Two-Dimensional Meshing

Although the material and element models are there, OpenSees is not well known for solid finite element analysis. Creating a good mesh is key to solid FEA and there aren't many meshing tools implemented in OpenSees. The OG block2D and block3D commands work fine, but you have to manually join or tie adjacent meshes with … Continue reading Two-Dimensional Meshing →

Trying to Get a Reaction

OpenSees does not compute reactions automatically because this can be a time consuming process--OpenSees assembles reactions over all nodes in a model, not just over the nodes that are constrained. When performing response history analysis, assembling reactions is likely not something you want or need to do at every time step. You probably just want … Continue reading Trying to Get a Reaction →

Like Spinning Nodes

After posting on reasons that the solution to Ax=b fails, I realized I omitted an important case: truss nodes in a frame model. Although this post might be a stretch for an LBU (least bloggable unit), the blogging equivalent of an LPU, there are important factors to consider for structural models comprised of truss and … Continue reading Like Spinning Nodes →

Failure to Solve

Solving a system of simultaneous linear equations, canonically referred to as solving Ax=b in math speak, is at the heart of every equilibrium solution algorithm for nonlinear analysis. In the context of OpenSees, A is the effective tangent stiffness matrix, x is the vector of displacement increments, and b is the residual force vector. However, … Continue reading Failure to Solve →

Verifying Ain’t Easy

I've posted a few modeling challenges on frame analysis (strongback, Ziemian, and stability) and soil-structure interaction. However, I recently accepted a challenge from George Chamosfakidis to see if OpenSees can give the same periods and mode shapes reported in the ETABS verification example shown below. Published verification examples typically just show the "correct" result and … Continue reading Verifying Ain’t Easy →

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 →

Make Room for Storage

In a previous post, I showed how equation numberers can reduce the bandwidth of the tangent stiffness matrix. In addition to reducing the solution time for linear systems of equations, a smaller bandwidth reduces the data required to store the tangent stiffness matrix. To discuss matrix storage in this post, I'll use the frame model … Continue reading Make Room for Storage →

Reduce Your Bandwidth

For large structural models, the solution to $latex {\bf K}_T\Delta {\bf U}={\bf R}$ can be the computational bottleneck during an analysis. Although computing speed and algorithms to solve $latex {\bf K}_T\Delta {\bf U}={\bf R}$ are very good, you still want to make sure the solution happens as quickly as possible, particularly when inside the double … Continue reading Reduce Your Bandwidth →

Closing the Loop on Direct Assembly

All structural engineering students learn the direct assembly method, where you fix all degrees of freedom (DOFs) in a structural model, then impose a unit value of displacement at and in the direction of the $latex j^{th}$ DOF in order to get the $latex j^{th}$ column of the stiffness matrix from the fixed-end forces of … Continue reading Closing the Loop on Direct Assembly →

Most Solvers Can Be Marplots

Have you ever tried to replicate the familiar beam stiffness coefficients $latex 12EI/L^3$, $latex 6EI/L^2$, $latex 4EI/L$, and $latex 2EI/L$ (there's a poem about them here) by imposing unit displacements and rotations at fixed supports? It should be one of the first sanity checks you make when using or developing new structural analysis software. You … Continue reading Most Solvers Can Be Marplots →