Finite Element Methods in Aerospace Structures
Learning Objective:The goal of AAE 558 is to introduce the theory behind finite element calculations of stress, strain, and deformation in structures and materials and describe the role of a commercial finite element package in structural analysis and design. Please note that it???s a 5-level course (senior elective and graduate introductory)
OBJECTIVES AND ENVISIONED OUTCOMES:
- Understand the relationship between the finite element shape functions and constitutive behavior and element stiffness matrices
- Develop the weak form of the equations of mechanics
- Relate mesh and loading to the assembled stiffness matrix
- Provide criteria for engineering judgement required to assess the appropriateness of the choice of a finite element model for a particular structure
- Provide training to understand the equations guiding black-box software such as ABAQUS
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 2021 Syllabus
- Introduction - Background and Applications of Finite Elements (Chapter 1-Text Book)
- Direct Approach for Discrete Systems - One Dimensional Problems (Chapter 2)
- Direct Approach for Discrete Systems - Two Dimensional and Three Dimensional Problems (Chapter 2)
- Formulation: Strong and Weak Forms in one dimensional problems (Chapter 3-Text Book)
- Approximation of Trial Solutions, Weight Functions and Gauss Quadrature (Chapter 4-Text Book)
- Introduction to ABAQUS (Chapter 11-Text Book)
- Finite Element Formulation for One-Dimensional Problems and Error Analyses (Chapter 5-Text Book)
- Finite element formulation for beams (Chapter 10-Text Book)
- Multi-dimensional scalar field problems (Chapters 6, 7-Text Book)
- Multi-dimensional vector field problems (Chapter 8, 9-Text Book)
- Plate and shell bending problems (Class lecture-no textbook coverage)
- Dynamics using finite element method (If time permits, class lecture-no text book coverage)
- Special Topics: Fracture, Bending (plates and shells), dynamics, non-linear material models (If time permits: class lecture-no text book coverage)
Prerequisites:THE COURSE NEEDS HEAVY EXPERIENCE IN MATRIX ALGEBRA AND MATLAB PROGRAMMING. FIRST FEW ASSIGNMENTS REQUIRE HEAVY MATLAB PROGRAMMING
Applied / Theory:50 / 50
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 firstname.lastname@example.org 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.