InfoCoBuild

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)

 Introduction

 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

 References 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.