Page 29 - Using ANSYS for Finite Element Analysis A Tutorial for Engineers

16 • Using ansys for finite element analysis
The identity matrix (or unit matrix) is denoted by the symbol [I]:

[][] Ia a
aI = [][] = []

10 0 
 
I [] = 01 0 

 00 1  

Differentiating a matrix:

d a [] =  da 
ij
dx   dx  

Example of differentiating a matrix:

x
1
U = [ x y]  a  11 a  
12
  
y
a
2  21 a 22  
 U
∂ 

 ∂  a a  
x
 x
 ∂U  =  11 12   
y
a
   21 a 22  
 y 
∂ 

Integrating a matrix:
[] � a dx
ij ∫
�
adx =
The inverse of a matrix is such that:
[][] −1 = I []
aa
To find the inverse of a matrix, first find the determinant of the matrix:
|a| = determinant of the matrix [a]
Next, calculate the cofactors of [a]. Cofactors of [a ] are given by:
ij
+
ij
1
c =−() d
ij