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FINITE ELEMENT METHODS (NME-012)

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Syllabus of FINITE ELEMENT METHODS (NME-012)

Unit 1
Introduction, exact solution vs approximate solution, principle of FEM, general procedure for finite
element analysis, pre-processing, solution, post processing, various approximate methods, weighted
residual method, variational or Rayleigh Ritz method, principle of minimum potential energy.
Review of matrices, definition, types, addition or subtraction, multiplication, inverse of a matrix, calculus
of matrix.
8
Unit II
Direct stiffness methods, linear spring as finite element, direct formulation of uni-axial bar, truss and
beam elements, local and global coordinates, nodes and elements, stiffness matrix, formulation of global
stiffness matrix, application of boundary conditions and forces, essential and natural boundary conditions,
elimination method, penalty methods, calculation of element stresses and strains.
8
Unit III
Finite element formulation of 1-d problems, method of weighted residuals, strong and weak form, the
Galerkin finite element method, application of Galerkin’s method to uni-axial bar and truss elements,
Galerkin method for one dimensional heat conduction problems like heat transfer through wall, heat
transfer through fin etc., one dimensional conduction with convection.
8
Unit IV
Interpolation or shape functions, compatibility, completeness and convergence requirements, shape
functions for one and two dimensional elements, finding shape function using Lagrange polynomials.
Application of FEM in scalar field problems, heat transfer in two dimensions, time dependent heat
transfer.
8
Unit V
Concepts of plane stress and plain strain, displacement relation, stress-strain relations, equilibrium and
compatibility equations, vector field problems, derivation of constant strain triangular element stiffness
matrix and equations, treatment of body and surface forces, stress and strain computation.
Practical considerations in finite element application, programming aspects, commercially available FEM
packages, desirable features of a FEM packages, problem solving on a general purpose FEM software
package like ANSYS, ABAQUS, NISA etc.

Books and References:
1. Fundamentals of Finite Element Analysis by David V Hutton, McGraw-Hill Learning
2. A First Course in Finite Element Method 5e by Daryl L Logan, Cengage Learning
3. Finite Element Analysis by G L Narasaiah, BS Publications.
4. An Introduction to Finite Element Method, 3e by J N Reddy, McGraw-Hill
5. Finite Element Method with Application in Engineering by Desai, Eldho and Shah, Pearson
Education.
6. Introduction to Finite Element Analysis and Design by Kim & Shankar, John Wiley & Sons.
7. Introduction to Finite Elements in Engineering by Chandrupatla&Belagundu, Pearson Education.

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