Finite Element Analysis and Constitutive Modelling in Geomechanics

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 streamPREREQUISITES: Exposure to Mechanics courses & Shear strength of soilsINDUSTRY SUPPORT: Most design companies working in Geotechnical Engineering like L&T ECC, AFCONS, HCC, Keller, Golder Associates, etc

Week 1: Introduction to course, introduction to matrix algebra, concepts of finite element analysis through prismatic elements (spring, bar & beam elements) and matrix structural analysisWeek 2:Variational principles & Rayleigh-Ritz procedures in structural mechanics as a prelude to finite element techniquesWeek 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 statesWeek 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 & convergenceWeek 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 mediumWeek 8:Infinite elements for simulating semi-infinite soil domains subjected to static and dynamic loadingWeek 9:Stress and strain tensors & invariants,Introduction to nonlinear finite element techniquesDifferent types of constitutive modelsWeek 10: Nonlinear constitutive models like variable moduli models, Hyperbolic models,>Mohr Coulomb model, stress correction methods & numerical proceduresWeek 11:Elastic-Plastic constitutive models Simulation of dilation of soils Hardening soil models for excavation problemsWeek 12:Undrained and drained response of soils Consolidation analysis of soils Introduction to simulation of impact and dynamic loadingIntroduction to nonlinear finite element techniques
Different types of constitutive models