Finite element method (FEM) - definition
Finite element method (FEM) - definition
Finite element method (FEM) is a numerical technique for solving partial differential equations, used to analyse complex physical phenomena such as stress mechanical, heat flow, electromagnetic fields, acoustics or fluid dynamics. It involves the discretisation of a continuous computational region into a finite number of smaller, simple sub-areas - so-called finite elements - in which the solution functions are approximated in a local way, usually by basis functions.
The basic idea of FE is to transform the equations describing a given phenomenon into a system of linear or non-linear algebraic equations that can be solved using numerical methods. The process involves a geometric modelling step, the definition of material properties, the determination of boundary conditions and loads, and then the generation of an element mesh. This mesh consists of elements with a defined shape (e.g. triangles, quadrilaterals, cubes) that share nodes and cover the entire area under analysis.
In each element, an approximate form of the solution is assumed, allowing the continuous problem to be reduced to a discrete one and solved iteratively or directly. The denser and more homogeneous the mesh, the more accurate the representation of the actual distribution of physical quantities, albeit at the cost of greater computational resources. FEM allows the analysis of non-linear and dynamic phenomena in areas with irregular geometry and boundary conditions that are difficult to capture analytically.
The finite element method is used in mechanical engineering, construction, electrical engineering, aeronautics, biomedicine and the design of mechatronic systems. It enables verification of designs at the virtual stage, prediction of the behaviour of structures under different conditions and optimisation of their structural and operational parameters. Today's CAE (Computer-Aided Engineering) environments offer integrated Tools for conducting FEA analyses taking into account coupled multi-physics phenomena.
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