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# Finite Element Methods in Aerospace Structures

## AAE55800

3

### Learning Objective:

To introduce the theory behind finite element calculations of stress, strain and deformation in structures and materials, and to describe the role of a commercial finite element package in structural analysis and design. Students will understand the relationship between shape functions, constitutive behavior, mesh, and loading to the assembled element stiffness matrices. Criteria for engineering judgment required to assess the appropriateness of the choice of a finite element model for a particular structure will also be provided.

### Description:

Introduction to the use of advanced finite element methods in the calculation of deformation, strain, and stress in aerospace structures. Topics include 1-D, 2-D, axisymmetric, and 3-D elements, isoparametric element formulation, convergence, treatment of boundary conditions and constraints. Emphasis is on the theoretical knowledge of the finite element method. Applied experience is gained by solution of aerospace structural analysis problems through use of a commercial package. Fall 2019 Course Syllabus

### Topics Covered:

Introduction-Background and Applications of Finite Elements (Ch.1-Text book)
2. Direct Approach for Discrete Systems - One Dimensional Problems (Ch. 2)
3. Direct Approach for Discrete Systems - Two Dimension and Three Dimensional Problems (Ch. 2)
4. Finite element formulation for beams (Ch. 5-Text Book
5. Formulation: Strong and Weak Forms in one dimensional problems (Ch. 3 - Textbook)
6. Intro to ABAQUS (Ch.11 - Textbook)
7. Approximation of Trial Solutions, Weight Functions and Gauss Quadrature (Ch. 4 - Textbook)
8. Finite Element Formulation for One-Dimension Problems and Error Analyses (Ch. 5 - Textbook)
9. Formulation: Strong and Weak Forms in two dimensional problems (Ch. 6, 7 - Textbook)
10. Finite Element Formulation for two dimensional Problems: Linear Elasticity (Chapter 11-Text book)
11. Error, estimation, and convergence (Ch. 8 - Textbook)
12. Three dimensional Finite element analyses (Ch. 7, 9 - Textbook))
13. Plate and shell bending problems (Class lecture - no textbook coverage)
14. Dynamics using the finite element method (if time permits: class lecture - no textbook coverage)
15. Special Topics: Fracture, Bending (plates and shells), dynamics, non-linear material models (If time permits: class lecture - no textbook coverage).

### Prerequisites:

AAE 453 or consent of instructor (THE COURSE NEEDS HEAVY EXPERIENCE IN MATRIX ALGEBRA AND MATLAB PROGRAMMING. FIRST FEW ASSIGNMENTS REQUIRE HEAVY MATLAB PROGRAMMING)

### Applied / Theory:

50 / 50

https://mycourses.purdue.edu/

### Web Content:

In Blackboard: Syllabus, grades, lecture notes, homework assignments, solutions, and quizzes plus link to course website. Plan to use Piazza to support course.

### Homework:

Weekly assignments; will be accepted via email to tomar@purdue.edu or Blackboard. Performance in course will be measured by homeworks, exams and final project.

### Projects:

Required - Final term project will include use of commercial finite element analysis software to solve complex, real-world oriented problems and is to be related to your job or research interests.

### Exams:

There will be two (2) midterm exams (one is take-home), and one final project (See "Projects" below for details).

### Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Tentative: Required-- A First Course in Finite Elements [Paperback] by Jacob Fish and Ted Belytschko. Wiley 2012 Edition, ISBN: 978-0470035801.

### Computer Requirements:

The course will involve an intermediate level of MATLAB programming.

### Other Requirements:

ABAQUS student version, MATLAB

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