Tuesday, 20 September 2016

Finite Element Method(FEM)?

The Finite-Element Method(FEM) is a computational numerical solution method that divides a physical model or digital(CAD) model into very small but finite-sized elements of geometric shapes. The collection of all these shapes make a set that called finite-element mesh and the junction points of these shapes or elements called as node. In other words, mesh discretization take place in FEM. This is modeled by approximating the field conditions within each element as a simple function, such as a linear or quadratic polynomial, with a finite number of degrees of freedom (DOFs).

Alexander Hrennikoff (Russian; 1896 — December 31, 1984) was a Russian-Canadian Structural Engineer, and known as a founder of the Finite Element Method.

Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. R. Courant's name is also known for the finite element method, with his numerical solution of the plain torsion problem for multiply-connected domains, published a paper in 1943.

This method was first applied to structural analysis problems. Over the last ten years or so, it has been realized that the finite element method(FEM) is also suitable and fit for a large class of multi-physics problems. There are three mathematical ways or methods that FEM can use to evaluate the values at the nodes.

  • Non-variational method ( Ritz method)
  • Residual mehod (Galerkin ethod)
  • Variational method and(Rayleigh-Ritz method)
Finite Element Method is also known as Finite Element Analysis (FEA) and it is a technological application of FEM. You can not compute the solution of the equestions, created in the FEM. To solve these questions, you need to use computer adied technology which is FEA. FEA is applied in engineering as a computational tool for performing engineering analysis with the help of computer adied technology and use of software program coded with FEM algorithm. It includes the use of mesh generation techniques for dividing a complex field problem into small elements. The complex field problem is usually a physical system with the underlying physics such as the Euler-Bernoulli beam equation, the heat equation, or the Navier-Stokes equations expressed in either PDE or integral equations.

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