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Basics of Finite Element Analysis

Basics of Finite Element Analysis. Instructor: Prof. Nachiketa Tiwari, Department of Mechanical Engineering, IIT Kanpur. This course is intended for all those who want to learn Finite Element Analysis from an application standpoint. Currently, many users of FEA have limited understanding of theoretical foundation of this powerful method. The consequence is that quite often they use commercial codes inaccurately, and do not realize that their results may be flawed. The course is intended to address this limitation by making the student aware of the underlying mathematics in easy to understand format. The course is open to all engineering students who have at the minimum successfully completed two years of their B. Tech (or equivalent) degrees. The course is also open to all professionals in industry who wish to learn fundamentals of FEA in a semi-formal but structured setting, and plan to use this knowledge in their workplace. (from nptel.ac.in)

Lecture 11 - Gradient and Divergence Theorems (cont.)

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Lecture 01 - Introduction to Finite Element Analysis (FEA)

Lecture 02 - Philosophy of FEA, Nodes, Elements and Shape Functions

Lecture 03 - Nodes, Elements and Shape Functions

Lecture 04 - Polynomials as Shape Functions, Weighted Residuals, Elements and Assembly Level Equations

Lecture 05 - Types of Errors in FEA, Overall FEA Process and Convergence

Lecture 06 - Strengths of Finite Element Method, Continuity Conditions at Interfaces

Lecture 07 - Key Concepts and Terminologies

Lecture 08 - Weighted Integral Statements

Lecture 09 - Integration by Parts - Review

Lecture 10 - Gradient and Divergence Theorems

Lecture 11 - Gradient and Divergence Theorems (cont.)

Lecture 12 - Functionals

Lecture 13 - Variational Operator

Lecture 14 - Weighted Integral and Weak Formulation

Lecture 15 - Weak Formulation

Lecture 16 - Weak Formulation and Weighted Integral: Principle of Minimum Potential Energy

Lecture 17 - Variational Methods: Rayleigh Ritz Method

Lecture 18 - Rayleigh Ritz Method

Lecture 19 - Method of Weighted Residuals

Lecture 20 - Different Types of Weighted Residual Methods

Lecture 21 - Different Types of Weighted Residual Methods (cont.)

Lecture 22 - FEA Formulation for Second Order Boundary Value Problem

Lecture 23 - FEA Formulation for Second Order Boundary Value Problem (cont.)

Lecture 24 - Element Level Equations

Lecture 25 - Second Order Boundary Value Problem

Lecture 26 - Assembly of Element Equations

Lecture 27 - Assembly of Element Equations, Implementation of Boundary Conditions

Lecture 28 - Assembly Process and Connectivity Matrix

Lecture 29 - Radially Symmetric Problems

Lecture 30 - One Dimensional Heat Transfer

Lecture 31 - 1D-Heat Conduction with Convective Effects; Examples

Lecture 32 - Euler-Bernoulli Beam

Lecture 33 - Interpolation Functions for Euler-Bernoulli Beam

Lecture 34 - Finite Element Equations for Euler-Bernoulli Beam

Lecture 35 - Assembly Equations for Euler-Bernoulli Beam

Lecture 36 - Boundary Conditions for Euler-Bernoulli Beam

Lecture 37 - Shear Deformable Beams

Lecture 38 - Finite Element Formulation for Shear Deformable Beams

Lecture 39 - Finite Element Formulation for Shear Deformable Beams (cont.)

Lecture 40 - Equal Interpolation but Reduced Integration Element

Lecture 41 - Eigenvalue Problems

Lecture 42 - Eigenvalue Problems: Examples

Lecture 43 - Introduction to Time Dependent Problems

Lecture 44 - Spatial Approximation

Lecture 45 - Temporal Approximation for Parabolic Problems

Lecture 46 - Temporal Approximation for Parabolic Problems (cont.)

Lecture 47 - Temporal Approximation for Hyperbolic Problems

Lecture 48 - Explicit and Implicit Methods, Diagonalization of Mass Matrix