# Finite Element Analysis method

## 1) Introduction to Finite Element Method

• ### What is the Finite Element Method?

Finite elements method is a very common approach used these days by engineers, designers; architects… It is a powerful numerical method that is used in solving complicated problems of both mathematical physics, and engineering. The Finite Element Method is usually used in problems that are related to certain fields such as structural analysis, heat transfer, mass transport and other fields. So what is the history of this method?

The idea and the concept of the Finite Element approach are much older than we think. It dates back to the early years of the 1940’s. One of the very first if not the first founder of the Finite Element Method was a Russian structural engineer named Alexander Pavlovich Hrennikoff. He developed an idea and an approach that would help him solve complex elasticity and structural analysis problems in civil engineering. People who are unfamiliar with advanced mathematical systems may have a problem understanding what the Finite Element Method is and what its basics are; however, Alexander Pavlovich identified the essential characteristic of this approach as a mesh discretization of a continuous domain into a set of discrete sub-domains.

• ### Why is the Finite Element Method useful?

In the 20’s century, the FEM was considered to be a revolutionary idea and a tool that would help engineers solve civil and aeronautical problems. Why is the Finite Element Method is considered to be so useful?  FEM has so many benefits such as:

• It allows engineers to accurately represent a complex geometry.
• It easily allows designers to represent the total solution.
• It allows engineers to capture local effects.
• It improves the design process.
• ### How can it be applied?

First, it is important to know that the engineers who design for example a bridge must know how the structure will behave under different loads. The equation of the distributional structural stresses is well known for engineers. However, they cannot be directly solved for a complicated shape such as a bridge. Finite elements method makes this possible by dividing the complex shape into an equivalent network of smaller and simple shapes. These shapes are called the finite elements and the pattern is called the finite element mesh. The designer first chooses what the finite elements will look like, squares, triangles, lines… The next step is the proper choice of the number of elements in the mesh; the more elements, the more accurate the results are going to be.

## 2) Introduction to Finite Element Analysis (FEA)

• ### what is Finite Element Analysis?

Finite Element Analysis is the simulation of a physical phenomenon using the FEM. This process can be achieved by using a computer and a CAD software such as Abaqus software. So in conclusion, Finite Elements Analysis or FEA is just an advanced version of the Finite Element Method.

• ### Applying FEA to a real case

This assembly is a Mold for a composite material (aluminum and carbon fiber), and it will be put in an oven as part of the process of creating the composite material.  As we all know, when things are exposed to high heat such as in our case to 650 °C, they delate. However, the material that delates inside the mold, has nowhere to go.  Hence, it goes back to the middle part creating compressive stress which is necessary in order to have the perfect amount of aluminum and carbon fiber. For a designer, the goal is to accurately find the stresses and loads necessary in order to eliminate the excess amount of aluminum. However, such a calculation by hand is probably impossible. That is where FEA comes in handy. Using a CAD software such as Abaqus, the mold will be divided into finite elements mesh such as this:

After the software finishes making its calculations using advanced algorithms and Artificial intelligence, it is possible to accurately know the von Mises stresses and strains that are necessary in order to eliminate the extra aluminum.

Applying FEA to any problem will help engineers and designers to solve problems and find solutions with a great accuracy without being worried about creating prototypes.

• ### Benefits of Finite Elements Analysis

Using Finite Elements Analysis brings a lot of benefits such as:

• Allowing designers to virtually test their designs.
• Allowing designers to solve problems without creating prototypes using a CAD model as a testing prototype.
• Allowing designers to test car crashes, in order to validate the pedestrians and the drivers’ safety.
• Allowing designers to predict and locate where a stress is concentrated, and strains and displacements for complicated structures.
• Allowing the calculation of dynamic properties.
• Allowing solutions for complex problems.
• Allowing an increase in the productivity.
• Allowing companies to profit more by minimizing the number of prototype iterations
• ### Disadvantages of Finite Element Analysis

Finite elements analysis is not immune to drawbacks. In fact, using this technique may lead to some challenges and problems such as:

• If the results are taken blindly without double checking by testing an actual prototype, it may lead to serious problems.
• The efficiency and accuracy of the analysis heavily depend on the input.

## 3) Conclusion

In conclusion, the FEA method is a great approach in finding solutions to complex and advanced problems that the regular human brain cannot solve on its own. However, this technique is not perfect and not fully optimized, as the results are not 100 percent accurate. Therefore, they should not be taken blindly. Although by dividing an object into many small finite elements, the result can be close to reality; however, this will take more time and thus will cost more money. However, these small drawbacks pale in comparison to the many advantages that FEA and FEM offer to the engineering designers.