Basics of Finite Element Analysis-I

Total Lectures

48

Introduction to Finite Element Analysis(FEA)

Lectures

Introduction to Finite Element Analysis(FEA)
Philosphy of FEA, Nodes, Elements & Shape Functions
Nodes, Elements & Shape Functions
Polynomials as Shape Functions, Weighted Residuals, Elements & Assembly Level Equations
Types of Errors in FEA, Overall FEA Process & Convergence
Strengths of FE Method, Continuity conditions at Interfaces
Key concepts and terminologies
Weighted integral statements
Integration by parts -Review
Gradient and Divergence Theorems-Part I
Gradient and Divergence Theorems Part-II
Functionals
Variational Operator
Weighted integral & Weak formulation
Weak Formulation
Weak Formulation & Weighted Integral : Principle of minimum potential energy
Variational Methods : Rayleigh Ritz Method
Rayleigh Ritz Method
Method of Weighted Residuals
Different types of Weighted Residual Methods - Part I
Different types of Weighted Residual Methods - Part II
FEA formulation for 2nd order BVP - Part I
FEA formulation for 2nd order BVP - Part II
Element Level Equations
2nd Order Boundary Value Problem
Assembly of element equations
Assembly of element equations, and implementation of boundary conditions
Assembly process and the connectivity matrix
Radially Symmetric Problems
One dimensional heat transfer
1D-Heat conduction with convective effects : examples
Euler-Bernoulli beam
Interpolation functions for Euler-Bernoulli beam
Finite element equations for Euler-Bernoulli beam
Assembly equations for Euler-Bernoulli beam
Boundary conditions for Euler-Bernoulli beam
Shear deformable beams
Finite element formulation for shear deformable beams : Part - I
Finite element formulation for shear deformable beams : Part - II
Equal interpolation but reduced integration element
Eigenvalue problems
Eigenvalue problems : examples
Introduction to time dependent problems
Spatial approximation
Temporal approximation for parabolic problems : Part-I
Temporal approximation for parabolic problems : Part-II
Temporal approximation for hyperbolic problems
Explicit and implicit method, diagonalization of mass matrix, closure
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