Developing actuator and sensor influence matrix.

The strain vector can be written in another form as

(20.13)

where

and

(20.14)

(20.15)

A_q is the shape function matrix

(20.16)

,

(20.17)

Finally, multiplying T₂ and A_q

(20.18)

Substituting the expression of strain from Equation (20.8) into Equation (20.5), we get

(20.19)

Since at the element level, the force by the actuator is from Equation (20.11), it may be written as

(20.20)

(20.21)

or

(20.22)

Matrix is the integration part of .