It is fairly well known that you can use a single force-based element to simulate the material nonlinear response of a frame member. Likewise, using a corotational mesh of displacement-based elements is an effective approach to simulate combined material and geometric nonlinearity. A previous post looked at geometric nonlinearity with linear-elastic response in a single … Continue reading One Is All You Need
Tag: Frame elements
It Takes Two
While it might be advantageous for some modes of response in some solid finite element formulations, using a single integration point in a frame element is not OK because the element needs to integrate quadratic polynomials--something you just can't do with one integration point. The result of using one integration point is generally pretty bad … Continue reading It Takes Two
One and Only One
Two element formulations in OpenSees--forceBeamColumnCBDI and mixedBeamColumn--are capable of handling geometric nonlinearity within the basic system, i.e., P-little-delta effects. The CBDI formulation, described in Neuenhofer and Filippou (1998), approximates the transverse deflection using Lagrange polynomials fit through the curvature at each integration point. Due to the added computational expense and coding details, the forceBeamColumnCBDI element … Continue reading One and Only One
Converging to Something
Is it better to have converged and lost than never to have converged at all? The displacement-based and force-based frame elements are both distributed plasticity formulations--just one is way better at simulating the spread of plasticity than the other. Despite this fairly well known fact, I still see people use four, five, six, or more … Continue reading Converging to Something
Transformation Cross-Training
Athletes often cross-train in secondary activities in order to improve performance in their primary sport. For example, football players may practice ballet in order to improve their flexibility and endurance. Using OpenSees, you practically have to be a mathlete to understand the geometric transformation in three dimensions. But instead of fumbling your way through space … Continue reading Transformation Cross-Training
The Basic Natural Kernel in a Corotating Frame of Reference
Frame elements in OpenSees are formulated in a basic, or natural, system that removes rigid body displacement modes from the element displacement field, leaving only the deformational modes. The basic forces that correspond to the deformational modes depend on the element force-deformation relationship while the remaining local forces are found from rigid body equilibrium. The … Continue reading The Basic Natural Kernel in a Corotating Frame of Reference
Nonlinear Sections, Elastic Elements
I often make seemingly minor tweaks to OpenSees--tweaks that don't usually make it into the documentation, but that in some cases could be quite useful. For example, did you know that you can create an elasticBeamColumn element by passing a section tag instead of directly specifying material and section properties--E, A, and Iz for 2D, … Continue reading Nonlinear Sections, Elastic Elements
Shear Verse, Same as the First
In the same vein as a previous post, this post will show a basic comparison of material nonlinear displacement-based and force-based formulations with axial-flexure-shear interaction in frame elements. The timoshenkoBeamColumn element interpolates constant shear deformation along its length, along with constant axial deformation and linear curvature. Two-point Gauss-Legendre integration over the element is sufficient to … Continue reading Shear Verse, Same as the First
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
Repeated Section Modes
If you use a section with linear-elastic response in the displacement-based, force-based, and mixed beam-column elements in OpenSees, you will get the same response from all three elements. True False It depends The answer is it depends on the type of "section with elastic response" you use. Also, I wouldn't include "It depends" as a … Continue reading Repeated Section Modes
Portwood Digital 