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Course10510814140 lectures

Finite Element method for vibration and Stability analyses

Prof. C.S. Manohar · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Approximate methods and FEM

  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

Finite element analysis of dynamics of planar trusses and frames

  1. FEM: motivations. Analysis of axially vibrating rods and Euler-Bernoulli beams Video
  2. Beam elements. Reference systm. Assembly of matrices. Imposition of BCS. Final equation of motion. Video
  3. FE modelling of planar structures Video
  4. FE modelling of planar structures (continued) Video

Analysis of equations of motion

  1. FRF-s and damping models-1 Video
  2. FRF-s and damping models-2 Video
  3. Material damping models. Dynamic stiffness and transfer matrices Video

Analysis of grids and 3D frames

  1. Twisting of circular bars and rectangular bars. Analysis of grids Video
  2. 3D frames Video

Time integration of equation of motion

  1. Mathematical preliminaries and terminologies; Euler’s forward and backward difference methods. Video
  2. Forward and backward Euler method. Central difference method Video
  3. Second order implicit methods Video
  4. Energy conservation. Nonlinear systems. Video

Model reduction and substructuring schemes

  1. Model reduction schemes Video
  2. Substructuring schemes Video

Analysis of 2 and 3 dimensional continua

  1. Plane stress models Video
  2. Plane stress models (continued) Video
  3. 3d Solid element Video
  4. Axisymmetric models. Plate bending elements. Video
  5. Plate bending elements (continued) Video
  6. Plate bending elements (continued). Video
  7. Plate bending elements [continued] Video

Structural stability analysis

  1. Introduction Video
  2. Introduction (continued) Video
  3. Nonlinear dynamical systems, fixed points and bifurcations Video
  4. Energy methods in stability analysis Video
  5. FEM for stability analysis. Euler-Bernoulli beam and general formulations Video
  6. 3D beam element; plate element; imperfection sensitive structures; beams on elastic foundations; rings and arches. Video
  7. Dynamic analysis of stability and analysis of time varying systems Video
  8. Dynamic analysis of stability and analysis of time varying systems. Video
  9. FE modelling of vehicle structure interactions Video

FE model updating

  1. Inverse response sensitivity analysis Video
  2. Inverse response sensitivity analysis (continued) Video

Nonlinear FE models

  1. Introduction and review of continuum mechanics Video
  2. Review of measures of strain and stress; balance laws. Video
  3. Total and updated Lagrangian formulations Video
  4. Closure Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Civil Engineering
Teacher
Prof. C.S. Manohar
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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