Finite Element Analysis and Constitutive Modelling in Geomechanics

By Prof. K.Rajagopal | Andhra University

Learners enrolled: 339 | Exam registration: 34

ABOUT THE COURSE:

The course will introduce the students to both theoretical and practical aspects of finite element methods applicable to geotechnical engineering. The course will start from the fundamental aspects of matrix structural analysis and move into finite element techniques through variational principles. Special focus of this course will be on topics related to geotechnical problems like modelling of infinite soil media, construction and excavation sequences, jointed mass, and nonlinear analysis techniques. Fundamentals of different topics of isoparametric computations and nonlinear & elastic plastic analysis are explained through simple to use computer programs and detailed flow-charts.

INTENDED AUDIENCE: Senior level UG Civil Engineering & all PG level Civil Engineering students in geotechnical engineering stream

PREREQUISITES: Exposure to Mechanics courses & Shear strength of soils

INDUSTRY SUPPORT: Most design companies working in Geotechnical Engineering like L&T ECC, AFCONS, HCC, Keller, Golder Associates, etc

Summary

Course Status :	Ongoing
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Civil Engineering
Credit Points :	3
Level :	Postgraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	02 Feb 2026
Exam Registration Ends :	20 Feb 2026
Exam Date :	19 Apr 2026 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Introduction to course, introduction to matrix algebra, concepts of finite element analysis through prismatic elements (spring, bar & beam elements) and matrix structural analysis

Week 2: Variational principles & Rayleigh-Ritz procedures in structural mechanics as a prelude to finite element techniques

Week 3: Continuum, stress & strain states, equations of equilibrium, compatibility & linear elastic constitutive equations, derivation of equilibrium equations for continuum, Plane stress, plane strain and axisymmetric and 3-d stress states

Week 4: Generalized Coordinate methods for deriving shape functions, Lagrange methods for shape functions 3-node CST element for finite element analysis and some simple calculations using this element

Week 5: Numerical integration techniques, Isoparametric transformations, shape functions in isoparametric space, Patch test & convergence

Week 6: Isoparametric element calculations - numerical examples & computer programs for different computations like stiffness matrix, load vector due to self-weight, stresses, etc.

Week 7: In situ stress states in soil medium, Simulation of construction and excavation sequences in finite element analysis, Joint elements for simulating discontinuities in geologic medium

Week 8: Infinite elements for simulating semi-infinite soil domains subjected to static and dynamic loading

Week 9: Stress and strain tensors & invariants,Introduction to nonlinear finite element techniquesDifferent types of constitutive models

Week 10: Nonlinear constitutive models like variable moduli models, Hyperbolic models,>Mohr Coulomb model, stress correction methods & numerical procedures

Week 11: Elastic-Plastic constitutive models Simulation of dilation of soils Hardening soil models for excavation problems

Week 12: Undrained and drained response of soils Consolidation analysis of soils Introduction to simulation of impact and dynamic loading

Introduction to nonlinear finite element techniques
Different types of constitutive models

Books and references

1. Bathe, K.J. (1996) Finite Element Procedures in Engineering Analysis, Prentice Hall, Prentice-Hall of India Pvt. Ltd., New Delhi. (topics – 2, 3, 6, 11 & 12)

2. Bhatti, M. A. (2005) Fundamental Finite Element Analysis and Applications, John Wiley & Sons, Inc., Hoboken, NJ, USA.

3. Britto, A.M and Gunn, M.J. (1987) Critical State Soil Mechanics Via Finite Elements, Ellis Horwood Publishers, Chichester, England.

4. Cook. R.D., Malkus, D.S. and Plesha, M.E. (2000) Concepts and Applications of Finite Element Analysis, 4th Edition, Prentice Hall-India, New Delhi. (all topics)

5. Desai, C.S. and Siriwardane, H.J. (1984) Constitutive Laws for Engineering Materials, Prentice-Hall, Inc., Englewood Cliffs, N.J.

6. Desai, C.S. and Zaman, M. (2014) Advanced Geotechnical Engineering: Soil-Structure Interaction Using Computer and Material Models, CRC press, Boca Raton, FL, USA.

7. Hinton, E. and Owen, D.R.J. (1977) Finite Element Programming, Academic Press.

8. Hinton, E. and Owen, D.R.J. (1979) An Introduction to Finite Element Computations, Pineridge Press, Swansea.

9. Krishnamoorthy, C.S. (1994) Finite Element Analysis: Theory and Programming, Tata McGraw Hill, New Delhi.

10. Owen, D.R.J. and Hinton, E. (1980) Finite Elements in Plasticity: Theory and Practice, Pineridge Press Limited, Swansea, U.K.

11. Potts D.M. and Zdravkovic, L. (2001) Finite element analysis in geotechnical engineering: Theory and application, Vols. 1 & 2, Thomas Telford, London, UK

12. Rao, S.S. (2001) The Finite Element Method in Engineering, Butterworth Heinemann, New Delhi. 13. Zienkiewicz, O.C. and Taylor, R.L. (1989) Finite Element Method (4th edition) McGraw-Hill, London, U.K.

Instructor bio

Prof. K.Rajagopal

Andhra University

Prof. K. Rajagopal joined as an Adjunct Professor at Andhra University, Visakhapatnam after retirement from the services of IIT Madras (Department of Civil Engineering). He has more than 25 years of experience with teaching and research in geosynthetics and reinforced soil structures.

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: : April 19, 2026 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

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

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 Madras .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