Local force Calculation using stress field


I would like to calculate the local force vector using a stress field of the size of (0, Vh). Assuming that the stress field is already projected on to the x, y and z components (so I have three stress components) how do I obtain F(0, Vh) ?


set a varf to compute the stress form the deformation
or do just interpolation

fespace VH3(TH,P1dc,P1dc,P1dc);
VH3 [sigma11,sigma22,sigma12 ] ; 
macro epsilon(u1,u2) [dx(u1),dy(u2),(dx(u1)+dy(u2)/2.]//
func A = [[...],[...],[...]]; // matrice form material 
[sigma11,sigma22,sigma12 ]   = A*epsilon([u1,u2]) ; 

Dear Dr. Hecht,

Thank you for your reply. In my case the stress vector is already calculated, i need to calculate the local force on each node using this stress vector. So i thought that i need to take the average stress on each cell then multiply by this cell area to get the force then project onto the nodes. I was wondering how can i implement it, or is there a better way to do it?


if your stress if S=[[s11,s21][s21,s22]] variables in 2d

we have on each element
\int_K F = \int_{\partial K} S .n where n is the unitary exterior normal to K

so write this in freefeem++ (5 mn)