Finite element analysis is a numerical technique used in structural engineering, fluid mechanics, and heat flow to obtain accurate solutions to complex problems. It breaks down a problem into smaller elements and integrates them to provide an overall solution. It is commonly used to solve stress distribution problems in irregularly shaped objects.
Finite element analysis, or FEA, is a computer-based tool for approximating the solution to an otherwise unsolvable problem. It is commonly employed in structural engineering, although it is also used in other problems such as fluid mechanics and heat flow. Most mathematical problems for practical applications are, in fact, too complicated to be solved analytically, although in most cases they do not require perfect solutions. Finite element analysis is a numerical technique, as opposed to an analytical one, for obtaining acceptably accurate solutions; it works by breaking down a complicated problem into many simpler ones.
Analytical methods involve solving a mathematical problem to provide a perfect and continuous solution. In other words, the solution is a function in terms of some variable, rather than a numerical approximation. There is no degree of estimation or error in the analytical solutions of a given equation. However, analytical solutions for formulations that model real-world problems are often not known. These require numerical methods, of which finite element analysis is an example, to obtain an approximate solution.
Finite element analysis is based on breaking down a complicated problem into a large number of less complex problems. When a problem solution exhibits very complicated behavior, it is sometimes acceptable to apply simplifications. Often, however, a large simplification introduces too many errors to be useful. This is when it helps to break the problem into many separate problems. Simplified solutions to each element of a problem can be integrated together to provide a highly accurate overall solution.
In finite element analysis, a problem domain is divided into many smaller zones called elements. The collective body of elements is called a mesh. The process of integrating, or summarizing, many different elements works because of how the elements interact at their boundaries. Once the boundary interactions of the elements are understood, a computer can extend the approximate solution from one element to another. Eventually, the computer will have “built” a rough solution that closely approximates real-world behavior.
One problem commonly solved with finite element analysis is the stress distribution within a solid piece of metal. When metal, or any other comparable material, is subjected to forces, every part of the object has a certain amount of stress placed on it. Even if the applied forces are known, irregularly shaped objects are usually too complex to know the exact distribution of internal stresses. At this point, finite element analysis can be used to compute an approximate, element-by-element solution to this problem. Visualization software can then be used to put this collection of information into an intuitive and coherent picture.
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