Finite Element Analysis (FEA) is a numerical method used to solve problems which are intractable, meaning they cannot be solved analytically. It is implemented by simulating relationships between forces and deflections of components in a structure subjected to an applied load or loads. This blog post will explain its different applications.
How FEA Works
FEA employs matrix mathematics that uses finite difference and finite element methods to find solutions for both static and dynamic problems. While the term “finite element analysis” may connote the idea of limited elements with a large number of nodes, this is not always the case with modern systems software in which each node could be assigned two degrees-of-freedom (DOFs).
In order to make this clear, the term “simulation” is often used instead of “analysis” (even though the word is used in both). FEA is also used to solve problems that have become intractable, irrespective of whether or not they’re “numerically stable.”
What Are Finite Elements? How Do They Work?
Finite elements are simplified models of a structure and its components. The geometric details are approximated by linear or piecewise-linear functions referred to as stiffness matrix. A unique characteristic of finite elements is that they provide finite element discretization, meaning the model parameters such as mass and stiffness can be separately computed at each point within a finite element domain. This procedure reduces the communication between nodes in mesh (i.e. discrete elements) to only that which is necessary for the solution of the problem.
To solve a finite element analysis problem, you begin by creating or selecting a mesh. A regular grid of nodes is created, usually using tetrahedral elements (though other types are available).
The boundaries of each element are then defined and refined until the local stiffness matrix and forces generated by each point are known within 1% error. Once this mesh has been created, the solution to one problem can be used as a template for solving many more problems.
Uses of FEA
Finite element analysis has found applications in a large number of fields, including chemical and mechanical engineering, aerospace engineering, structural engineering, civil engineering, geological engineering, and electrical and computer systems. It is used to solve problems that are intractable with other techniques, such as boundary value problems in heat transfer and fluid flow.
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