How to implement Stress-Free BC

I have a question about the implementation of stress free BC, actually i have a system of equations with 6 unknown (u1,u2…u6), i want to impose this BC on the u2 and u4.

dn(u1)=-u2/(4*r0) with dn the normal derivative of u1
and dn(u4)=2(r-r0)*u4/(r *r0)

Is it possible to implement this two conditions at the same time with FreeFem++ ?
Any help,
Thank you,

The short answer is yes, but the way you enforce such conditions depends on your weak formulation. Usually, you would try to apply the Divergence Theorem in deriving your equation such that a Neumann-type boundary integral term appears. Then homogeneous Neumann conditions will be naturally enforced by skipping this boundary integral in your variational form (hence the nickname “do-nothing” boundary condition). In your case, you will need to add an integral along the boundary to account for the inhomogeneous part.

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