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# Finite Element Modeling of Centrifuge Test

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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1. Finite Element Modeling of Centrifuge Test Term Project for ECI 281A Instructor: Prof. Boris Jeremić Guanzhou Jie Fall 2003

2. 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

3. 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

4. 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)

5. 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)

6. 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

7. Kinematics in Centrifuge Test • Transformation of velocity vectors • Note that

8. Kinematics in Centrifuge Test • Note • Theorem: any general relation valid for one vector is valid for all vectors

9. 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

10. 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.

11. FE Modeling of Centrifuge Test • Basic equation: • Equilibrium:

12. FE Model of Centrifuge Test • Follow the classic displacement-based FE discretizing procedure (weighted residual Galerkin method) • Coriolis element matrix

13. FE Model of Centrifuge Test • Equivalent nodal force vector of Centrifugal acceleration

14. FE Model of Centrifuge Test • Assembled global FE equation

15. Any questions? Thanks so much for your attention! o(@~@)o

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