Introduction to Finite Element Method

Course Numbers: 20-MECH-5025;   Fall Semester

Instructor: Dr. Yijun Liu, Professor of Mechanical Engineering


Contents of the Lectures

Chapter 1. Introduction

  • Lecture 1. Introduction to FEM
  • Lecture 2. Review of Matrix Algebra
  • Lecture 3. Stiffness Matrix for Spring Element; FE Equations
  • Lecture 4. Assembly of Stiffness Matrices; Examples
  • Homework Problems

Chapter 2. Bar and Beam Elements. Linear Static Analysis

  • Lecture 1. Linear Static Analysis; Bar Element
  • Lecture 2. Examples
  • Lecture 3. Distributed Load; Transformation of Coordinate Systems; Element Stress
  • Lecture 4. Examples
  • Lecture 5. Introduction to ANSYS (Computer Lab Session 1)
  • Lecture 6. Beam Elements
  • Lecture 7. Examples; Distributed Load
  • Review
  • Midterm Exam
  • Lecture 8. More Examples of Beam Elements, Frame Analysis
  • Lecture 9. Use of ANSYS (Computer Lab Session 2)
  • Homework Problems

Chapter 3. Two-Dimensional Problems

  • Lecture 1. Review of the Basic Theory in 2-D Elasticity
  • Lecture 2. Stiffness Matrices for 2-D Problems; T3 Element
  • Lecture 3. T6, Q4 and Q8 Elements; Example
  • Lecture 4. Distributed Loads; Stress Calculation; Discussions
  • Review
  • Homework Problems

Chapter 4. FE Modeling and Solution Techniques

  • Lecture 1. Symmetry in FEA
  • Lecture 2. Use of ANSYS (Computer Lab Session 3)
  • Lecture 3. Nature of FEA Solutions; Error, Convergence and Adaptivity
  • Lecture 4. Substructures (Superelements) in FEA; Equation Solving
  • Computer Lab Assignment 1

Chapter 5. Plate and Shell Elements

  • Lecture 1. Plate Theory
  • Lecture 2. Plate Elements;   Shell Theory and Shell Elements
  • Lecture 3. Use of ANSYS  (Computer Lab Session 4)
  • Computer Lab Assignment 2

Chapter 6. Solid Elements for 3-D Problems

  • Lecture 1. Review of 3-D Elasticity; FE Formulation 
  • Lecture 2. 3-D Solid Elements; Element Formulation; 3-D Examples
  • Lecture 3. Use of ANSYS (Computer Lab Session 5)
  • Lecture 4. Solids of Revolution; Axisymmetric Elements; Examples
  • Computer Lab Assignment 3

Chapter 7. Structural Vibration and Dynamics

  • Lecture 1. Review of Basic Dynamic Equations
  • Lecture 2. Free Vibration (Normal Mode) Analysis
  • Lecture 3. Use of ANSYS (Computer Lab Session 6)
  • Lecture 4. Damping; Modal Equations; Frequency Response Analysis
  • Lecture 5. Use of ANSYS (Computer Lab Session 7 - Preview of the final projects)
  • Lecture 6. Transient Response Analysis; Examples
  • Computer Lab Assignment 4
  • Final Project Assignment

Chapter 8. Thermal Analysis

  • Lecture 1. Introduction; Temperature Field; Thermal Stresses
  • Presentation of the Final Project - I
  • Presentation of the Final Project - II

 Contact Info

E-mail:   Yijun.Liu@uc.edu
Tel.
:         (513) 556-4607 (Voice),    (513) 556-3390 (Fax)
S-mail:    Mechanical Engineering, University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072


  1997-2013 Yijun Liu, University of Cincinnati

Last updated April 26, 2013 .