Solution of Posissons equation Using a Constant Strain Triangle

1 Solution of Posisson s equation Using a Constant Strain Triangle 

In this section, we will proceed to develop a finite element formulation for the two-dimensional Poisson s equation using a linear displacement, constant strain triangle. Poisson s equation has many applications in polymer processing, such as injection and compression mold filling, die flow, potential problems, heat transfer, etc. The general form of Poisson s equation in two-dimensions is 

The first step when formulating the finite element solution to the above equations, is to discretize the domain of interest into triangular elements, as schematically depicted in Fig. 9.13. In the constant strain triangles, represented in Fig. 9.14, the field variable within the element is approximated by, 

We can use eqn. (9.54) to evaluate the field variable, 4 at every node location to get, 

The above equation can be used to solve for the coefficient vector 

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