Module I
Historical Background, Mathematical modeling of field problems in engineering, governing equations, Discrete and continuous models, Boundary, Initial and Eigen Value problems, Weighted Residual methods, Weak (Variational) formulation of boundary value problems, Ritz technique, Basic concepts of Finite Element Method
6 hours
Module II
One-dimensional finite element analysis, Generic form of finite element equations, linear bar finite element, quadratic bar element, determination of shape functions, element matrices, fluid mechanics and heat transfer problem, Truss, Stiffness matrix for a truss element, Finite element equation for a two-node truss element, Space Trusses, Beam element, Determination of shape functions, element matrices, Frame element 6 hours

Module III
Two-dimensional scalar variable problems, Plane stress and plane strain, Finite element modelling, Constant Strain Triangular (CST) element, Shape function for CST element, Strain displacement matrix, Stress-Strain relationship matrix for two-dimensional element, Stiffness matrix equation for CST element, Temperature effect, Heat transfer in 2-Dimension (thermal problems), four-noded rectangular element, six-noded triangular element 6 hours

Module IV
Two-dimensional Vector variable problems, Equations of elasticity, Axisymmetric problems-Body forces, Temperature effect, Plate element, Displacement models for plate analysis, triangular and rectangular plate bending element, Finite element analysis of Shell element 6 hours

Module V
Isoparametric Formulation, Isoparametric, super parametric and sub parametric elements, One dimensional shape functions for isoparametric formulation of the bar element, shape function for 4 noded rectangular parent element by using natural coordinate system and co-ordinate transformation (Two Dimensional), element force vector
6 hours
Module VI
Dynamic analysis using finite elements, vibration problems, Equation of Motion based on Weak Form, axial vibration of a rod, Transverse vibration of a beam, Equation of Motion using Lagrange’s approach, Formulation of Finite Element Equations, Consistent Mass Matrices for various elements, Consistent and Lumped mass matrices, Form of Finite Element Equations for vibration problems 6 hours


Prerequisite: Sound knowledge about applied elasticity, plasticity and vibration is essential.

Designing and analysis of structural elements.

CO1: Knowledge will be gained on basic concept of FEM method.
CO2: Able to apply FEM to practical problems.
CO3: Knowledge will be enhanced to implement the concept to analyze a theoretical law.
CO4: Able to develop a plan/programme for innovation.
CO5: Knowledge can be utilized to create a startup.

O.C. Zienkiewicz, R. L. Taylor & J.Z. Zhu, The Finite Element Method Its Basic& Fundamentals, Elsevier,8th Edition 2024 , Ch. 2,3,4,67,13

J. N. Reddy, Introduction to Finite Element Method, Mc Graw Hill, 4th Edition 2020 , Ch. 1,2 ,3,4

Saeed Moaveni, Finite Element Analysis Theory and Application with ANSYS, Pearson, 5th Edition 2020 , Ch. 9,10,11

Daryl L. Logan, A First Course in Finite Element Method, CENGAGE Learning, 6th Edition, 2022 , Ch. 9,10,12