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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo and Text Based

Courses and Certificate Fees

Fees InformationsCertificate AvailabilityCertificate Providing Authority
INR 1000yesIIT Guwahati (IITG)

The Syllabus

Variational Methods
  • Functional and Minimization of Functional
  • Derivation of Euler Lagrange equation
    • First variation of Functional
    • Delta operator Functional with 
      • Several dependent variables
      • Higher order derivatives
  • Variational statement Weak Form
  • Variational statement to Minimization problem relation between Strong form, Variational statement and Minimization problem
  • Different approximation methods with Computer Programming: Galerkin method, Weighted Residual method, Rayleigh Ritz method

One dimensional Finite Element Analysis
  • Gauss Quadrature integration rules with Computer Programming
  • Steps involved in Finite Element Analysis
  • Discrete system with linear springs
  • Continuous systems: Finite element equation for a given differential equation 
  • Linear Element
  • Explaining Assembly, Solution, Post- processing with Computer Programming 
  • Quadratic element with Computer Programming
  • Finite element equation, Assembly, Solution, Post-processing
  •  Comparison of Linear and Quadratic element

Structural Elements in One dimensional FEM
  • Bar Element with Computer Programming
  • Variational statement from governing differential equation
  • Finite element equation, 
  • Element matrices, Assembly, Solution, Post-processing
  • Numerical example of conical bar under self-weight and axial point loads
  • Truss Element with Computer Programming
  • Orthogonal matrix, Element matrices, Assembly, Solution, Post-processing
  • Numerical example

Beam Formulation
  • Variational statement from governing differential equation
  • Boundary terms
  • Hermite shape functions for beam element Beam Element with Computer Programming
  • Finite element equation, Element matrices, Assembly, Solution, Post-processing, Implementing arbitrary distributive load
  • Numerical example

Generalized 1D Finite Element code in Computer Programming
  • Frame Element with Computer Programming: Orthogonal matrix, Finite element equation
  • Element matrices, Assembly, Solution, Post- processing
  • Numerical example
  • Step by step generalization for any no. of elements, nodes, any order Gaussian quadrature
  • Generalization of Assembly using connectivity data
  • Generalization of loading and imposition of boundary condition
  • Generalization of Post-processing using connectivity data

Brief background of Tensor calculus
  • Indicial Notation: Summation convention, Kronecker delta and permutation symbol, epsilon-delta identity
  • Gradient, Divergence, Curl, Laplacian
  • Gauss-divergence theorem: different forms

Two dimensional Scalar field problems
  • 2D Steady State Heat Conduction Problem
  • Obtaining weakform
  • Introduction to triangular and quadrilateral elements
  • Deriving element stiffness matrix and force vector
  • Incorporating different boundary conditions
  • Numerical example
  • Computer implementation: obtaining connectivity and coordinate matrix, implementing numerical integration, obtaining global stiffness matrix and global force vector, incorporating boundary conditions and finally post-processing.

Two dimensional Vector field problems
  • 2D elasticity problem
  • Obtaining weak form
  • Introduction to triangular and quadrilateral elements
  • Deriving element stiffness matrix and force vector
  • Incorporating different boundary conditions
  • Numerical example
  • Iso-parametric, sub-parametric and super-parametric elements Computer implementation: a vivid layout of a generic code will be discussed Convergence, Adaptive meshing, Hanging nodes, Post- processing
  • Extension to three dimensional problems 
  • Axisymmetric Problems: Formulation and numerical examples

Eigen value problems
  • Axial vibration of rod (1D)
  • Formulation and implementation Transverse vibration of beams (2D)
  • Formulation and implementation

Transient problem in 1D & 2D Scalar Valued Problems
  • Transient heat transfer problems
  • Discretization in time: method of lines and Rothe method
  • Formulation and Computer implementations

  • Choice of solvers: Direct and iterative solvers

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