Civil Engineering - Finite Element method for vibration and Stability analyses (English)

   Sunday, May 18, 2025   

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Lecture 1: Equations of motion using Hamilton’s principle

Lecture 2: Equations of motion for continuous systems and Rayleigh’s quotient

Lecture 3: Rayleigh Ritz method and method of weighted residuals

Lecture 4: FEM: motivations. Analysis of axially vibrating rods and Euler-Bernoulli beams

Lecture 5: Beam elements. Reference systm. Assembly of matrices. Imposition of BCS. Final equation of motion.

Lecture 6: FE modelling of planar structures

Lecture 7: FE modelling of planar structures (continued)

Lecture 8: FRF-s and damping models-1

Lecture 9: FRF-s and damping models-2

Lecture 10: Material damping models. Dynamic stiffness and transfer matrices

Lecture 11: Twisting of circular bars and rectangular bars. Analysis of grids

Lecture 12: 3D frames

Lecture 13: Mathematical preliminaries and terminologies; Euler’s forward and backward difference methods.

Lecture 14: Forward and backward Euler method. Central difference method

Lecture 15: Second order implicit methods

Lecture 16: Energy conservation. Nonlinear systems.

Lecture 17: Model reduction schemes

Lecture 18: Substructuring schemes

Lecture 19: Plane stress models

Lecture 20: Plane stress models (continued)

Lecture 21: 3d Solid element

Lecture 22: Axisymmetric models. Plate bending elements.

Lecture 23: Plate bending elements (continued)

Lecture 24: Plate bending elements (continued).

Lecture 25: Plate bending elements [continued]

Lecture 26: Introduction

Lecture 27: Introduction (continued)

Lecture 28: Nonlinear dynamical systems, fixed points and bifurcations

Lecture 29: Energy methods in stability analysis

Lecture 30: FEM for stability analysis. Euler-Bernoulli beam and general formulations

Lecture 31: 3D beam element; plate element; imperfection sensitive structures; beams on elastic foundations; rin

Lecture 32: Dynamic analysis of stability and analysis of time varying systems

Lecture 33: Dynamic analysis of stability and analysis of time varying systems.

Lecture 34: FE modelling of vehicle structure interactions

Lecture 35: Inverse response sensitivity analysis

Lecture 36: Inverse response sensitivity analysis (continued)

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