#### How accurate is Finite Element Analysis (FEA) Simulation?

We are often asked by clients on how accurate FEA is and the reply to this simple question is actually not easy. We hope this article will give a better understanding of the abilities and limitations of FEA’s accuracy.

A few decades back, the manual hand calculation was the common tool for structural design work. However, given the complexity of numerous engineering challenges in sectors such as Aerospace, Civil, and Offshore & Marine, the FEA method was created to match those complex needs.

As mentioned in our introduction to FEA article, FEA is a numerical method that solves complex problems with approximate solutions. While the technology might appear modern to many, FEA has been around way longer than you would think. Over the last half a century, the method has been researched extensively and with methodologies and algorithms constantly evolving and refined to provide better and reliable answers.

FEA at its most basic is a tool to simulate physical reactions. Given that the correct input such as load or boundary condition is represented appropriately, the results that one can achieve from FEA while not 100% accurate, is reliable within a certain percentage of error.

Analytical vs Numerical Method

There are generally three methods to solve structural problems: Analytical, Numerical and Experimental. Given the latter method generally being the most resource intensive, the analytical and numerical methods are more commonly applied during the design phase and before any experimental testing. In this section, we will look more into when to choose the analytical or numerical method.

The following is a simple quick exercise one can use to compare and validate results between the analytical and numerical method (FEA).

A simple cantilever beam with one fixed end and a point load at the opposite end. We will perform both methods to determine the maximum deflection in the beam.

Point Load,  P = 1000 N
Beam Length, L = 0.3 m
Width of Beam, b = 0.05 m
Height of Beam, h = 0.05 m
Young’s Modulus,  E = 2.07×1011 N/m2
(Carbon Steel)

Numerical Method (FEA)

Max Deflection = 0.0854 mm

Analytical Method
2nd Moment of Area, I = 5.208×10-7 m4
Max Deflection, = 0.0835 mm

 Analytical FEA Simulation Similarity Max Deflection 0.0835 mm 0.0854 mm 97.7 %

With the simple beam design, both methods are able to provide an answer with high percentage similarity.

The situations in which the different methods should be used can be categorized into the following:

1. For non-complex models (such as the example we just went through) with simple geometry, boundary condition and loads, in most cases can be solved using the analytical approach. The traditional hand calculation will prove sufficient to understand the problem.
2. For more complex models, where either the analytical approach becomes too tedious or is impossible to solve with, the numerical method will be able to provide a reliable approximation of the problem.

Conclusion

So back to the original question: How accurate is FEA simulation?

We would say that FEA is sufficiently accurate and has been an effective tool for the engineering industry to simulate numerous complex structural problems, and reduce the number of physical prototyping and manual calculations. That being said, FEA results are still an approximation and will benefit from comparing results with other methods such as physical experiment.

Lastly, the integrity of the FEA results also heavily depends on the individuals performing the analysis. Here at NAC Consultancy, our consultants have numerous years of experience in Analytical, Experimental and Numerical methods to ensure that the correct parameters have been input and the calculations are valid.

In a future article, we will discuss these parameters and how they affect the FEA results. Matt Goh Consultant NAC Consultancy Pte Ltd