The correct option is (b) They are secondary variables and must be carried as primary nodal degrees of freedom

For explanation I would say: An examination of the weak form, 0=∫Ωehe\([\frac{\partial w_1}{\partial x}(c_{11}\frac{\partial u_x}{\partial x}+c_{12}\frac{\partial u_y}{\partial y}) + c_{66}\frac{\partial w_1}{\partial y} (\frac{\partial u_x}{\partial y} + \frac{\partial u_y}{\partial x})\)+ρw1ux]dxdy-∫Ωehew1fxdxdy-∮┌dhew1txds reveals the following:

(i) ux and uy are the primary variables, which must be carried as the primary nodal degrees of freedom.

(ii) only first derivatives of ux and uywith respect to x and y, respectively, appear.