Heavy as a Chebyshev

Numerical integration, or quadrature, is essential for material nonlinear finite element formulations. Gauss, Gauss-Lobatto, or a plastic hinge approach is all you need for frame elements. And for fiber sections, midpoint integration gets the job done. Besides some highly specialized cases, there's no need to use other types of numerical integration in nonlinear structural analysis. … Continue reading Heavy as a Chebyshev

Plastic Rotation

Plastic rotations are a common damage measure for frame members and frequently define limit states of structural performance under seismic loading. The calculation of plastic rotations for frame elements in OpenSees is based on a decomposition of deformations in to elastic and plastic components. The elastic deformations are obtained by elastic unloading of the basic … Continue reading Plastic Rotation

Nonlinear Elements, Elastic Sections

There's very little reason to use the elasticBeamColumn element in OpenSees. Using nonlinear elements, particularly the forceBeamColumn element, with elastic sections is just as good, if not better for many reasons. Not only do force-based elements with elastic sections make the transition to material nonlinearity easy, they also facilitate debugging your model. Another reason I … Continue reading Nonlinear Elements, Elastic Sections

When a Deal Breaker Is Not a Deal Breaker

We often place too much emphasis on obtaining mathematically exact solutions for structural models. While it's important to obtain exact solutions, e.g., for element development and comparing softwares, it's not always necessary and definitely not always a deal breaker. The important thing is to know whether or not an exact solution is possible and the … Continue reading When a Deal Breaker Is Not a Deal Breaker

Rigid Joint Offsets

The geometric coordinate transformation objects handle rigid joint offsets for frame elements in OpenSees. This is nice because the code for the transformations of displacements and forces is not duplicated in the element state determinations. There are three things to keep in mind when using rigid joint offsets. First, the offsets are global with respect … Continue reading Rigid Joint Offsets