Category: Nonlinear Analysis

Ways to Analyze This

A previous post challenged readers to analyze a simple frame model subjected to static loads. The model had material nonlinearity via tension-only diagonal cables and geometric nonlinearity via the P-Δ effects in the columns. The Challenge Despite these rather simple nonlinearities, analysis of the frame for the given vertical and lateral loads will fail using the default analysis options … Continue reading Ways to Analyze This →

Positive OpenSees Contact

Flipping through J.C. Smith’s Structural Analysis textbook, I’m confident OpenSees can handle every problem. Same goes for any other textbook on structural analysis. However, I totally paused on Problem 9.34 as it hinted at contact nonlinearity. The cantilever and the simple span have flexural stiffness EI=5120 kip-ft2, something in the ballpark of W6x12 steel members, but fudged to … Continue reading Positive OpenSees Contact →

A Model of Inconsistency

Except for matrix storage schemes, I can explain every high level analysis piece of OpenSees with a simple two DOF spring model. The model has three springs, each with bilinear force-deformation response. This model first appeared in Scott and Fenves (2010) and then in a post to demonstrate what happens when you use an inconsistent tangent with Newton-Raphson and … Continue reading A Model of Inconsistency →

Buckling of Restrained Plates

The plate buckling analysis in a previous post demonstrated flexural buckling–definitely minimal and definitely necessary if you’re going to tackle more complex cases of plate buckling. Having passed the minimal example, Mark Denavit, a frequent collaborator, suggested I take a look at buckling of plates that are restrained on all four sides. Mark always has good … Continue reading Buckling of Restrained Plates →

Minimal Plate Buckling Example

OpenSees is not built to perform linear buckling analysis. But a few years ago, Luigi Caglio shared a workaround described in this post. In the post, the example application is a frame model, but there’s no reason the approach cannot work for shell models. So, here’s a minimal working example. Consider a rectangular steel plate with simple boundary … Continue reading Minimal Plate Buckling Example →

Long Term Column Loading

Practically all analyses of reinforced concrete columns in OpenSees assume the loading is short term--concrete as strong as it was at 28 days out of the hopper. Depending on what you're doing, not accounting for long term load effects, i.e., concrete creep and shrinkage, may not be a big deal. But the effects of creep … Continue reading Long Term Column Loading →

Murum, cura te ipsum

OpenSees has its fair share of element implementations that are computationally inefficient. Fortunately, most of those elements are never used. But among elements that are used, SFI-MVLEM is the undisputed champion. Whereas the standard MVLEM element uses a uniaxial material in each fiber, the SFI-MVLEM element accounts for the interaction of axial and shear stress ($latex \sigma_{11}$ … Continue reading Murum, cura te ipsum →

Secant Accelerated Newton Algorithm

I do not consider myself an expert with numerical methods. I know just enough to be dangerous, and root-finding algorithms is one of the subjects where I pose a threat. OpenSees uses root-finding algorithms like Newton-Raphson and Modified Newton to find the nodal response for which equilibrium is satisfied at every analysis time step. No … Continue reading Secant Accelerated Newton Algorithm →

Static Analysis with Uniform Excitation

The UniformExcitation defines reference nodal loads in proportion to the mass (nodal plus element contributions), multiplied by negative acceleration, which is specified in a time series. There's nothing inherent in its implementation that ties the UniformExcitation to only dynamic analysis and earthquake excitations. So, if I had known sooner that the UniformExcitation load pattern works … Continue reading Static Analysis with Uniform Excitation →