NPTEL : NOC:Finite Element Method: Variational Methods to Computer Programming (Mechanical Engineering)

Co-ordinators : Prof. Arup Nandy, Prof. Atanu Banerjee


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