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Finite Element Modeling of Centrifuge Test. Term Project for ECI 281A Instructor: Prof. Boris Jeremi ć Guanzhou Jie Fall 2003. Outline. Brief introduction to centrifuge modeling Theoretical analysis of the kinematics of circular motion in the centrifuge

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## Finite Element Modeling of Centrifuge Test

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**Finite Element Modeling of Centrifuge Test**Term Project for ECI 281A Instructor: Prof. Boris Jeremić Guanzhou Jie Fall 2003**Outline**• Brief introduction to centrifuge modeling • Theoretical analysis of the kinematics of circular motion in the centrifuge • Set up the finite element formulation to include the Coriolis force and centrifugal force**About Centrifuge…**• To create an inertial acceleration field by rotating to simulate the gravity • To replicate the soil behavior both in terms of the strength and stiffness by a reduced scale version of the prototype**Kinematics in Centrifuge Test**• Use Rotating Frame of Reference to study the circular motion of the model (PHYSNET, http://http://35.8.247.219/home/modules/pdf_modules/m17.pdf)**Kinematics in Centrifuge Test**• We have to observe time-dependent vectors in • 1. Non-Rotating (NR) coordinate system, outside the centrifuge • 2. Rotating (R) coordinate system, fixed with the centrifuge (PHYSNET, http://http://35.8.247.219/home/modules/pdf_modules/m18.pdf)**Kinematics in Centrifuge Test**• Concern: the model inside centrifuge (Rotating) • Basic Laws (Newton): applicable to Non-Rotating (NR) coordinate system, outside the centrifuge Rotating Frame of Reference Non-Rotating Frame of Reference**Kinematics in Centrifuge Test**• Transformation of velocity vectors • Note that**Kinematics in Centrifuge Test**• Note • Theorem: any general relation valid for one vector is valid for all vectors**Kinematics in Centrifuge Test**• Transformation of acceleration • Solve for the acceleration of the object as seen in the rotating reference frame : Coriolis terms : Centrifugal terms**Coriolis Effect in Centrifuge Test**• We need the centrifugal term to simulate the artificial gravitation • Coriolis errors, in liquefaction test, blast test… It is clear that if the relative velocity of particles in the model is greater than 5% of the rotational velocity of the centrifuge, 10% of error can be introduced to neglect the Coriolis term.**FE Modeling of Centrifuge Test**• Basic equation: • Equilibrium:**FE Model of Centrifuge Test**• Follow the classic displacement-based FE discretizing procedure (weighted residual Galerkin method) • Coriolis element matrix**FE Model of Centrifuge Test**• Equivalent nodal force vector of Centrifugal acceleration**FE Model of Centrifuge Test**• Assembled global FE equation**Any questions?**Thanks so much for your attention! o(@~@)o

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