Hi I am solving some fluid equation with some embedded inclusion, and I would like to find the force and torque on this object. The inclusion is a polygon and the boundary of this inclusion is marked with
ds = Measure(“ds”)[boundaries]
The unit normal vector is denoted by s0.mx, s0.my.
I solved the equation
which basically gives me the (2D) stress tensor T.
I know how to find the force on the inclusion, for example the force in x direction is given by
fx = - (Txx * s0.mx + Txy * s0.my) * ds(0) + …
Fx = assemble(fx)
However I am not sure how to find the torque on this inclusion with respect to its center of mass(whose coordinate is given) since I am not sure how to include the position vector of the points on boundary in the integral. I wonder what I need to do.