Most structural earthquake engineering deals with staged analyses of built infrastructure in one way or another. In the most common scenario, we apply gravity loads to a structural model, get the model in equilibrium, then simulate the model response to earthquake loading. Analysis of structural systems and components during construction is also important. Temporary construction … Continue reading Going Through Stages
Category: Nonlinear Analysis
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
Norms and Tolerance
Convergence tests in OpenSees measure how close the algorithm is to finding equilibrium at a time step. Several convergence tests are available, and they all operate on the linearized system of equations that is solved at every equilibrium iteration within a time step $latex {\bf K}_T \Delta {\bf U} = {\bf R}$ where $latex {\bf … Continue reading Norms and Tolerance
Don’t Try This at Home
The central difference method is an explicit integrator that forms a linear combination of the mass and damping matrices to advance the solution to the next time step. So, if the mass matrix is lumped and there's no damping, or only mass-proportional damping, the left-hand side matrix is diagonal. Then, you can solve the system … Continue reading Don’t Try This at Home
It’s Not Load Control
The static integrators in OpenSees, including displacement control, arc length, and minimum unbalanced displacement norm (MUDN), are based on an incremental-iterative framework. After an initial load increment, each integrator imposes a constraint on the change in load factor at subsequent equilibrium iterations within a pseudo-time step. Displacement control calculates the change in load factor necessary … Continue reading It’s Not Load Control
Load Patterns and Time Series
In nonlinear structural analysis, loads add together, just not the load effects. So, the total mechanical load applied to a structural model can be expressed as the sum of time-varying load vectors. $latex {\bf P}(t)={\displaystyle \sum_{i=1}^N} \lambda_i(t){\bf P}_{ref,i}$ Each load vector is the product of a time-varying scalar function, $latex \lambda(t)$, and a non-time-varying reference … Continue reading Load Patterns and Time Series
Sensitivity Training
Sensitivity of structural response with respect to modeling parameters provides search directions for gradient-based algorithms in reliability analysis, optimization, and system identification. In addition to these applications, stand-alone sensitivity analysis gives useful information about the effect of parameters on the structural response. There are three methods to compute response sensitivity for nonlinear, path-dependent analysis of … Continue reading Sensitivity Training
Every Ending Is a New Beginning
Simulation of structural response to sequential hazards, e.g., fire following earthquake or tsunami following earthquake, is something OpenSees can handle. But suppose you want to look at different tsunami scenarios after a single earthquake. Tsunami loading occurs over a few seconds where the preceding earthquake lasted a minute or two. Do you want to repeat … Continue reading Every Ending Is a New Beginning
OpenSees Fire v2.0
OpenSees modules for thermal loading and thermo-mechanical behavior were developed by Usmani et al in the early 2010s. This was the first foray for OpenSees outside its earthquake engineering comfort zone and highlighted the benefits of an open, collaborative software framework--an opportunity for the research community to share modeling methodologies, develop new applications, and ensure … Continue reading OpenSees Fire v2.0
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