The document provides an introduction to the finite element method. It compares the finite element method to classical methods and the finite difference method. Some key differences highlighted include: - Classical methods obtain exact solutions for simple cases while finite element methods obtain approximate solutions for all problems. - Finite element methods can handle problems with complex geometry, multi-materials, and non-linearities, while classical methods have difficulties with these. - Finite difference methods make point-wise approximations while finite element methods make piece-wise approximations, allowing for continuity along element boundaries. - Finite element methods can evaluate values between nodes through interpolation, while finite difference methods only provide values at nodes.

1. FINITE ELEMENT
METHOD

2. FINITE ELEMENT METHOD
UNIT 1
INTRODUCTION
Er. Manoj Kumar
LOVELY PROFESSIONAL UNIVERSITY

3. finite element method vs classical method
Classical Methods Finite Element method
1) Exact equations are formed and exact
solutions are obtained.
1) Exact equations are formed but
approximate solutions are formed.
2) Solutions can be obtained for few
standard cases.
2) Solution can be obtained for all problems.
3) For the solution of shape, Boundary
conditions and loading some assumptions are
made.
3) No assumptions are made problem is
treated as it is.
4) When material is not isotropic, solution
for the problems becomes very difficult.
4) All type of property can handle without
any difficulty.
5) If structure consist more than one
material, it is difficult to analyze.
6) If structure consist more than one material
then it can be analyzed without any difficulty.

4. finite element method vs classical method
Classical Methods Finite Element method
6) Geometric non-linearities can not be
handled.
1) There is no difficulty.
7). Less superior method 7) More superior method.

5. Finite difference method vs Finite element method
Finite difference method
(FDM)
Finite Element method
(FEM)
1) FDM makes the point wise approximation
to governing equations. Thus continuity
only at node points not along the sides of
elements.
1) FEM makes the piece wise approximation
thus continuity at node points and also
along the sides of elements.
2) FDM gives the value at on node point only
means it do not give any approximating
function to evaluate the basic values
(deflection).
2) FEM can give the value at any point other
than node also by interpolation.
3) FDM makes stair type approximation to
sloping and curved boundaries.
3) FEM can consider the sloping boundaries
exactly .
4) FDM needs large numbers of nodes to
obtained good result.
4) FEM need few nodes.
5) FDM fairly complicated problems can be
handled.
5) FEM can be handled all complicated
problems.

6. Thanks!