# Finite Element Method

By Prof. Biswanath Banerjee, Prof. Amit Shaw   |   IIT Kharagpur
Learners enrolled: 210
This is an introductory level course on Finite Element Method. After attending the course, the students will be able to comprehend FEM as a numerical technique to solve partial differential equations representing various physical phenomena in structural engineering. The proposed course also provides a hands-on training on translating FEM formulation into computational code in MATLAB.

INTENDED-AUDIENCE: BE/B.Tech (Elective), M.Tech, PhD.

PRE-REQUISITES : Solid Mechanics/Numerical methods in Engineering.

INDUSTRY-SUPPORT : Civil/Mechanical/Aerospace/Ocean and naval Architecture.
Summary
 Course Status : Upcoming Course Type : Elective Duration : 12 weeks Start Date : 23 Jan 2023 End Date : 14 Apr 2023 Exam Date : 29 Apr 2023 IST Enrollment Ends : 30 Jan 2023 Category : Civil Engineering Credit Points : 3 Level : Undergraduate/Postgraduate

### Course layout

Week 1: Introduction, Boundary value problems and solution methods, Direct approach – example, advantage and limitations.
Week 2: Elements of calculus of variation, Strong form and weak form, equivalence between strong and weak forms, Rayleigh-Ritz method.
Week 3: Method of weighted residuals – Galerkin and Petrov-Galerkin approach; Axially loaded bar, governing equations, discretization, derivation of element equation, assembly, imposition of boundary condition and solution, examples.
Week 4: Finite element formulation for Euler-Bernoulli beams.
Week 5: Finite element formulation for Timoshenko beams.
Week 6: Finite element formulation for plane trusses and frames computer implementation.
Week 7: Finite element formulation for two-dimensional problems - completeness and continuity, different elements (triangular, rectangular, quadrilateral etc.), shape functions, Gauss quadrature technique for numerical integration.
Week 8: Finite element formulation for two-dimensional scalar field problems; Iso-parametric formulation Application to Heat conduction and torsion problems.
Week 9: Finite element formulation for two-dimensional problems in linear elasticity; Formulation.
Week 10: Finite element formulation for two-dimensional problems in linear elasticity; Examples and computer implementation.
Week 11: Implementation issues, locking, reduced integration, B-Bar method.
Week 12: Finite element formulation for three-dimensional problems; Different elements, shape functions, Gauss quadrature in three dimension, examples.

### Books and references

1. An Introduction to Finite Element Method by J. N. Reddy.
2. A First Course in Finite Elements by Jacob Fish and Ted Belytschko.
3. Concept and Applications of Finite Element Analysis by Robert D. Cook, David S. Malkus, Michael E. Plesha, Robert J. Witt.
4. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by Thomas J. R. Hughes.

### Prof. Biswanath Banerjee

Prof. Biswanath Banerjee is presently an Assistant Professor in the Department of Civil Engineering, IIT Kharagpur. He obtained his Bachelors degree in Construction Engineering from Jadavpur University in 2000, MTech in Structures from IIT Kharagpur in 2004 and PhD in Computational Mechanics from IISc Bangalore in 2009. Prior to joining IIT Kharagpur, Professor Banerjee spent two years as Post-doctoral Research Fellow in Cornell University, USA. He has also spent for some time in industries like Gammon India Limited, TRF Limited (A Tata enterprise) and Research labs in SERC Chennai (A CSIR Unit) as a Scientist.Professor Banerjees research area is in the field of Computational Mechanics and Reverse Engineering Problems.

### Prof. Amit Shaw

IIT Kharagpur
Prof. Amit Shaw is presently an Associate Professor in the Department of Civil Engineering, IIT Kharagpur. He obtained his Bachelors degree in Civil Engineering from IIEST Shibur (formerly Bengal Engineering College Shibpur) in 2000, MTech in Structures from IIT Roorkee in 2003 and PhD in Computational Mechanics from IISc Bangalore in 2007. Prior to joining IIT Kharagpur, Professor Shaw spent two years as Research Fellow in University of Aberdeen, UK. He also worked for some time in industries like Gammon India Limited and L&T ECC.

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams:
29 April 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team