Course11210419348 lectures
Basics of Finite Element Analysis - I
Prof. Nachiketa Tiwari · IIT Kanpur
About
This course is intended for all those who want to learn FEA 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.
Intended audience: UGs, PGs, professionals in industry who want to learn about basics of sound and acoustics
Prerequisites: Must be enrolled into a B.Tech. program or equivalent and should have completed second year of his 4-year program
Lectures
Week 1
- Lecture 1: Introduction to Finite Element Analysis (FEA)
- Lecture 2: Philosophy of FEA, Nodes , Element and Shape Functions
- Lecture 3: Nodes, Elements and Shape Functions
- Lecture 4: Polynomials as Shape Functions, Weighted Residuals, Element and Assembly level equations
- Lecture 5: Types of Errors in FEA, Overall FEA process, Convergence
- Lecture 6: Strengths of FE Method, Continuity conditions at Interfaces
Week 2
- Lecture 7: Key concepts and terminologies
- Lecture 8: Weighted integral statements
- Lecture 9: Integration by parts -Review
- Lecture 10: Gradient and Divergence Theorems-Part I
- Lecture 11: Gradient and Divergence Theorems Part-II
- Lecture 12: Functionals
Week 3
- Lecture 13: Variational Operator
- Lecture 14: Weighted Integral & Weak Formulation
- Lecture 15: Weak Formulation
- Lecture 16: Weak Formulation & Weighted Integral : Principle of minimum potential energy
- Lecture 17: Variational Methods : Rayleigh Ritz Method
- Lecture 18: Rayleigh Ritz Method
Week 4
- Lecture 19: Method of Weighted Residuals
- Lecture 20: Different types of Weighted Residual Methods - Part I
- Lecture 21: Different types of Weighted Residual Methods - Part II
- Lecture 22: FEA formulation for 2nd order BVP - Part I
- Lecture 23: FEA formulation for 2nd order BVP - Part II
- Lecture 24: Element Level Equations
Week 5
- Lecture 25: 2nd Order Boundary Value Problem
- Lecture 26: Assembly of element equations
- Lecture 27: Assembly of element equations, and implementation of boundary conditions
- Lecture 28: Assembly process and the connectivity matrix
- Lecture 29: Radially Symmetric Problems
- Lecture 30: One dimensional heat transfer
Week 6
- 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
Week 7
- Lecture 37 : Shear deformable beams
- Lecture 38 : Finite element formulation for shear deformable beams : Part - I
- Lecture 39 : Finite element formulation for shear deformable beams : Part - II
- Lecture 40 : Equal interpolation but reduced integration element
- Lecture 41 : Eigenvalue problems
- Lecture 42 : Eigenvalue problems : examples
Week 8
- Lecture 43 : Introduction to time dependent problems
- Lecture 44 : Spatial approximation
- Lecture 45 : Temporal approximation for parabolic problems : Part-I
- Lecture 46 : Temporal approximation for parabolic problems : Part-II
- Lecture 47 : Temporal approximation for hyperbolic problems
- Lecture 48 : Explicit and implicit method, diagonalization of mass matrix, closure
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Kanpur
- Department
- Mechanical Engineering
- Teacher
- Prof. Nachiketa Tiwari
- Level
- Undergraduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed