Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 5M

Year: Dec 2015

Shape function:

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and low order polynomials are typically chosen as shape function.

nature of element	No. of nodes	shape function	graphic representation
Linear	2	$\phi_1(1-\frac{\bar{x}}{he})\\ \phi_2 =\frac{\bar{x}}{he}$
Quadnatic	3	$\phi_1= (1-\frac{2\bar{x}}{he}) (1-\frac{\bar{x}}{he})\\ \phi_2=\frac{4\bar{x}}{he^2}(1-\frac{\bar{x}}{he})\\ \phi_3= - \frac{\bar{x}}{he}(1-\frac{2\bar{x}}{he})$