8ME4.3: FINITE ELEMENT METHODS
4L+ 0T 100 Marks Ex. Hrs: 3
UNIT 1
Introduction to FEM and its applicability, Review of mathematics: Matrix algebra, Gauss elimination
method, Uniqueness of solution, Banded symmetric matrix and bandwidth.
Structure analysis: Two-force member element, Local stiffness matrix, coordinate transformation, Assembly,
Global stiffness matrix, imposition of Boundary conditions, Properties of stiffness matrix.
UNIT 2
One-dimensional Finite Element Analysis: Basics of structural mechanics, stress and strain tensor,
constitutive relation, Principle of minimum Potential, General steps of FEM, Finite element model concept /
Discretization, Derivation of finite elements, equations using potential energy approach for linear and quadratic
1-D bar element, shape functions and their properties, Assembly, Boundary conditions, Computation of stress
and strain.
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UNIT 3
Two Dimensional Finite Element Analysis: Finite element formulation using three nodded triangular (CST)
element and four nodded rectangular element, Plane stress and Plain strain problems, Shape functions, node
numbering and connectivity, Assembly, Boundary conditions, Isoparametric formulation of 1-D bar elements,
Numerical integration using gauss quadrature formula, computation of stress and strain.
UNIT 4
Finite Element Formulation from Governing Differential Equation: Method of Weighted Residuals,
Collocation, Sub domain method, Least Square method and Galerkin’s method, Application to one dimensional
problems, one-dimensional heat transfer, etc. introduction to variational formulation (Ritz Method.)
UNIT 5
Higher Order Elements: Lagrange’s interpolation formula for one and two independent variable, Convergence
of solution, compatibility, element continuity, static condensation, p and h methods of mesh refinement, Aspect
ratio and element shape, Application of FEM, Advantages of FEM, Introduction to concept of element mass
matrix in dynamic analysis.
List of Recommended Books
1. Text Book of Finite Element Analysis, Seshu P., Prentice Hall India.
2. Finite Element Procedure in Engineering Analysis, Bathe K.J., Prentice Hall India.
3. An Introduction to the Finite Element Method, Reddy J.N., Tata McGraw-Hill, New Delhi.
4. Concepts & Applications of Finite Element Analysis, Cook and Plesha, Willey India New Delhi.
5. Introduction to Finite Elements in Engineering, Chandupatla and Belegundu, Prentice Hall India.