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Course11210329535 lectures

Finite Element Method: Variational Methods to Computer Programming

Prof. Atanu Banerjee and Prof. Arup Nandy · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

Week 1: Variational Calculus and Minimization Problem

  1. Lec 1: Functional, First variation, Euler Lagrange equation; Several Dependent variables YouTube
  2. Lec 2: Functional with higher order derivatives; Variational statement YouTube
  3. Lec 3: Differential equation, Variational statement and Minimization problem; Rayleigh-Ritz method YouTube

Week 2: One dimensional Finite Element Analysis

  1. Lec 4: FEM steps: Explained with discrete linear springs; Gaussian Quadrature rule for integration YouTube
  2. Lec 5: Solving one Ordinary Differential Equation using Linear Finite Element YouTube
  3. Lec 6: Solving one Ordinary Differential Equation using Quadratic Finite Element YouTube

Week 3: Structural Elements in One Dimensional FEM

  1. Lec 7: Bar Element: Elemental equation; Matlab Implementation with Example YouTube
  2. Lec 8: Bar Element: Postprocessing; Comparison with Analytical Solution; Bar with linear springs YouTube
  3. Lec 9: Truss Element: Elemental equation; Matlab Implementation with Example YouTube

Week 4: Structural Elements in One Dimensional FEM

  1. Lec 10: Beam Element: Variational statement; Hermite shape function YouTube
  2. Lec 11: Beam Element: Elemental equation; Matlab implementation with Example YouTube
  3. Lec 12: Beam Element: Matlab implementation for the example with Non-uniform distributed load YouTube

Week 5: Structural Elements in One Dimensional FEM, and Generalized One Dimensional Finite Element Code in Computer…

  1. Lec 13: Frame Element: Derivation of elemental equation in global reference frame YouTube
  2. Lec 14: Frame Element: Matlab implementation with one Example YouTube
  3. Lec 15: Generalization of Geometry data; Stiffness matrix, Load vector formation at element level YouTube
  4. Lec 16: Generalization of Assembly, Imposition of Boundary condition and Load information YouTube

Week 6: Brief Background of Tensor Calculus

  1. Lec 17: Indicial Notation: Summation convention, Kronecker delta, Permutation symbol YouTube
  2. Lec 18: Second order tensor; Gradient, Divergence, Curl and Laplacian in Indicial notation YouTube
  3. Lec 19: Gauss Divergence theorem and its application in Heat transfer and Structural analysis YouTube

Week 7: Two dimensional Scalar field problems

  1. Lec 20: Derivation of weak form of 2D steady-state heat conduction problem YouTube
  2. Lec 21: Triangular element, calculating element stiffness and element force vector YouTube
  3. Lec 22: Numerical example, assembly, mapping YouTube

Week 8: Two dimensional Scalar field problems

  1. Lec 23: Numerical integration, Neumann boundary, and higher order shape functions YouTube
  2. Lec 24: Quadrilateral element, Lagrange shape functions, Serendipity elements YouTube
  3. Lec 25: Development of a MATLAB code for solving 2D steady-state heat conduction problem YouTube

Week 9: Two dimensional Scalar and Vector field problems

  1. Lec 26: Demonstration of the MATLAB code YouTube
  2. Lec 27: Elasticity problems in two dimension and obtaining the weak form YouTube
  3. Lec 28: Deriving element stiffness matrix and element force vector, numerical example YouTube

Week 10: Two dimensional Vector field and Eigen value problems

  1. Lec 29: Development of a MATLAB code for solving planar elasticity problems YouTube
  2. Lec 30: Superconvergent Patch Recovery, error estimator, adaptive refinement YouTube
  3. Lec 31: Solving eigenvalue problem in bar and beam, writing FEM code in MATLAB YouTube

Week 11:Eigen value problems and Transient problem in 1D & 2D Scalar Valued Problems

  1. Lec 32: Solving eigenvalue problem of membrane, writing FEM code in MATLAB YouTube
  2. Lec 33: Solving transient problems (parabolic type) YouTube
  3. Lec 34: Solving transient problems (hyperbolic type) YouTube

Week 12: FEM formulation for 3D Elastic problem and challenges

  1. Lec 35: Solving elasticity problems in 3D using FEM, Solvers YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mechanical Engineering
Taught by
Prof. Atanu Banerjee, Prof. Arup Nandy
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
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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