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Not All Elements are Created Equal

Updated: Jul 7, 2022

I posted this to LinkedIn previously (see here) and felt it should be archived here.

In short, when using elements in any finite element model you need to be aware of the limitations of the element formulation you are using. Some elements are formulated to be very accurate when solving a specific type of problem. Others are formulated to be fast and cheap (computationally) at the expense of accuracy. It is important to understand the limitations of each type of element and when they should, and shouldn't, be used.

In SAP 2000 and ETABS, we typically use shell elements to model walls and floors. Where we have complex geometry, abrupt changes in geometry, or openings, it is often necessary to incorporate triangular or trapezoidal shell elements. However, in these two programs (and likely others), triangular and trapezoidal shell elements are highly prone to shear-locking when subjected to in-plane (membrane) loading, especially where bending deformation governs the theoretical behavior.

Comparison of SAP 2000 and Fenix membrane elements

This is not a new discovery. Some folks know about this, while others do not. This information is buried in the SAP Validation Manual, and I only learned of this a few years ago. The shear-locking behavior is a result of the specific element formulation used. The particular formulation is great at predicting shear dominated behavior, but does a poor job when the system is bending dominated (in-plane).

The triangular membrane element formulation that Fenix uses (see here) incorporates three degrees-of-freedom at each node: two in-plane translation and a drilling DoF. It uses as its basis the Hu–Washizu formulation and combines both a basic and higher-order stiffness matrix. It is more computationally intensive than many other membrane formulations, but produces good results across a wide range of problems (both bending and shear dominated).

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