Module 3: Introduction to Finite Element Method
  Lecture 20:
 

 

Let us now consider the issue of evaluating the term of Eq. (19.5), for a typical element

(20.7)

where and for the element. Thus, the conduction contribution of an element to the residual equation at a node takes the form of a 3 ×3 matrix multiplied by a 3×1 vector. Substituting for and one can obtain all the entries of the 3 ×3 matrix .

For and we get

which yields

(20.8)

Next, for and we get

which yields

(20.9)

finally for and we get

which yields

(20.10)