Here are six advantages to this technique. It is usually used when a math equation is too complex to be […]. Name required. Email will not be published required.
Notify me of follow-up comments by email. Notify me of new posts by email. RSS - Posts. Metanav IEEE. Engineers can use these FEM to reduce the number of physical prototypes and run virtual experiments to optimize their designs.
Complex mathematics is required in order to understand the physical phenomena that occur all around us. These include things like fluid dynamics , wave propagation, and thermal analysis. Analyzing most of these phenomena can be done using partial differential equations, but in complex situations where multiple highly variable equations are needed, Finite Element Analysis is the leading mathematical technique. The beginnings of FEA date back to the famous mathematician Euler, in the 16th century.
However, a more rigid definition of "FEA" traces the first mention of the method back to the works of Schellbach in Finite Element Analysis was a process developed for engineers by engineers as a means to address structural mechanics problems in civil engineering and in aerospace. This practical intention of the methodology meant that from the beginning, these methods were designed as more than just mathematical theory. By the mids, the techniques of FEA had become advanced enough that engineers could start using it in real-world situations.
These programs are usually integrated into computer-aided design CAD software, making it much easier for engineers to go from design to running complex structural analysis. To run an FEA simulation, a mesh is first generated, containing millions of small elements that make up the overall shape. This is a way of transcribing a 3D object into a series of mathematical points that can then be analyzed.
The density of this mesh can be altered based upon how complex or simple a simulation is needed. Calculations are run for every single element or point of the mesh and then combined to make up the overall final result for the structure.
Since the calculations are done on a mesh, rather than the entirety of a physical object, it means that some interpolation needs to occur between the points. These approximations are usually within the bounds of what's needed. The points of the mesh where the data is known mathematically are referred to as nodal points and tend to be grouped around boundaries or other areas of change in an object's design.
The importance of FEA lies in its ability to take a complex design and offer insight into its efficiency and robustness of the design. With FEA, engineers can gain early information on system failures and improper design techniques. The finite element method involves constructing a digital mesh of the design. This design comprises of innumerable smaller elements. We can then map data for each of the finite elements. This breaks a large-scale equation down into multiple, smaller equations for each element.
These equations then combine to give a picture of the dynamics acting on the design. The equations usually required for this kind of calculation are often partial differential equations. In FEA, engineers can tweak the prediction accuracy of a complicated domain to maintain focus on the core problem. For instance, in an FEA of a human leg, they could focus prediction accuracy on the stresses acting on the knee during impact exercise.
FEA allows engineers to prototype a design in action without the need to create a physical working model. The nature of FEA offers a few more advantages.
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