# Structural boundary conditions - rotational/translational DoFs and displacement/tractions BCs

I am a little bit confused over the concept of translational and rotational degrees of freedom (DoFs) in structures, and their relation to displacement/traction BCs.

Do displacement boundary conditions constrain translational DoFs, only, or also rotational DoFs?

For example, for a 3-D case, if I specify the 3 translational components to be zero, I am effectively constraining all 3 translational DoFs. What does this do to the rotational DoFs? Intuitively, all 3 rotational DoFs would also be constrained.

How does traction BCs play into translational and rotational DoFs?

Part of my confusion is when I look at open-source or commercial structural mechanics solvers, I only see the ability to specify displacement or traction boundary conditions, not anywhere to specify translational or rotational constraints.

Some illustrations would be very helpful in my understanding.

Mathematical expressions would be helpful as well. In particular, I am wondering how rotational and translation DoFs are related to displacements and displacement gradients mathematically.

• If you are referring to classic elasticity in 3D, for example, there is no such a thing as a rotational degree of freedom. – nicoguaro Mar 4 '19 at 22:18
• See en.wikipedia.org/wiki/Kirchhoff%E2%80%93Love_plate_theory for how 3D and 2D descriptions are related (for the specific case of plates). – Biswajit Banerjee Mar 4 '19 at 22:50
• @nicoguaro Why does 3D elasticity have no rotational degrees of freedom? – structuralengineer Mar 5 '19 at 2:45
• Mmm, I think I don't know how to answer that question properly. But, let's give it a try. Let's consider your solid as a bunch or particles, where their relative positions can change. Thus, the whole configuration of the system is described by the displacements of all the particles (measured with respect the original configuration). – nicoguaro Mar 5 '19 at 2:52
• @nicoguaro hmm I agree based on my vague memory of molecular dynamics theory. But 2D elasticity has rotational DoFs? What about 3D inelastic materials? – structuralengineer Mar 5 '19 at 2:57