Syllabus

• Module I: [4 hrs]
Introduction to Finite element Method: Applications of the Finite Element method (FEM), Different approaches of FEM, Direct method, Variational Principle and Weighted Residual method. Equations of equilibrium, Strain displacement relations, Stress strain relations, Plane stress and Plane strain problems, Boundary Conditions. Different steps involved in FEM. Advantages and disadvantages of FEM.

Module II: [12 hrs]
One Dimensional elements: Formulation of a linear bar element, Shape Functions Polynomial, The Potential Energy Approach, derivation of stiffness matrix for different bar, beam, truss and frame elements, Properties of stiffness matrix, Assembly of Global Stiffness Matrix and Load Vector, Boundary conditions elimination method and penalty method. Numerical Problems on bars, beam, trusses and frames. Development of FEM program for analysis of bars, beams, trusses and frames in MATLAB environment.
Module III: [8 hrs]
FEM for Two and Three Dimensional Solids6:
Different coordinate systems, element properties, Convergence criteria, pascal triangle. Lagrangian and serendipity elements, Continuity of elements, Finite Element Formulation of Constant Strain Triangle(CST) element Linear Strain Triangle Rectangular Elements Numerical Evaluation of Element Stiffness Computation of Stresses, Finite Element Formulation of Axisymmetric Element Concept of three Dimensional Elements
Module IV: [4 hrs]
Dynamic considerations: Hamilton’s Principle, Lagrange equation for discrete systems, Differential Equation of motion for generalised systems, Kinetic energy, point mass and Consistent mass matrices, Geometric stiffness matrix, Formulation of vibration and buckling problems through eigenvalues and eigenvectors.
Module V: [8 hrs]
Iso-parametric Elements: Natural coordinate system, Numerical integration: Gauss quadrature, One Dimensional Two and Three Dimensional Numerical Integration, Iso parametric, sub parametric elements, super parametric elements, shape function of four node, eight node and nine node iso-parametric elements, Analysis of plate bending problems by finite element through rectangular elements, triangular elements and quadrilateral elements, Concept of 3D modeling.

To learn basic principles of computationally efficient finite element analysis procedures.

To apply finite element solutions to dynamic problems of vibration and stability of beams.

To learn the varieties of finite element formulations for analysis of engineering structures.

To develop MATLAB based finite element programs for analysis of structures.

CO1. Understand the fundamentals of Finite Element Method (FEM).
CO2. Understand the finite element formulation of a variety of structures and solve range of engineering
problems.
CO3. Understand the application of the Finite Element method for analysis of two-dimensional complex
engineering problems like plane stress and bending of plates and axisymmetric shells.

CO4. Development of FEM based programs for computational analysis of structures using MATLAB.

CO5. Analyse the complex problems of dynamics and stability of structures.

R. D. Cook, D S Malkus and M E Plesha, Concepts and Applications of Finite Element Analysis, John Wiley& Sons, New York , .

C. S. Krishnamoorthy, Finite Element analysis-Theory and Programming, Tata McGraw Hill , .

O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, McGraw Hill Publishing Company , .

J. N. Reddy, An introduction to Finite Element Method, Tata-Mc Graw Hill, New Delhi , .