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Basics of Finite Element Analysis II

Basics of Finite Element Analysis II. 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 41 - Numerical Integration Schemes for 2D Problems


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Lecture 01 - Overview of the Course
Lecture 02 - Fundamental Principles
Lecture 03 - Steps followed in Finite Element Analysis
Lecture 04 - Weak Formulation
Lecture 05 - Weak Formulation: Example Problems
Lecture 06 - Assembling Element Level Equations
Lecture 07 - Errors in FEA Solution
Lecture 08 - Measures of Errors in FEA Solution
Lecture 09 - Convergence and Accuracy of Solution
Lecture 10 - Convergence and Accuracy of Solution (cont.)
Lecture 11 - Discussion on Energy Convergence
Lecture 12 - Observations on Types of Convergences
Lecture 13 - Numerical Integration Schemes
Lecture 14 - Numerical Integration Schemes (cont.)
Lecture 15 - Approximations
Lecture 16 - Approximations: Shape functions, Jacobian
Lecture 17 - Approximations: Jacobian, Types of Formulation, Numerical Integration
Lecture 18 - Gauss Quadrature
Lecture 19 - Gauss Quadrature Review
Lecture 20 - Gauss Quadrature: Evaluation of Kij (cont.)
Lecture 21 - Gauss Quadrature: Evaluation of Kij (cont.)
Lecture 22 - Newton-Cotes Quadrature
Lecture 23 - Two Dimensional FEM Problem
Lecture 24 - Two Dimensional One Variable FEM Problem
Lecture 25 - 2D Finite Element Problems with Single Variable (Model Equation)
Lecture 26 - 2D Finite Element Problems with Single Variable (Weak Formulation)
Lecture 27 - Elemental Level 2D Finite Element Equations
Lecture 28 - Interpolation Functions for 2D Finite Element Problems
Lecture 29 - Interpolation Functions for Linear Triangular Elements
Lecture 30 - Interpolation Functions for Linear Triangular Elements (cont.)
Lecture 31 - Interpolation Functions for Triangular and Rectangular Elements
Lecture 32 - Equation of Stiffness and Force Matrices
Lecture 33 - Stiffness and Force Matrices for Triangular Element
Lecture 34 - Stiffness and Force Matrices for Rectangular Element
Lecture 35 - Boundary Elements for Finite Element Equations
Lecture 36 - Boundary Integrals for Triangular Element
Lecture 37 - Assembly of 2D Finite Elements
Lecture 38 - Assembly of 2D Finite Elements (cont.)
Lecture 39 - 2D Heat Transfer Problems
Lecture 40 - 2D Heat Transfer Problems (cont.)
Lecture 41 - Numerical Integration Schemes for 2D Problems
Lecture 42 - Jacobian and Transformation Matrix for 2D Problems
Lecture 43 - Numerical Integration Schemes for 2D Problems: Closure
Lecture 44 - Gaussian Quadrature Points, Post Processing
Lecture 45 - Plane Elasticity Problems
Lecture 46 - Plane Elasticity Problems: Development of Weak Form
Lecture 47 - Plane Elasticity Problems: Element Level Equations
Lecture 48 - Plane Elasticity Problems: Closure