NOC:Finite Element Method: Variational Methods to Computer Programming (USB)

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Arup Nandy, Prof. Atanu Banerjee

NPTEL Co-ordinating Institute : IIT Guwahati

NPTEL Lecture Count : 35

NPTEL Course Size : 5.5 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

Lecture 1 - Functional, First variation, Euler Lagrange equation; Several Dependent variables
Lecture 2 - Functional with higher order derivatives; Variational statement
Lecture 3 - Differential equation, Variational statement and Minimization problem; Rayleigh-Ritz method
Lecture 4 - FEM steps: Explained with discrete linear springs; Gaussian Quadrature rule for integration
Lecture 5 - Solving one Ordinary Differential Equation using Linear Finite Element
Lecture 6 - Solving one Ordinary Differential Equation using Quadratic Finite Element
Lecture 7 - Bar Element: Elemental equation; Matlab Implementation with Example
Lecture 8 - Bar Element: Postprocessing; Comparison with Analytical Solution; Bar with linear springs
Lecture 9 - Truss Element: Elemental equation; Matlab Implementation with Example
Lecture 10 - Beam Element: Variational statement; Hermite shape function
Lecture 11 - Beam Element: Elemental equation; Matlab implementation with Example
Lecture 12 - Beam Element: Matlab implementation for the example with Non-uniform distributed load
Lecture 13 - Frame Element: Derivation of elemental equation in global reference frame
Lecture 14 - Frame Element: Matlab implementation with one Example
Lecture 15 - Generalization of Geometry data; Stiffness matrix, Load vector formation at element level
Lecture 16 - Generalization of Assembly, Imposition of Boundary condition and Load information
Lecture 17 - Indicial Notation: Summation convention, Kronecker delta, Permutation symbol
Lecture 18 - Second order tensor; Gradient, Divergence, Curl and Laplacian in Indicial notation
Lecture 19 - Gauss Divergence theorem and its application in Heat transfer and Structural analysis
Lecture 20 - Derivation of weak form of 2D steady-state heat conduction problem
Lecture 21 - Triangular element, calculating element stiffness and element force vector
Lecture 22 - Numerical example, assembly, mapping
Lecture 23 - Numerical integration, Neumann boundary, and higher order shape functions
Lecture 24 - Quadrilateral element, Lagrange shape functions, Serendipity elements
Lecture 25 - Development of a MATLAB code for solving 2D steady-state heat conduction problem
Lecture 26 - Demonstration of the MATLAB code
Lecture 27 - Elasticity problems in two dimension and obtaining the weak form
Lecture 28 - Deriving element stiffness matrix and element force vector, numerical example
Lecture 29 - Development of a MATLAB code for solving planar elasticity problems
Lecture 30 - Superconvergent Patch Recovery, error estimator, adaptive refinement
Lecture 31 - Solving eigenvalue problem in bar and beam, writing FEM code in MATLAB
Lecture 32 - Solving eigenvalue problem of membrane, writing FEM code in MATLAB
Lecture 33 - Solving transient problems (parabolic type)
Lecture 34 - Solving transient problems (hyperbolic type)
Lecture 35 - Solving elasticity problems in 3D using FEM, Solvers