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On the use of a mixed formulation for the dynamics of rigid bodies in the framework of Lie-group geometric methods

Dr. Alessandro Giusti
University of Florence / TU Braunschweig
Tuesday, October 25, 2016 - 14:30 to 16:00

The dynamics of rigid bodies is presented by using a mixed vision of the motion that consists in the simultaneous use of two different bases. The motion of the reference point (usually the center of mass) is referred to the basis of the inertial frame whereas the motion about the reference point is referred to the rotating basis of the body-attached frame. The consequent set of differential equations is solved with an efficient Lie-group time integrator based on the so called geometric methods. In this framework, the formulation of non-follower and follower loads is developed including the special case of linear transformations of the state variables and the associated tangent operators, i.e. the linearization of the dynamic problem with respect to the state variables. The numerical model is tested on a series of dynamic problems for which the exact analytic solution is known, allowing a detailed assessment of the capability of the method. The possibility of truncating the tangent stiffness operator is discussed. The nonlinear dynamic model is then used for the study of moored floating platforms (buoyancy stabilized concept). Mooring line loads and hydrodynamic actions are considered as external loads related to the state variables, i.e. configuration of the body, velocity and acceleration. In particular, the mooring lines are modeled by a quasi-static theory while the hydrodynamic problem is solved in the linear wave theory framework. The effect of different strategies of simulation on the system response as well as the role of the main parameters affecting the motion is discussed.

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