# FEM Analysis – Do not be afraid of numerical methods when calculating strength

Machines surround us from every side. Whenever anyone thought of using a branch to lift a heavy stone, he probably considered its strength. Since then, we have made great progress as humanity. At first, there were simple strength calculations with large coefficients. By learning more about phenomena inside the working material, we learned to describe them better – mathematically, of course. Machines have become less unreliable, lighter, faster. We have now reached a high level of civilizational development. By some sociologists, our civilization has been named a scientific and technical civilization. All this was possible thanks to the synergy of scientists, who observed interesting phenomena and engineers and as a result were able to properly apply them. This process is obviously not complete and is still ongoing. In practice, we are limited by the strength of materials and the general imperfection of the world. This is where FEM analysis will find its application.

*FEM Analysis, Finite Elements Analysis s
Source: https://blogs.solidworks.com/teacher/2012/07/fea-simulation-analysis-tutorial-on-frame.html*

## Computer supported …

A large part of this world are computers that have allowed you to automate some repetitive tasks. They distract us from ant-like work, pushing us in the direction of creativity. It seems that the natural consequence is using computers to construct machines. The idea arose to implement pre-existing methods for determining strength using the Finite Element Method (FEA) for short (also FEM calculations, FEM analysis). Part of this are also ways of interpreting the results, for example, effort hypotheses (Huber-von Mieses, Coulomb-Treska). For greater clarity, the software has been divided into several groups, the main of which are:

- CAD – Computer-aided design
- CAM – Computer-aided manufacturing
- CAE – Computer support for engineering analysis

## Problems with traditional methods

Prototyping and manual calculations are logical alternatives to simulation methods. I will support myself with the Aberdeen Group research “The Value of Virtual Simulation Versus Traditional Methods”. The study asked about the biggest problems with prototyping and calculations step by step.

## Prototyping – The biggest problems

*3D Printed model of turbine
*

*Source: https://3dprinterchat.com/2017/06/3d-printing-projects-for-kids/*

The following problems have been identified:

- Time needed to build a prototype – 65%
- The cost of building a prototype – 65%
- There are usually many prototypes – 50%
- Time to test the prototypes – 40%
- There are limits in prototype testing – 31%
- The prototype is not 100% corresponding to the element- 20%

## Step by step calculations

*Source: https://retirementjourney.blog/2018/02/04/indecipherable-tax-time/*

I always stress that calculations, which I call “step by step calculations” should be appreciated. There are many powerful buildings from before the time of computers, and even calculators that are living monuments of their effectiveness. Unfortunately, they are also burdened with problems through which they are being replaced faster and faster. The most important is (in reference to the same research):

- Geometry is often too complicated for manual calculations – 61%
- Big simplifications – 55%
- The time for manual calculations is usually large – 42%
- Difficult optimization (usually you have to count again) 36%

## How will simulation methods help?

Several of the aforementioned problems are unsolvable – at least at the moment. Let’s not forget that simulations are not something completely different from calculations “step by step”. Plainly, there are many more calculations, the methods are slightly different, and the computer performs them, automatically giving us results in the form of charts and 3D models. This different approach to calculations reduces or even eliminates the nuisance of some problems, and the way in which results are presented reduces the need for prototyping. But what exactly will they help us with?

a) **Prototype construction costs decrease**

After CAE calculations, we usually don’t have to build as many prototypes. Of course, sometimes we can’t avoid it, but we do more tests inside the computer. We reduce cost and time – which is often even more expensive.

b) **Time optimization related to strength analysis**

Modern CAE software is able to test many different types of geometry (various configurations), suggest shape (topology study), make changes in the project (design study) and do it on its own – all you have to do is do homework. Maybe sometimes it will take longer than the calculation on a piece of paper (in very simple constructions) – but after setting the assumptions, it no longer directly involves the constructor.

c) **Less simplification**

I do not mean simplifications of geometry here – both during normal and CAE calculations, we decide on the degree of simplification. It is about the number of phenomena operating “at once”. It is much easier to include gravity and extension in one temperature test for CAD than for manual counting.

No method of calculating strength will perfectly reflect the situation – simulations are no different. **Unfortunately, some unfair black PR and some fair criticism have accumulated around the simulation process.**

## Among others:

## I can’t cope with the simulations

This statement has an element of truth and falsehood in it every time. First of all, it depends on what simulations we are talking about. I would venture to say – “if someone knows strength calculations, he can handle numerical methods.” We also have different FEM calculation programs, maybe the one we are working on is too complicated? Maybe I didn’t get the proper training?

## I am a normal engineer, not a scientist.

There are various FEM simulation programs on the market, from high flight super programs used by several companies around the world to simple macros – designed only for some specific calculation. The program is to speed up and facilitate our work, regardless of what we do. Engineers are the largest group of recipients, which is why most programs are tailored to their needs. Of course, it takes some time to start up, but it’s not a matter of years and months – rather days and weeks.

## I calculated it manually and …

The results of simulation calculations are never compared to ordinary calculations. This usually doesn’t make sense. Sometimes a small check will not hurt, but the results of ordinary calculations will always give higher stresses than alternative static analysis of the structure in FEM. A good example is also a comparison of FEM buckling analysis with experimentally determined buckling.

On the chart we can see a difference of up to 40% – I am aware that these are glass columns, but the principle is the same. There are also studies comparing analytical methods to experimental methods – they also slightly overestimate 18.7% to 23.2% (source: “Experimental and numerical study on the behavior of axially compressed high strength steel box-columns”. Yan-BoWang, Guo-QiangLi, ChenSu-Wen, SunFei -Fei). Usually, however, it is a lesser value than when calculating in a normal way.

