Introduction to Finite Element Method :
Engineering Analysis, History, Advantages, Classification, Basic steps, Convergence criteria, Role of finite element analysis in computer-aided design., Mathematical Preliminaries, Differential equations formulations, Variational formulations, weighted residual methods
One-Dimensional Elements-
Analysis of Bars and Trusses, Basic Equations and Potential Energy Functional,1D Bar Element, Admissible displacement function, Strain matrix, Stress recovery, Element equations, Stiffness matrix, Consistent nodal force vector: Body force, Initial strain, Assembly Procedure, Boundary and Constraint Conditions, Single point constraint, Multi-point constraint, Truss Element, Shape functions for Higher Order Elements, Co , C1 elements
Two-Dimensional Elements-Analysis of Plane Elasticity Problems:
Three- Triangular Element, Four-Noded Quadrilateral Element (QUAD 4), Shape functions for Higher Order Elements (LST, QUAD 8), Lagrange element, Strain-Displacement [B] matrix, Stiffness[K] matrix and Jacobian of CST and QUAD4 elements.
Axi-symmetric Solid Elements-
Analysis of Bodies of Revolution under axi-symmetric loading: Axisymmetric Triangular and Quadrilateral Ring Elements. Strain-Displacement [B] matrix, Stiffness[K] matrix.
Three-Dimensional Elements-Applications to Solid Mechanics Problems:
Basic Equations and Potential Energy Functional, Four-Noded Tetrahedral Element (TET 4), Eight-Noded Hexahedral Element (HEXA 8), Tetrahedral elements, Hexahedral elements: Serendipity family, Hexahedral elements: Lagrange family. Shape functions for Higher Order Elements
Beam Elements-Analysis of Beams and Frames:
1–D Beam Element, Problems.
Heat Transfer /Fluid Flow:
Steady state heat transfer, 1 D heat conduction governing equation, boundary conditions, One dimensional element, Functional approach for heat conduction, Galerkin approach for heat conduction, heat flux boundary condition, 1 D heat transfer in thin fins. Basic differential equation for fluid flow in pipes, around solid bodies, porous media.
Dynamic Considerations:
Formulation for point mass and distributed masses, Consistent element mass matrix of one dimensional bar element, truss element, beam element. Lumped mass matrix, Evaluation of eigen values and eigen vectors, Applications to bars, stepped bars, and beams.