Category: Nonlinear Analysis

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 →

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 →

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 →

Start with the Correct Static Resisting Force

Thanks to my involvement with OpenSees, I have been asked to review several manuscripts on nonlinear dynamic structural analysis. It's always wonderful to see what other researchers are up to and how they use OpenSees or other software to achieve their research objectives. A brief overview of the governing dynamic equilibrium equation, i.e., the equation … Continue reading Start with the Correct Static Resisting Force →

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 →