Introduction:
General, General Description methods, Brief description of FEA for stress analysis problem, Finite element method v/s Classical method. FEM v/s FDM a brief history of FEM, need for studying FEM.
Basic equations in Elasticity:
Introduction, Stress in typical element, Equations of equilibrium, Strains, Strain displacement equations, Linear constitutive law.
Finite element basics:
Introduction, Elements, Shape functions, Co-ordinate transformation, Strain displacement relations, Stiffness equations, Body forces, Surface tractions, Geotechnical considerations: effective stress method loadings, Initial stresses, excavation, fills.
Variable – Elastic stress – Strain laws:
Introduction, Bi-linear elastic model, K-G model, Hyperbolic model, Comparison of models.
Critical state model:
Introduction, the geometric model, Hardening law, Yield function, Flow rule, Stress- strain invariant relation, Stress – strain component relation, Parameter values, Examples.
Seepage analysis:
Introduction, Finite element discretization of seepage equation, computation of velocities and flows, treatment of free surface boundary.
Analysis of jointed rock mass:
Introduction, Characteristics and discontinuities in rock masses, models behaviour of jointed rocks, generalized plane strain analysis in rock mechanics, effective stress analysis in undrained rock masses.