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35 Years of FEA Boundary Condition Errors
I think it is important that engineers new to simulation learn a little about the history of industry applications of the finite element method. If for nothing else, then to learn a few things from us "old farts" or at least appreciate how far FEA technology has progressed.
My career in finite element analysis began in 1980 as a new grad out of UC Davis looking to "change the world!” I hoped to analyze something really exciting, but was pretty disappointed when my first project was to analyze a cantilever beam. The objective was to match stresses and displacements with classic beam theory. The software I was using at the time was STAGS (STructural Analysis of General Shells). A quick Google search (after weeding through all the deer references) finds the software is still being used at NASA Langley. To quote from the "current" STAGS user manual found online: "The earliest versions of STAGS were research-oriented, special-purpose programs that were developed on and designed to exploit the high-speed, large-problem computational capabilities of the CDC-6000-series mainframe computer systems that were the cream of the crop in the computer world during that time frame." I am sure the computing power of most smartphones and even the "dumb" ones is orders of magnitudes greater than the old CDC machines.
I was sad to learn that one of the main developers of STAGS, Dr. Charles C. Rankin, recently passed away after more than 40 years of working with finite elements. "Many of Charles’ fundamental contributions have found their way (with Charles’ cooperation) into the most widely used current commercial structural computer programs such as MSC_NASTRAN, ANSYS and ABAQUS." 1
Back to my first analysis. Since the ultimate goal for the cantilever beam model was for me to learn how to simulate a stiffened submarine hull, I was instructed to use shell elements. I was not given any instruction on how to support the beam, since this was the main objective of the learning experience. Fast forward 35 years and this is still a good test for a new analyst. It is still very easy to produce garbage even with the most sophisticated finite element software available today. The key to most finite element models, and the most common source of error, is boundary conditions. The only difference between now and 35 years ago, is that you can potentially generate significantly more detailed garbage and you get it a lot faster!
My original model required me to map out my nodes, elements, element conductivity, materials, loads and boundary conditions onto the back of a piece of used computer paper and then punch the data onto IBM punch cards (See Figure 1).
Figure 1: Keypunch Machine
It was imperative to put each correct number into the correct field (column) on the card. There was no undo button; if you made a mistake you had to essentially start over. Once completed, the stack of cards was then fed into a card reader and the analysis was run on a computer 1000 miles away from my San Diego office on a CDC Government Mainframe in Albuquerque, New Mexico. An hour or so later, I could pick-up a stack of computer printouts (Figure 2) that would come streaming out of the dedicated printer, connected by a phone line, and examine the tabular results on a node and element basis. Computer graphics were still a few years away!
Figure 2: 1980s Printer
Whether in 1980 or in 2014, the key to predicting the correct stress in the classic cantilever beam model is to make sure the boundary conditions are representative of the real problem. The most common error is over-constraint of the support. While a normal direction constraint is required for all nodes on the fixed face, applying a vertical constraint only on the bottom node allows for the Poisson-induced shrinkage of the beam to naturally occur, and eliminates the local stress singularity induced by a fully fixed constraint. A finer meshed model with the fixed constraint just creates a larger stress. Figure 3 illustrates the two modeling methods.
Figure 3: Beam Model Boundary Condition Comparison
If more detailed results at this connection are required, expanding the model to simulate the actual connection to the supporting column will yield more accurate results. With an expanded model, stresses to be used in design are extracted away from the FEA boundary condition supports.
In 1980, we had no choice but to start with simple models since they were the only ones we could solve. Every CPU second spent cost the company real cash. In 2014, the most successful analysts are still those that start with simple models that run fast and are easily checked. Simple models provide the ground work for developing error-free complex models that we can readily solve today.
I hope you find this blog, along with the historical perspective, informative. I look forward to your comments!
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