ConcordiaUniversity

Faculty of Engineering & Computer Science

Department of Mechanical and Industrial Engineering

MECH 460- FINITE ELEMENT ANALYSIS

WINTER 2007

Instructor:

R. Ganesan, Ph.D., P.Eng., Associate Professor

Dept. of Mechanical and Industrial Engineering

Office: EV04-211, Tel: 848-2424 (ext. 3164)

E-mail: ; Office hours:Fridays, 12:30p.m. - 2p.m.

Objectives:

This course should lead to a sound understanding of the fundamentals underlying the theoretical aspects of the FINITE ELEMENT METHOD, and of the way the basic concepts are employed in the analysis of engineering problems. The ability of the students to apply the concepts involved in this field will be developed and it will be enhanced through adequate training in the solution of representative simple problems. Commercial software packages (ANSYS and CATIA) currently used in industry for design purposes will be introduced and students should become familiar with their utilization. Course tests will assess mainly the students understanding of the theory and their skill in solving simple problems.

Design Soft Skill:

TEACHING – Engineering Tool Usage: An ability to create, select and apply appropriate techniques, resources, and modern engineering tools, including prediction and modelling, to a range of engineering activities, from simple to complex, with an understanding of the associated limitations.

PRACTICE – Problems given in the assignments and project will involve significantly the activities and tools as mentioned in the above.

EVALUATION –The grade for assignments is given below. The project report and presentation will be assessed for the corresponding components in the grade for project.

Text:

D.L.Logan, A First Course in the Finite Element Method, 4thEdition,Thomson, 2007.

Course Grading:

Assignments (10%)

Project (10%)

Labs (20%)

Mid-term exam (20%) on Wednesday, February 14, 2007

Final exam (40%) scheduled during regular examination period.

NOTE:

Mid-term and Lab aremandatory, and students must complete satisfactorily all the labs in order to obtain a passing grade in the course.

There will be no make up test. Students who miss the Mid-term test will lose 20%. However, students who miss the test for university accepted valid reason would write the final for 60%.

COURSE OUTLINE:

1. Introduction

Background and the Basic Concept of the Finite Element Method.

2. Introduction to the Stiffness or Displacement Method

Element Stiffness Equation. Element Stiffness, Displacement, and Force Matrices.From Element Equations to System Equations.Compatibility and Equilibrium Equations. Assembly Process. Structure Stiffness, Displacement, and Force Matrices.Boundary Conditions. Solution Procedure.Potential Energy Approach.

3. Development of Truss Element

Truss Stiffness Equation. Element and Global Coordinate Systems. Global Stiffness Matrix and its Form. Boundary Conditions. Truss Element in 3D Space.

4. Development of Beam and Frame Elements

Beam Stiffness Equation. Frame Element: Beam Element with Combined Bending and AxialDeformations.Beam Element with a Nodal Hinge. 3D Beam and Frame Elements. Element and Global Reference Axes. Global Stiffness Matricesfor 2D and 3D Beam and Frame Elements.

5. Derivation of Element Equations for Continuum Elements

Stresses and Strains. Strain-displacement Relations. Stress-Strain Relations. Shape (Interpolation) Functions. Derivation of Stiffness Equations using Potential Energy. Equivalent Nodal Force Vectors due to Surface Forces, Body forces, Initial Stresses and Initial Strains. Derivation of Inertia (Mass) Matrix using Kinetic Energy.

  1. Two-Dimensional Elements

Plane stress and Plane Strain Elements. Shape functions. Stiffness and Mass Matrices. Treatment of Body Forces, Surface Forces and Thermal Strains. Finite Element Solution of a Plane Stress Problem. Time Integration of Equations of Motion.Natural Coordinates and Isoparametric Formulation.

  1. Weighted Residual Methods

Basic Functions. Residual and Error. Method of Moments. Galerkin Method. Boundary Value Problems. Satisfaction of the Natural Boundary Conditions.

  1. Non-structural Problems

One Dimensional Finite Element Formulation using Galerkin weighted residual method. Finite Element Model for Heat Transfer with Convection.

LABORATORY

LAB # 1: STATIC ANALYSIS: TRUSS STRUCTURES

LAB # 2:STATIC ANALYSIS: FRAME STRUCTURES

LAB # 3: STATIC ANALYSIS: 2-D PROBLEMS

LAB # 4:DYNAMICANALYSIS (MODAL ANALYSIS-TRANSIENT ANALYSIS)

LAB # 5:NON-STRUCTURAL PROBLEMS (THERMAL and FLUID ANALYSIS)

LAB # 6:INTRODUCTION to CATIA