Finite Element Analysis is simply referred to FEA, which is a simulation of the one given physical phenomenon by using FEM (Finite Element Method).
Finite Element Method is a complex numerical method by which Mathematics related problems are solved efficiently. But Finite Element Method can do much more than just solving mathematics related problems. It can be used to solve Physics related problems and even Engineering problems very quickly. This numerical method is implied in Finite Element Analysis. In FMB, laser cutting is ruling over metal integrity without raising any questionable eyebrows in case of profit. Laser cutting is usually the first step of the process before it continues down the line to undergo metal bending, metal rolling, and other types of metal fabrication in stainless steel, mild steel and aluminium.
Product designers and Engineers use it minimize the number of physical beta or prototype products. Even the required number of experiments for a product decreases when Finite Element Analysis is implied for optimizing components in the product design period to make high-quality products. And the best part is, the entire process becomes much faster than it used to be.
It is mandatory to use Mathematics to comprehensively quantify and understand a physical phenomenon like fluid and structural behavior, wave progression, cell growth in living body, thermal transport, etc. Almost all these processes are defined using PDEs or Partial Differential Equations. To solve thing kind of Partial Differential Equations with a computer, many numerical method and techniques are developed over the last few years. Among all of them, Finite Element Analysis or FEA is the most promising.
The differential equation cannot just describe the processes of nature. It can also describe the engineering mechanics and the physical phenomenon. These Partial differential equations are much complicated than regular engineering equation that determines any products rigidity, Young’s modulus dimension etc. These PDEs need to be solved in order to calculate related quantities of any structure like strains, stress, etc. so that a particular behavior of the considerate component under the specified load can be estimated.
One thing to remember that Finite Element Analysis or FEA can only give you an approximate solution to the problem at hand, and it is just a numerical approach for finding the original results of the partial differential equations.
To put it in a simple way, Finite Element Analysis is simply a prediction of how a specific part or assembly would behave under some specified conditions. There is no denying the fact that Finite Element Analysis has brought a revolution to the modern simulations software. They are a great help to manufacturers who want to find out the area of tension, the weak spots, etc. in their prototype or final production. The final result of the simulation based on Finite Element Analysis are generally depicted via a color scale which shows, for example, the pressure distribution over a physical object.
Simulations use Finite Element methods to compute the stresses and displacement in the product due to operational loads like:
- And contact between the components
How Finite Element Analysis was established?
If you want to consider any mathematical paper or documentation as the definite origin for Finite Element Analysis, the works by Courant (1943) and Schellbach (1851) is the answer of how it all started. But many believe that Finite Element Analysis has been in talks since the 16th century. They think that Euler’s works are the first chapter of today’s Finite Element Method and Finite Element Analysis.
Later, by different industries and companies, Finite Element Analysis was brought in development for addressing structural mechanics problem relevant to the civil engineering and aerospace sectors. In the mid-1950s the development for real-life use of Finite Element Analysis started through the papers by Turner, Martin, Clough, and Topp (1956), Aziz (1972), Babusuka, and Argyris (1957) show. Besides, the foundation for Finite Element Analysis was also strengthened by book written by Fix (1973), Strang, and Zienkiewicz (1971)
Stages of Finite Element Analysis
The Finite Element Analysis is comprised of 3 stages:
i) Before Processing: In this stage, analyst makes up a finite element mesh of material’s geometry & applies material’s properties, load, and boundary condition.
ii) Solution: In this part, the program derives its governing matrix equation ( Load = Stiffness X Displacement ) from product model. Then it solves for the strains, displacements, and strains.
iii) Post-Processing: Now, the analyst gets the result generally in deformed contour plots, shapes, etc. that shows how the actual result might look like. A wide range of reporting tools like text output, graphs, animations, vector plots, color contour, etc. are used to illustrate the analysis model’s behavior.
Why and where people use Finite Element Analysis?
At the beginning, Finite Element Analysis and Finite Element Method was developed for the betterment of Civil engineering and Aerospace industry. But its use has become limitless nowadays. It just started to reach towards its potential and everyone is positive that the use of Finite Element Analysis will keep increasing every day.
There are many industries that are benefiting from this numerical approach to solve problems because Finite Element Analysis is good at coupled problems like Thermo-mechanical, fluid-structure interaction, Thermo-chemo-mechanical problems piezoelectric, thermos-chemical, electromagnetics, ferroelectric, and many more relevant areas.
In short, Finite Element Analysis has at least something to offer to every sector that involves, engineering production, physics, mathematics, and relevant sectors.
Besides aeronautical and civil engineering, biochemical and automotive industries are now implementing Finite Element Analysis to design their resultant product more efficiently and faster. In any structural simulation, Finite Element Method helps a lot in producing strength and stiffness visualization and also in reducing weight, cost, and materials.
It lets you visualize where your structures bend, curve or twist, and also indicates you the distribution of stresses or displacements.
In short, these are the places where Finite Element Analysis is useful:
- Mechanical/Structural engineering design
- Manufacturing processes
- Product development
- Failure analysis investigation
- Improving the existing design’s efficiency
Limitations of Finite Element Analysis
As it was mentioned many times, Finite Element Analysis is an approximate numerical approach of solving engineering or mathematical problem. This means the result is close enough to the actual happening but not exact. The magnitude of error depends mostly on the size or type of model used for analysis.
Although approximate is not something that many manufacturers are against of, there are few industries where manufacturers want precision to take over approximate values and condition. These industries are too sensitive to be built upon any approximate value. In these cases, Finite Element Analysis won’t be the bar of reliability.
Availability of Finite Element Analysis lets the engineers obtain objectives that they otherwise couldn’t have, for example, designing modification on the highly stressed area. That’s why FEA is of importance to product designers and engineer because it saves their valuable and time and their money.