Finite Element MethodCourse Numbers: 20-MECH-7052 or 20-AERO-7052; Spring SemesterInstructor: Dr. Yijun Liu, Professor of Mechanical Engineering
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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 . |