Finite Element Analysis (FEA)
An understanding of structural dynamics is very important to sound Finite Element Analysis (FEA). We have been performing FEA analysis for over 30 years and in most cases we have used experimental data to guide our modeling. While our engineers have had undergraduate and graduate courses in FEA, it is the years of modeling and analysis of existing structures that has taught us the most by forcing a thoughtful analysis of the key structural dynamics and then going through the process of making adjustments to boundary conditions, expanding the dynamics of the model in places, and making simplifications and approximations where possible.
We perform many Dynamic Analyses using FEA using various forcing functions (including time variant) with both modal superposition and numeric integration. For example, we looked at stress due to measured time domain wind loads on giant heliostatic solar arrays.
Much of our FEA work has been for high-resolution fabrication and inspection equipment for the semiconductor and biotech industries for static, dynamic, and thermal finite element analysis. The image below is of an FEA model of a high resolution optical inspection tool.
The animations above represent an engine/generator/skid system, and is a good example for discussion. The upper image is from a finite element analysis of the system. The lower trace is the actual mode shape representation from the original experimental modal analysis (see Vibration Induced Fatigue). We used this mode shape, and dynamic testing, to guide the construction of our FEA model and to validate the FEA model of the original system. We then had confidence that the validated FEA model could be used to model various structural modification options to reduce both the inertial forces associated with the resonant motion and the modeled stress levels associated with the persistent fatigue cracks on the skid and generator housing. Using the validated FEA model we found a set of structural modifications that pushed the modeled critical resonances away from the operating speed and greatly reduced both the vibration and modeled stress levels. The modifications were fabricated and installed on the real physical system. Dynamic tests were performed on the system to ensure that the modifications were working as expected and matched the modified FEA model. They did, solving the fatigue cracking problem on the 1st try. Considering the down time that could have occurred had our client used a trial and error approach to the structural modifications, this method ( using Dynamic Testing, FEA development and verification, modification and repeat dynamic testing) saved much time, cost, and effort.
In the above example, an Engine/Generation set system was showing cracking of large frame members and also cracking of the generator housing. We performed Modal Analysis Testing to show that the system had a resonance at the operating speed and a mode shape, as well as an ODS Shape, that involved the generator and frame deforming in a way that would cause large strain at the failure locations. With this analysis, we understood why these areas had fatigue cracks.
The system was tested and found to match closely with the FEA predictions. No failures have since been reported and none are expected.
Again, experimental modal analysis and dynamic testing of a physical system is always used to "mold" a finite element model (FEA) to represent the important dynamics aspects of the actual physical system. Creating an FEA model to represent a physical system without modal testing is dangerous because the FEA model will always look "good" but will likely radically misrepresent the most important dynamics of the system. This is because actual physical boundary conditions are so hard to determine without modal and dynamics testing. It is also the case that it is hard work for the FEA modeler to put in the detail of the important boundary conditions necessary to have a hope of getting realistic and useful results. Performing a modal analysis first can tell the experienced FEA modeler HOW to start the modeling process and where to pay attention to which boundary conditions. This can save valuable time and effort in the modeling process.
Over the years we have learned the importance of getting the boundary conditions right, and how to modify the model to make it more realistic when some structural resonances and mode shapes do not agree with testing. We know how to deal with getting consistent units of force, mass, and displacement, and most important of all, we know when to trust (and not trust) the output of the FEA software and how to apply it to system design; these are skills necessary for making finite element analysis really useful in yielding sound structural modification decisions.
The animation below is a modal analysis representation of a 6 story building shaken by a multi-ton piece of process equipment located on the 5th floor (represented as the red elements with large exaggerated motions to make the floor system deformations visible).
We developed an FEA model for this 6 story building which was guided by our on-site experimental modal analysis, many dynamic stiffness tests, and ODS testing. We evaluated structural modifications that included major stiffening members to achieve the desired floor vibration levels. We evaluated custom vibration isolation options for mounting of the vibration source on the 5th floor. The most cost effective solution, however, was the use of tuned reaction masses (TRMs).
Although FEA is becoming more commonplace as FEA capabilities are bundled into 3D modeling programs, these modeling capabilities are useful only when well understood, but are usually quite limited compared to industry standard stand alone FEA packages. This is particularly true for dynamic analysis.
Modeling dynamics in FEA can be a great design tool when the FEA model is well understood and has been validated through either actual experimental testing (see Modal analysis and Vibration Testing), numerical or analytic modeling. Once an FEA model of an existing system is shown to capture the fundamental aspects of the structural dynamics, modification to the FEA modal can be made to experiment with different design options. This is very helpful in reducing prototype iterations and saving valuable engineering time and resources.
We often come into a project after the first few prototypes have not performed as expected. We have found that this is often caused by designers relying too much on FEA results without the skills needed to really know what the important boundary conditions are and how to get them modeled properly.
When we help the engineering team get off to a sound start in their modeling, prototyping and testing, the project will have the best chance at a smooth and successful progression to final product.
We plan on updating the web site periodically to include examples of our work. Our extensive Client List represents hundreds of projects, some involving days of work, others lasting several months, over the last 30+ years. Our website is put together by our engineers and has been evolving slowly since 2006, as we find the time to work on it.