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Finite Element Method (FEM) vs Classical Methods

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#1 ilLuSion



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Posted 30 May 2016 - 04:22 PM

FEM (Finite Element Method)  is the most flexible one in terms of dealing with complex geometry and complicated boundary conditions. FEM also allows the adaptive/local procedure to get higher order local approximation or battling singularities. FEM is the way to incorporate the intrinsic geometrical properties of the solutions.
Following are the differences in classical methods and FEM-
  1. In classical methods exact equations are formed and exact solutions are obtained where as in finite element analysis exact equations are formed but approximate solutions are obtained.
  2. Solutions have been obtained for few standard cases by classical methods, where as solutions can be obtained for all problems by finite element analysis.
  3. Whenever the following complexities are faced, classical method makes the drastic assumptions’ and looks for the solutions:
    (a) Shape
    (B) Boundary conditions
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  4. When material property is not isotropic, solutions for the problems become very difficult in classical method. Only few simple cases have been tried successfully by researchers. FEM can handle structures with an-isotropic properties also without any difficulty.
  5. If structure consists of more than one material, it is difficult to use classical method, but finite element can be used without any difficulty.
  6. Problems with material and geometric non-linearity  cannot be handled by classical methods. There is no difficulty in FEM.


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