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September 27, 2004. 2. Acknowledgement. TUdelft:Hans BesselingKlaas Van der WerffHelmut RankersTon Klein BretelerJaap Meijaard MSc students. UTwente:Ben JonkerRonald Aarts MSc students. September 27, 2004. 3. Contents. RootsModellingSome Finite ElementsEqn's of MotionExamplesDi
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1. 1 SPAÇAR: A Finite Element Approach inFlexible Multibody Dynamics UIC Seminar
2. September 27, 2004 2 Acknowledgement TUdelft:
Hans Besseling
Klaas Van der Werff
Helmut Rankers
Ton Klein Breteler
Jaap Meijaard
… MSc students
3. September 27, 2004 3 Contents Roots
Modelling
Some Finite Elements
Eqn’s of Motion
Examples
Discussion
4. September 27, 2004 4 Engineering Mechanics at Delft From Analytical Mechanics in 50’s:
Warner T. Koiter
On the Stability of Elastic Equilibrium, 1945
To Numercial Methods in Applied Mechanics in 70’s:
Hans Besseling
The complete analogy between the matrix equations and the continuous field equations of structural analysis, 1963
5. September 27, 2004 5 Mechanism and Machine Theory
6. September 27, 2004 6 Mechanism and Machine Theory, Kinematics
7. September 27, 2004 7 Mechanism and Machine Theory, Kinematics
8. September 27, 2004 8 Multibody System DynamicsFinite Element Approach
9. September 27, 2004 9 Multibody System DynamicsFinite Element Approach
10. September 27, 2004 10 Multibody System DynamicsFinite Element Approach
11. September 27, 2004 11 Multibody System Dynamics
12. September 27, 2004 12 3D Beam Element
13. September 27, 2004 13 3D Hinge Element
14. September 27, 2004 14 3D Truss Element
15. September 27, 2004 15 3D Wheel Element
16. September 27, 2004 16 3D Wheel Element
17. September 27, 2004 17 Ex. Universal or Cardan Joint
18. September 27, 2004 18 Ex. Universal or Cardan Joint
19. September 27, 2004 19 Dynamic Analysis
20. September 27, 2004 20 Ex. ILTIS Road Vehicle Benchmark
21. September 27, 2004 21 Ex. ILTIS Road Vehicle Benchmark
22. September 27, 2004 22 Ex. ILTIS Road Vehicle Benchmark
23. September 27, 2004 23 Ex. Slider-Crank Mechanism
24. September 27, 2004 24 Linearized Equations of Motion
25. September 27, 2004 25 Ex. Slider-Crank Mechanism
26. September 27, 2004 26 Linearized Equations of Motion at Nominal Periodic Motion
27. September 27, 2004 27 Linearized Equations of Motion at Nominal Periodic Motion
28. September 27, 2004 28 Ex. Slider-Crank Mechanism
29. September 27, 2004 29 Ex. Slider-Crank Mechanism
30. September 27, 2004 30 Ex. Slider-Crank Mechanism
31. September 27, 2004 31 Ex. Dynamics of an Uncontrolled Bicycle
32. September 27, 2004 32 Ex. Dynamics of an Uncontrolled Bicycle
33. September 27, 2004 33 Ex. Dynamics of an Uncontrolled Bicycle
34. September 27, 2004 34 Ex. Dynamics of an Uncontrolled Bicycle
35. September 27, 2004 35 Ex. Dynamics of an Uncontrolled Bicycle
36. September 27, 2004 36 Ex. Dynamics of an Uncontrolled Bicycle
37. September 27, 2004 37 Ex. Dynamics of an Uncontrolled Bicycle
38. September 27, 2004 38 Ex. Dynamics of an Uncontrolled Bicycle
39. September 27, 2004 39 Conclusions SPAÇAR is a versatile FEM based Dynamic Modeling System for Flexible and/or Rigid Multibody Systems .
The System is capable of modeling idealized Rolling Contact (Non-Holonomic Constraints).
The System uses a set of minimal independent state variables, which avoid the use of differential-algebraic equations.
The Equations of Motion can be Linearized Analytically at any given state.