JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Strength of Materials, Mathematics, Heat Transfer and Vibrations.

Course Objectives:

• To Introduce the basic concepts of the finite element method, the boundary element method
• To discuss the advantages and limitations of each method
• To Demonstrate the capabilities of each method on a variety of problems Course outcomes: After completing this course, the student should be able to
• Understand the background of mathematical equations used for development of modeling software modules to develop the various structural related applications
• Identify mathematical model for solution of common engineering problems of 2D & 3D.
• Solve structural, thermal, fluid flow problems.
• Know the application of plate bending and nonlinear finite element of solids.
• Use professional-level finite element software to solve engineering problems in boundary element method.

UNIT - I

One Dimensional Problems: Formulation of Stiffness Matrix for a Bar Element by the Principle of Minimum Potential Energy, Properties of Stiffness Matrix, Characteristics of Shape Functions, Quadratic shape functions. Analysis of Trusses: Derivation of Stiffness Matrix for Trusses, Stress and strain Calculations, Calculation of reaction forces and displacements. Analysis of Beams: Derivation of Stiffness matrix for two noded, two degrees of freedom per node beam element, Load Vector, Deflection, Stresses, Shear force and Bending moment, Problems on uniform and stepped beams for different types of loads applied on beams.

UNIT - II

Finite element – formulation of 2D Problems: Derivation of Element stiffness matrix for two- dimensional CST Element, Derivation of shape functions for CST Element, Elasticity Equations, constitutive matrix formulation, Formulation of Gradient matrix. Two dimensional Isoparametric Elements and Numerical integration. Finite element – formulation of 3D problems: Derivation of Element stiffness matrix for Tetrahedron Element, Properties of Shape functions for 3D Tetrahedral Element, Stress-Strain Analysis for 3D Element, Strain Displacement for Relationship Formulation.

UNIT - III

Steady state heat transfer analysis: One Dimensional Finite Element analysis of fin and composite slabs. Two-dimensional steady state heat transfer problems: Derivation of Thermal Stiffness matrix for 2D heat transfer problems-CST, Derivation of thermal force vector for 2D heat transfer problems. Dynamic Analysis: Formulation of mass matrices for uniform bar and beam Elements using lumped and consistent mass methods, Evaluation of Eigen values and Eigen vectors for a stepped bar and beam Problems.

UNIT - IV

R22M.Tech. CAD/CAM JNTUH

Plate Bending: Introduction – Plate behavior – C1(Kirchoff) Plate elements – C0(Mindlin) Plate elements – Mindlin beam – More devices for C0Plate elements – Boundary conditions - Analytical problems. Nonlinear finite element of solids: Material Nonlinearities, objective rates, nonlinear elasticity, Plasticity, viscoplasticity, viscoelasticity

UNIT - V

Boundary Element Method: Potential Problems: Introduction, boundary Element Approach- Fundamental solution. Numerical Implementation - Determination of Ci, Final Relation, Three- dimensional analysis, tackling kernel singularity. Boundary Element Formulation for Electrostatic Problems: Introduction, Basic Relation- Boundary condition, other relations. Discretization and Matrix Formulation – Determination of term C(p)m.

TEXT BOOKS:

• 1. Finite and Boundary Element Methods in Engineering by O.P. Gupta, Oxford &IBH Publishing Co. Pvt. Ltd
• 2. The finite element methods in Engineering by S.S. Rao, Elsevier, 4th edition

REFERENCE BOOKS:

• 1. Finite Element Methods by Alavala, PHI.
• 2. Introduction to Finite Elements in Engineering by Tirupathi K. Chandrupatla and Ashok D. Belagundu.
• 3. An Introduction to Finite Element Methods by J. N. Reddy, Mc Grawhill
• 4. The Finite element method in engineering science by O.C. Zienkowitz, Mc Graw hill.
• 5. Concepts and Applications of Finite Element Analysis by Robert Cook, Wiley R22M.Tech. CAD/CAM JNTUH M. TECH. I Year I Sem. (CAD/CAM)