Degree of Element (DOF) of Element in Finite Element Method (FEM)

 1-D element

• Rod     -    2 DOF/ node (U_x, θ_x) 
• Bar      -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Beam   -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Pipe     -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Axisymmetric shell   -    3 DOF / node (U_x, U_z, θ_y ) 

2-D element

• Plane Stress     -    2 DOF / node (U_x, U_y ) 
• Plane Strain     -    2 DOF / node (U_x, U_y ) 
• Plate                 -    3 DOF / node ( U_z , θ_x, θ_y ) 
• Membrane        -    3 DOF / node (U_x, U_y, θ_z ) 
• Thin Shell        -    6 DOF / node (U_x, U_y, U_z , θ_x, θ_y, θ_z ) 
• Axisymmetric Solid    -    2 DOF / node (U_x, U_y ) 

3-D element

• Tetra                    -    3 DOF / node (U_x, U_y, U_z  ) 
• Penta or Wedge   -    3 DOF / node (U_x, U_y, U_z  ) 
• Hexa or brick       -    3 DOF / node (U_x, U_y, U_z  ) 
• Pyramid               -    3 DOF / node (U_x, U_y, U_z  ) 

Degree of Freedom of Element

 Firstly let's study the degree of freedom, what is the degree of freedom (DOF)?

Degree of freedom is defined as the minimum number of parameters (Coordinates, motion, temp, pressure, etc ) required to define the position of any entity completely in space.

For Example: if we make a point in 2D space (XY-plane), it is required to define the coordinate of the point in the X and Y direction to specify a location, So, the point has 2 degrees of freedom in 2D space.

If the same point is in 3D space. then it is required to define the coordinate of the point in the X, Y, and Z direction to specify a location. So, Point has 3 degrees of freedom in 3D space.

Now, If we take a line in 2D space, we have to define the rotation angle of the line with respect to either X-axis or Y-axis, along with the X and Y direction coordinate of either endpoint. So, any point on the line in 2D space will have 3 Degree of freedom (DOF).

Lastly, If we take a line in 3D space, we have to define the rotation angle of the line with respect to all three axes (X, Y, and Z-Axis) along with all three coordinates of either endpoint. So, any point on the line in 3D space will have 6 Degree of freedom.

So, In space (3D environment) every node has 6 degrees of freedom(DOF) - 3 translational (U_x, U_y, U_z) and 3 rotational ( θ_x, θ_y, θ_z ). 

Degree of freedom (DOF) in FEM plays an important role. If we increase one element, then 6 DOF will increase. 

            Number of Nodes     =    10

            dof of per node        =    6

            Total DOF                =    60

For the Degree of freedom of different elements Click Here.

What is Finite Element Analysis/Method

 The Finite Element Method is self-explanatory, as the definition of the FEM is hidden in these three words.

• Finite: As we know, every continuous component has millions of Degree of Freedom as it is made up of millions of particles. We generally call the degree of freedom (DOF) of a continuous object is infinite. It is not possible to solve the problem of an infinite degree of freedom(DOF). So, for the sake of simplicity, we reduce the degree of freedom(DOF) from infinite to finite with the help of the discretization process, which is called the meshing (Node and Element). 

• Element: In the Finite Element Method, all the calculation activities are done on a limited number of points, which are called Nodes. Node is a specific point, which does not consume any space, it is an infinitesimal. The entity, which joins these nodes point, is called Element. There are many types of element shapes, i.e. Line, triangular, Quadrilateral, Box, Hexahedran, Penta, Tetrahedron. The result variable (i.e. stress etc.) is calculated on these nodes. Then the result variable is interpolated based on these elements based on an interpolated function that depends on the shape of the element.

•  Method: As there are 3 Methods to solve any engineering problem: Theoretical, Numerical, and Practical. The Finite Element method uses the Numerical method of Problem Solving. 

Line body analysis in ANSYS