- Local or element coordinates
- Natural coordinates
- Simple natural coordinates
- Area coordinator Triangular coordinates
- Generalised coordinates

- Since the properties of each element are evaluated separately different material properties can be incorporated for each element.
- There is no restriction in the shape of the medium.
- Any type of boundary condition can be adopted.

- The geometry of the body
- The number of independent space coordinates
- The nature of stress variation expected

- The computational cost is high.
- The solution is approximate and several checks are required.

**The various elements used in FEM are classified as:**

- One dimensional elements(1D elements)
- Two dimensional elements(2D elements)
- Three dimensional elements(3D elements)

- Discretization of the structure
- Selection of suitable displacement function
- Finding the element properties
- Assembling the element properties
- Applying the boundary conditions
- Solving the system of equations
- Computing additional results

**The various terms used in FEM are explained below:**

**Finite element-**Small elements used for subdividing the given domain tobe analysed are called finite elements. The elements may be 1D, 2D or 3D elements depend in on the type of structure.**Nodes and nodal points-**The intersection of the different sides of elements are called nodes. Nodes are of two types - external nodes and internal nodes.

**O External nodes -** The nodal point connecting adjacent elements.**O Internal nodes-** The extra nodes used to increase the accuracy of solution.

**Nodal lines -**The interface between elements are called nodal lines.**Continuum-**The domain in which matter exists at every point is called a continuum. It can be assumed as having infinite number of connected particles.**Primary unknowns-**The main unknowns involved in the formulation of the element properties are known as primary unknowns.**Secondary unknowns-**These unknowns are derived from primary unknowns are known as secondary unknowns. In displacement formulations, displacements are treated as primary unknowns and stress, strain, moments and shear force are treated as secondary unknowns.

**The properties of shape functions are:**

- Theno of shape functions will be equal to theno of nodes present in the element.
- Shape function will have a unit value at the node considered and zero value at other nodes.
- The sum of all the shape function is equal to @i. e. SNi =1

**The possible locations for nodes are:**

- Point of application of concentrated load.
- Location where there is a change in intensity of loads
- Locations where there are discontinuities in the geometry of the structure
- Interfaces between materials of different properties.