2D formulation for Electrostatic Problems
From KratosWiki
The 2D Electrostatic Poisson's equation given by the governing PDE and its boundary conditions:
can be written as (see the General formulation for Electrostatic Problems):
with (n is the number of nodes of the element):
2D formulation for Triangular Elements
After applying the numerical integration for triangular elements by using the natural coordinates, we obtain:
- x = N1x1 + N2x2 + N3x3 = (1 − α − β)x1 + αx2 + βx3
- y = N1y1 + N2y2 + N3y3 = (1 − α − β)y1 + αy2 + βy3
Stiffness Matrix K(e)