SF4003 Finite Element Method in Geotechnical Engineering Syllabus:
SF4003 Finite Element Method in Geotechnical Engineering Syllabus – Anna University PG Syllabus Regulation 2021
OBJECTIVES:
Students are focused on acquiring the basic knowledge and computational skills in terms of finite element formulation with respect to various kinds of Geotechnical Engineering problems.
UNIT I BASIC CONCEPTS
Basic concepts – discretization of continuum, typical elements, the element characteristic matrix, element assembly and solution for unknowns – applications. Variational principles, variational formulation of boundary value problems, variational methods of approximation such as Ritz and weighted residual (Galerkin) methods.
UNIT II DISPLACEMENT MODELS
Displacement based elements – element equations, convergence requirements, shape functions – element stresses and strains – element stiffness matrix – global equations – boundary conditions – solution of global equations – finite elements for axi-symmetric problem – one dimensional problem of stresses and strains – finite element analysis for two – dimensional problems.
UNIT III ISOPARAMETRIC FORMULATION
Isoparametric element – Local and Natural Co-ordinates systems, Line, Triangular, Quadrilateral and Tetrahedral Element-Interpolation – Displacement Models Formulation of Isoparametric – Finite element matrices in Local and Global Coordinate system – refined elements – numerical integration techniques.
UNIT IV GEOTECHNICAL CONSIDERATION
Total stress analysis – pore pressure calculation – FEM to model structural components, strain definitions, constitutive equation, finite element formulation, membrane elements – Finite elements to model interfaces – basic theory – finite element formulation – boundary conditions – finite element theory for nonlinear behavior of soils.
UNIT V APPLICATION IN GEOTECHNICAL ENGINEERING
Use of FEM to problems in soils – description and application to consolidation – seepage – FEM to simulate soil – structure interaction problems – finite element theory for simulating and analyzing the real foundation problem such as footing, pile foundation and deep excavations.
OUTCOMES:
On completion of the course, the student is expected to be able to
CO1 understand the basic concept involved in finite element method using variational principles
CO2 differentiate various types of displacement models, select suitable finite element model and able to solve geotechnical problems
CO3 understand the basic concept of isoparametric finite element formulation and its use in solving geotechnical related problems
CO4 consider the various geotechnical concept in the finite element formulations including interfacial behaviour
CO5 develop finite element formulation for different geotechnical engineering related problems
REFERENCES:
1. Cook, R.D., Malkus, D.S., and Plesha, M.E., Concepts and applications of finite element analysis, John Wiley, New York., 1989.
2. Krishnamoorthy.C.S., Finite element analysis Theory and Programming, Tata McGraw-Hill, New Delhi, 1990.
3. Naylor, Pande, Finite elements in geotechnical engineering, Simpson and Tabb., Pineridge Press Ltd, Swansea, U. K, 1981.
4. Zienkiewicz, O.C., The Finite Element Method, 3rd Edition, Tata McGraw-Hill publishing Co., New Delhi, 1983.
5. Logan, D.L., A First Course in the Finite Element Method, 5th edition, Cengage-Learning, United States, 2012.
6. Desai, Y. M., Eldho, T. L. and Shah, A. H., Finite element method with applications in engineering, Dorling Kindersley (India) Pvt. Ltd., New Delhi, 2014.
7. Potts, D.M. and Zdravkovic, L., Finite element analysis in geotechnical engineering – theory. Thomas Telford, London, 1999.
8. Potts. D. M. and Zdravkovic, L., Finite Element Analysis in Geotechnical Engineering: Application, Thomas Telford, London, 2001.
9. Reddy, J.N., An introduction to the finite element method, McGraw Hill, New York, 1984.
10. Rao, S.S., The Finite Element Methods in Engineering, Pergamon, New York, 1998.
11. Zienkiewicz, O. C., Taylor, R. L. and Zhu, J. Z., The Finite Element Method Its Basis and Fundamentals, Elsevier, Amsterdam, 2014.
12. Shen, J. and Kushwahs, R.L., Soil-machine introduction – A finite element perspective, Moral Dikker, Inc., 1998.
13. Smith, I.M., Programming the Finite Element Method with application to Geomechanics, John Wiley and Sons, New Delhi, 2000.