Learn · Finite Element method for vibration and Stability analyses

Lecture 28 of 40Structural stability analysis

Nonlinear dynamical systems, fixed points and bifurcations

Prof. C.S. Manohar · IISc Bangalore

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All the lectures

  1. Equations of motion using Hamilton’s principle Video
  2. Equations of motion for continuous systems and Rayleigh’s quotient Video
  3. Rayleigh Ritz method and method of weighted residuals Video
  4. FEM: motivations. Analysis of axially vibrating rods and Euler-Bernoulli beams Video
  5. Beam elements. Reference systm. Assembly of matrices. Imposition of BCS. Final equation of motion. Video
  6. FE modelling of planar structures Video
  7. FE modelling of planar structures (continued) Video
  8. FRF-s and damping models-1 Video
  9. FRF-s and damping models-2 Video
  10. Material damping models. Dynamic stiffness and transfer matrices Video
  11. Twisting of circular bars and rectangular bars. Analysis of grids Video
  12. 3D frames Video
  13. Mathematical preliminaries and terminologies; Euler’s forward and backward difference methods. Video
  14. Forward and backward Euler method. Central difference method Video
  15. Second order implicit methods Video
  16. Energy conservation. Nonlinear systems. Video
  17. Model reduction schemes Video
  18. Substructuring schemes Video
  19. Plane stress models Video
  20. Plane stress models (continued) Video
  21. 3d Solid element Video
  22. Axisymmetric models. Plate bending elements. Video
  23. Plate bending elements (continued) Video
  24. Plate bending elements (continued). Video
  25. Plate bending elements [continued] Video
  26. Introduction Video
  27. Introduction (continued) Video
  28. Nonlinear dynamical systems, fixed points and bifurcations Video
  29. Energy methods in stability analysis Video
  30. FEM for stability analysis. Euler-Bernoulli beam and general formulations Video
  31. 3D beam element; plate element; imperfection sensitive structures; beams on elastic foundations; rings and arches. Video
  32. Dynamic analysis of stability and analysis of time varying systems Video
  33. Dynamic analysis of stability and analysis of time varying systems. Video
  34. FE modelling of vehicle structure interactions Video
  35. Inverse response sensitivity analysis Video
  36. Inverse response sensitivity analysis (continued) Video
  37. Introduction and review of continuum mechanics Video
  38. Review of measures of strain and stress; balance laws. Video
  39. Total and updated Lagrangian formulations Video
  40. Closure Video