Finite Element Methods

FINITE ELEMENT METHOD

Objectives:

It covers the fundamental and theoretical approach beginning with a review of differential equations, boundary conditions, integral forms, interpolation, parametric geometry, numerical integration, and matrix algebra.

Next, engineering applications to field analysis, stress analysis and vibrations are introduced. Time-dependent problems are also treated.

Students are also introduced, employing selected tutorials, to the commercial finite element system SolidWorks which is similar to one they could be expected to use upon graduation. Graduate students will also be introduced to the more powerful (and difficult to use) Ansys system.

UNIT–I

Introduction to Finite Element Method for solving field problems. Stress and Equilibrium. Strain – Displacement relations. Stress-strain relations. One Dimensional problems : Finite element modeling coordinates and shape functions. Potential Energy approach : Assembly of Global stiffness matrix and load vector. Finite element equations, Treatment of boundary conditions, Quadratic shape functions.

UNIT–II

Analysis of Trusses : Stiffness Matrix for Plane truss element, Stress Calculations and Problems. Finite element modeling of two dimensional stress analysis with constant strain triangles and treatment of boundary conditions.

UNIT–III

Axisymmetric solids subjected to Axisymmetric loading with triangular elements.Two dimensional four noded isoparametric elements and numerical integration.

UNIT–IV

Steady state heat transfer analysis : one dimensional analysis of a fin and two dimensional analysis of thin plate. Analysis of a uniform shaft subjected to torsion.

Analysis of Beams: Element stiffness matrix for two noded, two degrees of freedom per node beam element and simple problems

UNIT-V

Dynamic Analysis : Formulation of finite element model, element matrices, evaluation of Eigen values and Eigen vectors for a stepped bar and a beam.

TEXT BOOKS:

Finite Element Analysis by S.M.D.Jalaluddin, Anuradha Publishers.

Introduction to Finite Elements in  Engineering / T.R.Chandraputla, Ashok D. Belegundu/Prentice – Hall. The Finite Element Method for Engineers – Kenneth H. Huebner, Donald L. Dewhirst, Douglas E.Smith and Ted G. Byrom / John Wiley & sons (ASIA) Pte Ltd.

REFERENCE BOOKS:

An introduction to Finite Element Method / JN Reddy / Me Graw Hill

The Finite Element Methods in Engineering / SS Rao / Pergamon

Finite Element Analysis/ C.S.Krishna Murthy.

Outcomes:

Upon completion of the course students should be able to:

Develop an integral form of a given differential form of equilibrium condition

Understand parametric interpolation and parametric geometry enforce essential boundary conditions to a matrix system

Graduate students to know the more powerful and difficult to use Ansys system.

UNIT I

INTRODUCTION: The finite element analysis is a numerical technique. In this method, the complexities of the problems, like varying shape, boundary conditions, and loads are maintained as they are but the solutions obtained are approximate. The fast improvements in computer hardware technology and slashing of cost of computers have boosted this method, since the computer is the basic need for the application of this method. Many popular brand of finite element analysis packages are now available commercially Some of the popular packages are STAAD-PRO, GT-STRUDEL, NASTRAN, NISA and ANSYS.