Some researchers consider rotation variables as work-conjugate with moments, others think that the displacement derivatives is, and others use semi tangential rotation as work-conjugate to conservative moments
Any explanation or more references?
When you talk about work-conjugate with moments, it is actually energy and energy generated by moment surely is related to the rotation variables and moment itself, i.e. E = W = M.θ.
Dear Khaled Megahed,
in finite elements, rotations can be derived from displacements for some elements like plates and beams for other element they can be defined lonely like in triangles. The total potential energy is E=(1/2)*{d}t*[K]*{d}-{d}t*{R}=(strain energy - external works) to be minimized where {d}t=linear displacements & rotations, and {R}t=corresponding forces & moments and [K]=stiffness matrix.
Have you ever heard about theory of Cosserat brothers https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/34209/31151000327233.pdf ? Micropolar, couple-stress, asymmetric (non-symmetric) elasticity? Mindlin, Tiersten, Truesdell, Nowacki? And about micropolar models with independent and constrained rotations?
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