# How Accurate is Your Finite Element Analysis – Part I

Accuracy is a relative term. When taken in context with Finite Element Analysis (FEA), it could be in comparison to a theoretical calculation, other numerical methods or physical measurements on prototypes. Errors in FEA can be classified under three categories, namely:

1. Improper understanding of the physical phenomena or inappropriate choice of analysis
2. Modelling strategies not in alignment with objectives of FEA
3. Lack of understanding of the limitations and strengths of FEA

Let us take the example of two plates welded together as shown in Fig. 1.

A Simple theoretical calculation would reveal that the shear stress along the smallest throat area of the weld, as shown by the 45 degree line, can be calculated easily.

When we try and replicate the same problem using FEA, the following aspects are introduced:

1. One of the Forces (on the face) is replaced by a constraint to introduce reaction, thereby loading the structure in equilibrium condition (a pre-requisite for obtaining a non-singular solution)
2. Since the analysis results have to be compared with analytically calculated results, the throat area of the weld needs to be modelled with the shear section defined explicitly
3. Contact is established between the plate faces
4. Loading is done one the free face in the in-plane direction, with a pressure loading (for accurate work-done calculation intrinsic to FEA that is better than nodal force application with a point loading approximation)

When we analyze the condition with the boundary conditions as stated above, we get the stress and deflections as shown in Figs. 2 and 3 shown below.

If we try to understand this response (in terms of deflections and stresses), we realize that the bending component arises out of the bending moment due to the line of action of the force being away from the axis of loading.  This is a consideration that we would have normally ignored when doing the manual calculation.

If we were to replicate the analytical calculations in the FEA study, we would have to introduce restraints on the top fibre of the top plate and the bottom fibre of the bottom plate to arrest out-of-plane movement.  This effectively prevents bending and enforces in-plane loading only that forms the basis of the analytical calculation.

When these approximations are introduced into the FEA, the theoretical calculations and FEA results are comparably within limits of accuracy that is acceptable.

Imagine if the loading is cyclical with a tensile mean.  Then, there will be inplane stresses that would influence the mean while the bending would influence the fluctuating component.  This is a consideration that would never have been evident if the FEA had not been performed.

What is the benefit of this kind of an exercise?

Firstly, it helps us to streamline our FE analysis procedures and ratify our approach towards an accurate simulation.  Secondly, the underlying assumptions made in hand-calculations are re-visited along with the validity of the same.  This is important, as we move one step closer to real-world simulation.

A good correlation to an analytical solution is the first step that builds confidence in the simulation process.  Once this is established, complexity of the analysis can be increased to ascertain the influence of each of the complexity in terms of its sensitivity to the desired solution.  This helps us in augmenting our designs with better methods and a higher level of refinement in design parameters, leading to optimal designs improving reliability and confidence in design performance,

If this exercise had not been done, we would not have known the influence of the bending component that could have proven to be life-threatening in real-world situation.

Next Part of this series would deal with more interesting examples that provide us with insights into rightful simulations for accurate FEA…..  Stay tuned…

#### Natarajan Ramamoorthy

Design Professional with almost 3 decades of experience working with numerous companies, providing designs for new products, VAVE on existing products, conducting Design Audits and Dimensional Management programs. Teaching Finite Element Analysis, Geometric Dimensioning & Tolerancing (GD&T), Tolerance Stack Up Analysis for well over 2 decades. Certified ASME GDTP Technologist. Education: MSME from The University of Toledo, Toledo, OH, USA Past: Consultant, Ford Motor Company, Dearborn, MI, USA

#### +Natarajan Ramamoorthy

• brokedownsystem

The issue with all of this is time…most people are work don’t have the luxury of time and budget to do iterative investigations. You’d also probably get ridiculed for turning what may look like a simple question into a science project.

I wish there was an easier way for software to account for “real-world behavior” without manual inputs from the user. Better yet, a Star Trek holodeck that magically simulates reality.

But…until that day, FEA is the tool that we have available.