Finite Element Method

Course Numbers: 20-MECH-7052 or 20-AERO-7052;   Spring Semester

Instructor: Dr. Yijun Liu, Professor of Mechanical Engineering

Course Syllabus

FEM (Spring Semester)

Showcase: Finite Element Analysis in Actions

Contents of the Lectures (For FEM and Advanced FEM)

Chapter 1. Introduction

  • Lecture 1.  Introduction to the Finite Element Method; An Example - Spring Elements
  • Lecture 2.  Review of the Linear Elasticity - I
  • Lecture 3.  Review of the Linear Elasticity - II
  • Lecture 4.  Review of the Linear Elasticity - III
  • Homework Problems

Chapter 2. FEM for the Plane Truss and Frame

  • Lecture 1.  Bar Element and Coordinate Transformation
  • Lecture 2.  Examples; Truss Analysis
  • Lecture 3.  Beam Element
  • Lecture 4.  Examples; Distributed Loads
  • Lecture 5.  More Examples; Frame Analysis
  • Lecture 6.  Introduction to ANSYS (Computer Lab Session 1)
  • Lecture 7.  Review
  • Homework Problems

Chapter 3. Foundations of the FEM - Energy Principles

  • Lecture 1.  Introduction
  • Lecture 2.  The Principle of Stationary Potential Energy - Multi-DOF Systems
  • Lecture 3.  The Principle of Stationary Potential Energy - Elastic Bodies
  • Lecture 4.  Rayleigh-Ritz Method; Examples
  • Lecture 5.  Interpolations and FEM Formulations
  • Lecture 6.  Examples
  • Lecture 7.  Review
  • Homework Problems

Chapter 4. Displacement-Based Elements for Structural Mechanics

  • Lecture 1.  General Formulation for Element Stiffness Matrices and Equivalent Load Vectors
  • Lecture 2.  Overview of Element Stiffness Matrices and Equivalent Load Vectors
  • Lecture 3.  Use of ANSYS/I-DEAS Master Series (Computer Lab Session 2)
  • Lecture 4.  Equilibrium, Compatibility, Convergence and the Patch Test
  • Homework Problems
  • Computer Lab Assignment No. 1

Chapter 5. Straight-Sided Triangles and Tetrahedra

  • Lecture 1.  Natural Coordinates on Lines, Triangles and Tetrahedra
  • Lecture 2.  FE Formulations on Straight-Sided Triangles and Tetrahedra
  • Homework Problems
  • Computer Lab Assignment No. 2

Chapter 6. Isoparametric Formulation

  • Lecture 1.  Introduction; 1-D Isoparametric Element
  • Lecture 2.  Plane Bilinear Elements;  the Jacobian Matrix
  • Lecture 3.  Use of ANSYS (Computer Lab Session 3)
  • Lecture 4.  Gauss Quadrature,  Plane Quadratic Elements
  • Lecture 5.  Hexahedral Elements; Plane Triangular Elements; Tetrahedron Elements
  • Homework Problems
  • Computer Lab Assignment No. 3

Chapter 7. Plates and Shells

  • Lecture 1.  Introduction to Plate Theories
  • Lecture 2.  Plate Elements
  • Lecture 3.  Shells and Shell Elements
  • Homework Problems
  • Computer Lab Assignment No. 4
  • Final Exam Project Assignment

Chapter 8. Topics in Structural Mechanics

  • Lecture 1.  Symmetries in the FE Modeling and Analysis
  • Lecture 2.  Superelements
  • Lecture 3.  Preview of the Final Project (Computer Lab Session 4)
  • Lecture 4.  Fracture Mechanics Analysis
  • Lecture 5.  Solutions of FEM Equations; FEA Error Estimates
  • Lecture 6.  Presentations of the Final Projects - I
  • Lecture 7.  Presentations of the Final Projects - II
  • Homework Problems
  • Final Exam Project Report Due

Chapter 9. Vibration Analysis

  • Lecture 1.  Structural Dynamics Equations - Single DOF Systems
  • Lecture 2.  Structural Dynamics Equations - Multiple DOF Systems
  • Lecture 3.  Mass Matrix
  • Lecture 4.  Damping Matrix
  • Lecture 5.  Free Vibration Analysis - I
  • Lecture 6.  Free Vibration Analysis - II
  • Lecture 7.  Use of ANSYS (Computer Lab Session 5)
  • Computer Lab Assignment No. 1 (Spring Quarter)
  • Computer Lab Assignment No. 2

Chapter 10. Frequency Response Analysis

  • Lecture 1.  Modal Equations
  • Lecture 2.  Modal Method for Frequency Response Analysis
  • Lecture 3.  Direct Method for Frequency Response Analysis
  • Lecture 4.  Use of ANSYS (Computer Lab Session 6)
  • Computer Lab Assignment No. 3

Chapter 11. Transient Response Analysis

  • Lecture 1.  Direct Methods - Explicit Integration
  • Lecture 2.  Direct Methods - Implicit Integration
  • Lecture 3.  Modal Methods
  • Lecture 4.  Advanced Topics in Dynamic Analysis
  • Lecture 5.  Use of ANSYS (Computer Lab Session 7)
  • Computer Lab Assignment No. 4
  • Final Project Assignment

Chapter 12. Nonlinear Analysis

  • Lecture 1.  Introduction; Solution Methods
  • Lecture 2.  Large Deformation, Elastic-Plastic and Contact Stress Analyses
  • Final Project Presentation - I
  • Final Project Presentation - II
  • Final Project Report Due

 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 .