FEM & Constitutive Modelling in Geomechanics

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

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.

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.