1. APPENDIX A EXAMPLES

2. What’s in this appendix: –Industrial Robot –Low-Voltage Circuit Breaker –Flexible Go-Kart –Comfort Tire Model –Satellite with Flexible Panels and Antennas –Flexible Vehicle Suspension –Shell Panels for Missile Separation –Landing Aircraft –Flexible Vehicle Frame and Chassis –Flexible Car Body in Passing Maneuver –Pothole Passing with a Truck –Rail Vehicle Comfort Calculations

3. INDUSTRIAL ROBOT –Effects of flexibility on joint forces –Rigid versus flexible graphic results RigidFlexible

4. INDUSTRIAL ROBOT

5. LOW-VOLTAGE CIRCUIT BREAKER –Simple geometry –Structural springs including mass –Very rapid dynamics –Rigid versus flexible results

6. LOW-VOLTAGE CIRCUIT BREAKER Courtesy of ABB Research

7. LOW-VOLTAGE CIRCUIT BREAKER Courtesy of ABB Research

8. LOW-VOLTAGE CIRCUIT BREAKER Structural springs, including mass, become one-dimensional FE Where: –K = Spring stiffness –M = Spring mass –A = Area of internal spring helicoid –L = Spring length

9. LOW-VOLTAGE CIRCUIT BREAKER Courtesy of ABB Research

10. FLEXIBLE GO-KART Account for frame flexibility to accurately simulate full-vehicle dynamics Model data: –Weight: kart=55 Kg, driver=70 Kg –About 7000 MSC Nastran shell elements Dynamic data: –Initial velocity: 100 Km/h –Steering step maneuver: 30 deg at time = 1

11. FLEXIBLE GO-KART

12. COMFORT TIRE MODEL Full ABAQUS nonlinear tire model translated into a flexible body ABAQUS model –Material nonlinearities –Inflation pressure –Rim contact and friction –Road contact interaction –120,000 DOFs Adams model –Nonlinear multiple contact impacts –3D Linearized tire forces at the hub –Nonlinear global displacements –No spinning –Speed-dependent tread forces –< 50 active DOFs for 15 contact points

13. COMFORT TIRE MODEL Courtesy of Pirelli Tires

14. SATELLITE WITH FLEXIBLE PANELS AND ANTENNAS Stabilizing the satellite’s orientation during deployment of flexible solar panels Control system equation integrated with mechanical equations Six flexible bodies are present in the system Original MSC Nastran meshes made with CQUADR and CTRIAR element types

15. SATELLITE WITH FLEXIBLE PANELS AND ANTENNAS

16. FLEXIBLE VEHICLE SUSPENSION Nonlinear deformation as an assembly of linear flexible bodies Courtesy of VW

17. SHELL PANELS FOR MISSILE SEPARATION Two flexible bodies are present in the system Sudden explosion of the connecting bolts is simulated Contact forces on the structure supports have been defined Radial distance is dependent on internal pressure distribution

18. SHELL PANELS FOR MISSILE SEPARATION Internal pressure fourbar

19. LANDING AIRCRAFT Airframe flexibility affects loading at control-surface hinges and landing-gear points Aeroelasticity effects could be included

20. LANDING AIRCRAFT

21. FLEXIBLE VEHICLE FRAME AND CHASSIS Courtesy of Fiat Research

22. FLEXIBLE CAR BODY IN PASSING MANEUVER Obstacle-passing maneuver of a full-vehicle model including a flexible body Handling maneuvers on a vehicle with flexible chassis

23. FLEXIBLE CAR BODY IN PASSING MANEUVER Courtesy of Leyland Trucks

24. POTHOLE PASSING WITH A TRUCK Pothole-passing maneuver of a full-vehicle truck model including a flexible frame Rigid versus flexible frame comparison of vertical accelerations at the driver’s seat Calculation of automatic stress distribution for the most critical dynamic loading condition

25. POTHOLE PASSING WITH A TRUCK Courtesy of Leyland Trucks

26. POTHOLE PASSING WITH A TRUCK Model characteristics Multibody model –Leaf springs - five-beam element per spring –Bushing mounts (cab, engine, spring-dampers) modeled, including frequency- dependent data –Tires modeled using University of Arizona Tire Model with Michelin data –Dampers modeled with nonlinear cubic spline characteristics –Steering system driven by simple closed-loop control algorithm –Total of 123 DOFs Courtesy of Leyland Trucks

27. POTHOLE PASSING WITH A TRUCK Flexible frame –About 45,000 nodes and 260,000 DOFs –About 45,000 CQUAD4 and TRIA3; about 5,000 CBAR element used –158 originally retained modes, of which 25 normal constrained and 133 static correction –18 modes after energy model reduction algorithm application Simulation –1.8 s run at 50 Km/h with right-sided 75 mm pothole –385 s CPU time on 250 MHz SGI Octane 1 GB Ram Courtesy of Leyland Trucks

28. POTHOLE PASSING WITH A TRUCK Simulation results in Adams –Vertical acceleration at driver’s seat. –Different response between rigid and flexible frame representation. –The most significant feature of the different response in terms of acceleration plot is the vertical component shown here. –With a rigid frame, the front wheel strike creates a shock, which dies away progressively. –With a flexible frame, the initial shock begins to diminish, but then increases once more as the rear wheel impact shock propagates along the frame. The driver can feel the impact shock when he drives the vehicle over such a disturbance. Rigid body models fail to predict this effect.

29. POTHOLE PASSING WITH A TRUCK Single-sided 75 mm pothole: 50 km/h impact Driver vertical acceleration Courtesy of Leyland Trucks

30. POTHOLE PASSING WITH A TRUCK Simulation results transferred to MSC Nastran –Once the Adams run is completed, it is possible to automatically create a Loadcase file for MSC Nastran which contains a selection of time steps from the original load history. –Equivalent static analysis with inertia-relief technique is then submitted in MSC Nastran. –Von Mises stress distribution after the right wheel has struck the trailing edge of the pothole are shown. –Little stress over-estimation due to tire enveloping effect and absence of bumpstops. –Impact occurs on the right-end side, but the highest stresses appear on the left of the frame due to the steering linkage forces.

31. POTHOLE PASSING WITH A TRUCK Courtesy of De Dietrich

32. RAIL VEHICLE COMFORT CALCULATIONS The purpose of this work is to evaluate coach flexibility influence on vehicle comfort Vehicle design ANSYS coach model Adams/Rail vehicle model with flexible coach

33. RAIL VEHICLE COMFORT CALCULATIONS Analysis on a Straight Track with Vertical, Transversal and Cant angle excitation Train Velocity = 38.9 m/s VerticalTransversal Cant

34. RAIL VEHICLE COMFORT CALCULATIONS ANSYS coach model Human factor filters Weighted Vertical Acceleration RMS Value Flexible coach RMS = 0.0448 m/s 2 Rigid coach RMS = 0.0362 m/s 2 UIC 513 acceleration weighting criteria Frequency weighting transfer functions Vertical acceleration time historyWeighting curve Weighted vertical acceleration PSD