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

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