Finite Element Method for Structural Dynamic and Stability Analyses
Finite Element Method for Structural Dynamic and Stability Analyses . Instructor: Prof. C. S. Manohar, Department of Civil Engineering, IISc Bangalore. This course will discuss Finite Element Method (FEM) in the context of structural mechanics problems. What are the issues to be dealt with, when the FEM, as developed for analysis of static problems, is extended to deal with problems of structural dynamic and elastic stability analyses. This is not a first course in FEM, Structural Dynamics and Structural Stability Analyses. Prerequisites are: matrix methods of static structural analysis, a first course in theory of vibrations, elements of static stability analysis, matrix algebra and ODEs.
(from nptel.ac.in )

Equations of Motion using Hamilton's Principle
VIDEO

Approximate Method and FEM
Lecture 01 - Equations of Motion using Hamilton's Principle
Lecture 02 - Equations of Motion for Continuous Systems and Rayleigh's Quotient
Lecture 03 - Rayleigh Ritz Method and Method of Weighted Residuals
Finite Element Analysis of Dynamics of Planar Trusses and Frames
Lecture 04 - FEM: Motivations, Analysis of Axially Vibrating Rods and Euler-Bernoulli Beams
Lecture 05 - Beam Elements, Reference System, Assembly of Matrices, Imposition of BCS
Lecture 06 - FE Modeling of Planar Structures
Lecture 07 - FE Modeling of Planar Structures (cont.)
Analysis of Equations of Motion
Lecture 08 - Frequency Response Functions and Damping of Models
Lecture 09 - FRFs and Damping of Models (cont.)
Lecture 10 - Material Damping Models, Dynamic Stiffness and Transfer Matrices
Analysis of Grids and 3D Frames
Lecture 11 - Twisting of Circular Bars and Rectangular Bars, Analysis of Grids
Lecture 12 - 3D Frames
Time Integration of Equation of Motion
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
Model Reduction and Substructuring Schemes
Lecture 17 - Model Reduction Schemes
Lecture 18 - Substructuring Schemes
Analysis of 2 and 3 Dimensional Continua
Lecture 19 - Plane Stress Models
Lecture 20 - Plane Stress Models (cont.)
Lecture 21 - 3D Solid Element
Lecture 22 - Axisymmetric Models, Plate Bending Elements
Lecture 23 - Plate Bending Elements (cont.)
Lecture 24 - Plate Bending Elements (cont.)
Lecture 25 - Plate Bending Elements (cont.)
Structural Stability Analysis
Lecture 26 - Introduction
Lecture 27 - Introduction (cont.)
Lecture 28 - Nonlinear Dynamical Systems, Fixed Points and Bifurcations
Lecture 29 - Energy Method 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; Rings and Arches
Lecture 32 - Dynamic Analysis of Stability and Analysis of Time Varying Systems
Lecture 33 - Dynamic Analysis of Stability and Analysis of Time Varying Systems (cont.)
Lecture 34 - FE Modeling of Vehicle Structure Interactions
FE Model Updating
Lecture 35 - Inverse Response Sensitivity Analysis
Lecture 36 - Inverse Response Sensitivity Analysis (cont.)
Nonlinear FE Models
Lecture 37 - Introduction and Review of Continuum Mechanics
Lecture 38 - Review of Measures of Strain and Stress; Balance Laws
Lecture 39 - Total and Updated Lagrangian Formulations
Lecture 40 - Closure