Source: *Experimental Verification of the Buckling Strength of Structural Glass Columns*

## What does FEM endurance analysis look like?

This element is more individual for each program, but the principle usually remains the same. The order almost doesn’t make a difference, but we must first carry out operations related to the so-called PREPROCESSING, among others – preparation of the study, later after the so-called POSTPROCESSING, for instance, processing the results – it is quite obvious: we cannot eat dinner before preparing it. An example would be FEM Static Analysis.

PREPROCESSING | Weight |

Fixations | |

Boundary conditions | |

Grid parameters | |

Material data | |

CALCULATIONS | Everything here is based on previously made decisions. |

POSTPROCESSING | Compilation of the results |

Strength check | |

Decision |

## PREPROCESSING

Let’s start from the beginning. With the help of computer modeling, a structure model is created. I assume that we have already achieved the desired level of simplification. The whole test process begins with replacing the part model with a discrete FEM model, which is in the background a system of many equations (yet without any loads). The model is divided into many “beams” that organize into finite elements. There are many types of finite elements, the most popular are tetragon and hexagon.

*Quadrilateral and Hexagon*

As you can see, the elements are solid, there are still varieties for shell simplification like for the triangle. As of now, we only have the discrete model of the part model. Let’s say it looks similar to the picture below.

*Source: https://mathematica.stackexchange.com/questions/173719/visualising-finite-element-mesh-in-3d-with-meshrefinementfunction*

## FIXATIONS

We need to map the weight and restraint pattern also called the test scenario. Let’s assume that we start with fastenings. Each attachment receives some degree of freedom (we often find the abbreviation DOF – Degree of Freedom), there are also attachments receiving several degrees at once. Each element has 6 of them – that is, it can move along and rotate around 3 axes.

*Six degrees of freedom for any stiff element*

The names of the fixtures differ between programs, the most popular is fixed geometry. Receiving all 6 degrees of freedom on the selected element.

*6 degrees of freedom were received. green arrows indicate received offsets, discs indicate gained “rotation”*

We can also pick up, let’s say, 3 degrees of freedom, leaving the possibility of sliding on the surface, without the possibility of “peeling off”

*The element can slide on the surface under the influence of force (arrows in purple), one degree of freedom of the bottom wall was taken away – as we “forbid” it to have linear movement, it cannot rotate around two axes – hence 3 DOF.*

## WEIGHTS

After thinking about it, we can take over, that practically any weight can be replaced by force. In practice, this would not be a convenient solution (a lot of conversion), so we have several shortcuts. Of course, strength remains the most popular option.

*Force added to the wall.*

A big part of the tests requires pressure loading, like strength calculations of pressure vessels.

*Open tank under pressure.*

There are also more complex weights, for example, thermal analysis loads. Just as the loads themselves are important, the way they increase is just as important. In dynamic analysis we need, for example, excitations, when doing vibration analysis.

## MATERIAL

A very important part is providing the data of the material from which we plan to make our element.

*Material data for static strength analysis, red – necessary data, blue – data improving accuracy*

There is also more complicated material data,like fatigue charts – for fatigue analysis. We also need additional factors for other calculation models.

## General comments on preprocessing

Preprocessing must accurately reflect the test conditions. The more accurately we do it, the better the results will be. Of course, there are restrictions: computer, program, method and also the criterion of meaningfulness. We should always build the “step by step” study more, and perform many iterations – at least in the beginning. We can quickly sense how the program works.

## Postprocessing

The program has conducted research and has results ready for us. It did a lot of work. My sample static test in SOLIDWORKS Simulation had 48066 equations to solve …

*Test data. SOLIDWORKS creates a file with the .out extension for each study.*

… and solves them in 2 seconds:

Unfortunately, the computer does not communicate in the way humans do, but it counts quickly so we forgive him. It will be easier to ask him what we mean. A bit like in life. The results are presented in the form of understandable charts. The stress chart is the most popular.

*Stress diagram from my research*

We can also ask for more detailed data, like strength on a given wall.

*Checking the strength of a given wall*

*The processing of results is, however, very individual for each program.*

## A few additional comments about Postprocessing

Postprocessing is a very important part, because based on the data, we decide whether we performed the test correctly and, above all, whether the tested object is safe and reliable enough. Good postprocessing is not difficult, the whole difficulty here is a good understanding of the results.

## CAE simulations. Are they worth using and why?

There is a saying that you can usually answer the questions asked in the headlines without reading them, so I leave the decisions to you. Simulations are designed to help. They do this by providing more information on a given structure before manufacture, or worse, installation and use.

*Source: https://www.engineering.com/DesignSoftware/DesignSoftwareArticles/ArticleID/14534/Engineering-Design-Platforms-and-Simulation-in-CAD-Benefit-Product-Development-Teams.aspx*

Any errors we detect at this stage are very cheap and quick to fix. Modern CAE software, which is undoubtedly SOLIDWORKS SIMULATION, for example, combines design and strength calculations in one window. In addition, it facilitates and speeds up the entire process. In addition, it moves the strength check part to the design stage. This reduces the total time it takes to produce a ready and tested design. In addition, research such as topology will allow you to optimize the shape and reduce the weight of the structure.

## Summary

My goal was to interest you in the subject of simulation. Unfortunately, I cannot say everything in one short article. I would like to invite you to solidmania.com – our blog where you will find a lot of interesting articles on many different topics, including simulation. A lot of great knowledge can also be found in the aforementioned webinars. We also run consultations and comprehensive trainings.

Author:

Piotr SZULTA | SOLIDEXPERT

CAD/SIM Technical Specialist