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I want to impose symmetry plane boundary condition for a solid mechanics problem. I googled around and found out that in many places people say to "forbid displacemnts out of symmentry plane and forbid rotations about any axis lying in this plane if you have rotational degrees of freedom".

If I have only disps degrees of freedom, how do I do it right? If my simmetry plane is e.g. YZ then I need to set $u_x=0$. It's only one equation, I think I need three to match the number of equations and unknowns. What are the others (if any)?

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The other two boundary conditions you need are \begin{equation} \frac{\partial u_y}{\partial x}=0;\quad \frac{\partial u_z}{\partial x}=0. \end{equation}

Thus the symmetry boundary condition is essentially identical to "rigid-smooth" boundary conditions.

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