorism that explains many actions in academia and elsewhere. For example, we often perceive omissions of important details in published work as intentional acts to prevent reproduction of the research. In some cases, this is true, while … Continue reading Incompetence, Not Malice →

Algorithmic Limerick

There once was a post-doc named Dave,Who ran OpenSees in his cave.Non-convergence, 'bout to miss dinner,He switched the algorithm to 'Linear'.Just think of all the trouble he saved. Although I changed the name and circumstances to protect the guilty, I have known more than one person who, when faced with convergence problems in OpenSees, decided … Continue reading Algorithmic Limerick →

Non-Convergence Does Not Mean OpenSees Crashed

I once had the following conversation with a concerned user (CU) of OpenSees: CU: "I was running a response history analysis, then all of a sudden OpenSees crashed." PD: "Really, it crashed? Did you get the blue screen of death?" CU: "No. The analysis stopped and I saw 'Failed to converge'. It crashed." PD: "Oh, … Continue reading Non-Convergence Does Not Mean OpenSees Crashed →