**Course Description:**

The finite element method is a widely used numerical procedure that can be applied to obtain solutions to a large class of engineering problems. A robust understanding of the finite element method assures that analyses are performed correctly, confidently and efficiently. This two-part course presents the fundamentals of the finite element method and modeling techniques for structural analysis applications. Theory of the finite element method, using several approaches is covered in Part 1. The direct method is mostly covered, but the Principle of Minimum Potential Energy is also mentioned.

The isoparametric formulation of the elements stiffness matrices and numerical integration are covered. This demonstrates how software solves large scale problems and provide an understanding which aids with setting up analyses and post-processing results, and sets the basis for more advanced uses, which are covered in Part 2. An introduction to non-linear finite element analyses and modal analyses is provided at the end of Part 1. The concepts covered in this course are enforced with practical problems and examples, and discussion on common errors and typical use of the finite element method in the aerospace industry. We find it particularly effective to insert real world applications into the lectures. Having accumulated decades of diverse industry experience, we have been able to provide actual examples of real situations from which the students gained additional useful insights.

Lastly, the concepts of verification and validation, their requirements and methods are presented throughout the course. Part 2 of the course builds upon the fundamentals covered in Part 1 and presents a well-balanced discussion on the theory and application of finite element modeling techniques for an array of disciplines. In Part 2 non-linear analyses, structural dynamics, stability, contacts, analysis of composite materials, and use of the finite element modeling in damage tolerance and fracture mechanics are discussed. Part 2 is currently under development.

**Course Includes:**

- A course notebook prepared by your instructors
- Supplemental material to enhance the subject matter
- Refreshments served each morning and afternoon

**Course Textbook:**

__Logan, Daryl L., A First Course in the Finite Element Method, Cengage Learning- Global Engineering Publisher, Fifth Edition, 2012__

**Course Outline:**

### Day 1

- Introduction and History of FEM – 1.5 Hrs.
- Review of Mathematical Fundamentals – 1.5 Hrs.
- First Taste of the FEM: Definition, 1-2D Truss Problems – 1.5 Hrs.
- Practical Aspect: Review of Bolted Joint Analysis – 1.5 Hrs.
- Practical Aspect: Bolted Joints Analysis using FEM: FEMAP, ABAQUS, and ANSYS – 1 Hr.
- Homework Assignment: 1 hand problem + Truss problem using FEM software

### Day 2

- Recap of Day 1 – 0.5 Hr.
- Quick discussion on principal of Minimum Potential energy – 1 Hr.
- Review of Beam Theory – 1 Hr.
- Beam Finite Elements: Euler-Bernoulli and Timoshenko’s – 1.5 Hrs.
- Practical Aspect: Discussion on A/C Floor Grid analysis – 0.5 Hr.
- Practical Aspect: FEA Demo using FEMAP – 1.5 Hrs.
- 2D Elements: Triangular and Quadrilateral Part 1 – 1 Hr.
- Homework Assignment: 1 hand problem + Floor Grid Analysis using FEM software

### Day 3

- Recap of Day 2 – 0.5 Hr.
- 2D Elements: Triangular and Quadrilateral Part 2 – 1 Hr.
- Higher Order Elements – 0.5 Hr.
- Shell and Continuum Shells Elements – 1 Hr.
- Practical Aspect: Discussion on Stress Concentrations and Metal Fatigue – 1.5 Hrs.
- Practical Aspect: FEA Stress Concentration Demo using ABAQUS + Convergence Study – 1 Hr.
- Practical Discussion on Rigid Elements with FEA Demos – 1.5 Hrs.
- Homework Assignment: 1 hand problem + FEA of complex details using FEM software and Fatigue analysis by hand

### Day 4

- Recap of Day 3 – 0.5 Hr.
- Practical Aspect: Review of Heat Transfer – 1 Hr.
- Practical Aspect: Heat Transfer using FEM – 1 Hr.
- Introduction to Non-Linear Analysis Techniques – 1 Hr.
- FEA Demo of Non-Linear Analyses – 1.5 Hrs.
- Verification & Validation – 2 Hrs.
- Homework Assignment: NL FEM or Heat Transfer using FEM Software

### Day 5

- Recap of Day 4 – 0.5 Hr.
- Isoparametric Formulation – 1 Hr.
- Practical Aspect: Review of Dynamics and Modal Analysis – 1 Hr.
- Practical Aspect: Determining Natural Frequencies using FEM – 1 Hr.
- Practical Aspect: Buckling Analysis using FEM – 1 Hr.
- Review of Direct Integration and FEM – 0.5 Hr.
- Example of Implicit vs. Explicit FEA using ABAQUS – 1.5 Hrs.
- Closing Remarks – 0.5 Hr.
- Homework Assignment/Course Project: Beam analysis 1D, 2D, and 3D elements