A previous post compared the natural periods computed by OpenSees for a relatively simple one-story, one-bay, elastic frame to published ETABS results. Many easy to make modeling choices (mass distribution, rigid joint offsets, relative stiffness, etc.) led to "incorrect" periods. The "correct" modeling choices gave periods from OpenSees that were very close to ETABS--close enough … Continue reading Verifying Will Never Be Easy
Category: Linear Analysis
The Stiffness Matrix Isn’t Everything
After several deliveries of graduate level courses in linear and nonlinear structural analysis, I have started to think that we over-emphasize the stiffness matrix in linear structural analysis. And this emphasis can lead to conceptual difficulties in nonlinear structural analysis. The steps to a linear analysis are presented as: Form the stiffness matrix Form the … Continue reading The Stiffness Matrix Isn’t Everything
Three-Dimensional Meshing
Two previous posts showed how to use Minjie's meshing functions to create line meshes for beam-column elements and 2D meshes for solid elements. This post will complete the trilogy by showing how to make a 3D mesh for solid elements. The bar shown below is the same model used in the post on 2D meshing. … Continue reading Three-Dimensional Meshing
Line Mesh
The DiscretizeMember function, which dates back many years, was recently superseded by the line mesh command, written by Minjie. In addition to creating boundaries for solid meshes, as shown in this post, you can use line meshes to discretize a frame member (2D or 3D) into beam-column elements--just pass the optional element type and arguments … Continue reading Line Mesh
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
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