# How to expand the C matrix for three aditional degrees of freedom for rotational forces?

E = 2000000
nu = 0.3
C = (E / ((1 + nu) * (1 - 2 * nu))) * np.array([
[1 - nu, nu, nu, 0, 0, 0],
[nu, 1 - nu, nu, 0, 0, 0],
[nu, nu, 1 - nu, 0, 0, 0],
[0, 0, 0, (1 - 2 * nu) / 2, 0, 0],
[0, 0, 0, 0, (1 - 2 * nu) / 2, 0],
[0, 0, 0, 0, 0, (1 - 2 * nu) / 2]
])


This C matrix I took from a textbook I have that says it should be good for three degrees of freedom for axial forces. How should such a C matrix be expanding if I also want to include three additional degrees of freedom for rotational forces (moment)?

• There also is a B matrix which consists of 6 rows and 12 columns. So for the additional three degrees of freedom for moment B would have to also expand. I don't quite get what you mean by those are additive since it doesn't really make sense to me that B would have to expand to make room for those new dogs. Could it be explained what happens with B and c for the new dogs? Maybe you mean that C is added on a diagonal? Commented May 23 at 3:18
• That looks like a compliance tensor in Voigt notation. It relates stress and strain. It is not a stiffness matrix. Commented May 23 at 12:40
• Either way, I think you have to more precisely say what the matrix represents, and in particular what exactly it is you want to do. I have no idea what your actual goal is. Commented May 23 at 12:40
• I was hoping to expand the tetrahedron from 3 dofs to six dofs (for moment and axial forces). I'm finding there is little written how to do so and also it might not be an accepted practice. Plates and shells with six dofs are recommended. All I know so far is that B and C would have to expand if that were possible. If there is an answer, I hope for it to include how to expand B and C from three axial dofs to six dofs 3 for forces and 3 for moment. Commented May 23 at 20:27