Description: The Finite Element Method (FEM) is a numerical technique used to find approximate solutions to boundary value problems for partial differential equations. This method divides a complex domain into a finite number of simpler subdomains, called finite elements. Each element is described by shape functions that allow approximating the solution within it. The combination of these elements provides an approximate solution for the original problem. FEM is particularly useful in situations where analytical solutions are difficult or impossible to obtain. Its ability to handle complex geometries and varied boundary conditions makes it an essential tool in engineering and applied sciences. Additionally, the method is based on solid mathematical principles, such as variational calculus and functional analysis, ensuring the accuracy and stability of the obtained solutions. As technology has advanced, FEM has evolved, integrating with powerful computational tools that allow solving large-scale and complex problems across various disciplines.
History: The Finite Element Method has its roots in the 1940s when it was initially used in structural engineering. However, it was in the 1960s that it was formalized as a numerical method, thanks to the work of researchers like Ray W. Clough, who introduced the term ‘finite element’. Over the years, FEM has evolved and expanded into various fields, including fluid mechanics, heat transfer, and electromagnetism, becoming a fundamental tool in computer simulation.
Uses: The Finite Element Method is widely used in civil engineering for structural analysis, in mechanical engineering for component design, and in aerospace engineering for simulating airflow around aircraft. It is also applied in biomedicine to model the behavior of tissues and organs, as well as in the automotive industry for impact analysis and vehicle safety.
Examples: A practical example of the use of the Finite Element Method is the stress analysis of bridges, where the structure is modeled to predict its behavior under different loads. Another example is the simulation of temperature distribution in an electronic component, which helps optimize its design to prevent overheating.
