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Sorry for boring you, my friends. Recently, I am haunted by a stupid question. It is probably a physics course question rather than a technique one.

Finite element method is now a very popular tool to perform the mechanical simulation. And, in order to model a volumic structure, the solid elements are often applied. In my knowledge, there are no rotational degrees of freedom in general brick(solid) element. If one wants to introduce them into rotating reference frame, the discretized mass system will possess their own inertia in rotating reference respecting to the axis of rotation. Thus, my stupid question is: Could effect of inertia influence the formation of the mass matrix (non rotational degrees of freedom), gyroscopic matrix and spin-stiffness matrix?

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In continuum mechanics, you split the continuum into infinitesimally small parts, which are effectively point particles. Each infinitesimal part does not have any rotational inertia itself. The rotational dynamics of the whole continuum arises from the relative motion of the infinitesimal parts.

That is analogous to the way a rotating rigid body is modeled from point particles in Newtonian mechanics.

In principle, it makes no difference whether you describe the position and deformation of the continuum using only translation variables, or a combination of translations and rotations.

Working in a non-inertial coordinate system does not change the mass matrix, but it does change the stiffness, and creates the Coriolis (gyroscopic) matrix. Note, there are (at least) two different effects which change the stiffness: one is the non-inertial movement of the reference frame, and the other is the internal stress field within the body created by its motion.

If you want a model that can represent (arbitrarily large) finite rotations, you need to use measures of stress and strain that represent these in a meaningful way - for example Green strain and Piola-Kirchhoff stress, not the "engineering" definitions of small strain and small stress that you probably learned in a first course on continuum mechanics.

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  • $\begingroup$ Thanks a lot for your answer. 'In principle, it makes no difference whether you describe the position and deformation of the continuum using only translation variables, or a combination of translations and rotations.' confused me. For example, the conventional solid element (only with translational dofs) cannot capture the moment of inertia, while hybrid solid element (Ansys solid72) with rotational dofs can do so. (Euler-Bernoulli beam vs Timoshenko beam) Thus, my further question is that the conventional solid element for rotor-dynamic analysis capable to capture moment of inertia? $\endgroup$ – Zihan Shen Jul 11 '18 at 13:30

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