AAE55800 - Finite Element Methods in Aerospace StructuresFall 2015 Days/Time:
MWF / TBACredit Hours:
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. Tentative Syllabus (https://engineering.purdue.edu/~tomar/Teaching/AAE558/Index.htm)Topics Covered:
1. Introduction: Background and Applications of Finite Elements (Chapter 1-Text Book); 2. Direct Approach for Discrete Systems-One Dimensional Problems (Sections 3.2, 3.3, 4.2-Text Book); 3. Direct Approach for Discrete Systems-Two Dimensional and Three Dimensional Problems (Sections 4.5, 4.6-Text Book); 4. Finite element formulation for beams (Chapter 5-Text Book); 5. Introduction to ABAQUS (class lecture-no textbook coverage); 6. Formulation: Strong and Weak Forms in one dimensional problems (Sections 2.1, 2.2, 2.4, 2.5-Text Book); 7. Approximation of Trial Solutions, Weight Functions and Gauss Quadrature (Sections 7.1,7.2-Text Book); 8. Finite Element Formulation for One-Dimensional Problems and Error Analyses (Chapter 4-Text Book); 9. Formulation: Strong and Weak Forms in two dimensional problems (Chapter 8-Text Book) 10. Finite Element Formulation for two dimensional Problems: Linear Elasticity (Chapter 11-Text Book); 11. Error, estimation, and convergence (Chapter 9-Text Book); 12. Three dimensional Finite element analyses (Class lecture-no text book coverage); 13. Plate and shell bending problems (Class lecture-no text book coverage); 14. Dynamics using the finite element method (If time permits: class lecture-no text book coverage); 15. Special Topics: Fracture, Bending (plates and shells), dynamics, non-linear material models (If time permits: class lecture-no text book coverage).Prerequisites:
Mechanics of materials, matrix mathematics, or consent of instructor. The course needs heavy experience in matrix algebra and MATLAB programming. First 4 assignments require heavy MATLAB programming.Applied/Theory:
50/50Web Address:http://www.itap.purdue.edu/learning/tools/blackboard/Web Content:
Syllabus, grades, lecture notes, homework assignments, solutions, quizzes, chat room, message board.Homework:
Weekly assignments; will be accepted via email to firstname.lastname@example.org or Blackboard.Projects:
Term project will include use commercial finite element analysis software to solve complex, real-world oriented problems and is to be job-related.Exams:
Two exams will account for one-half of the course grade.Textbooks:
Required--An A First Course in Finite Elements [Paperback] by Jacob Fish and Ted Belytschko. Wiley, ISBN: 978-0470035801. Disclaimer: final textbook listings are available in April for fall and summer semesters. Please visit the Listing of Textbooks by College or School for the most up-to-date information.
ProEd minimum computer requirements; access to PC-platform computer and internet connection. Matlab (available to registered students via Purdue Software Remote - https://goremote.ics.purdue.edu). Finite element software, preferably ABAQUS. Student have a choice of their software to be used in this course. However, instructor prefers ABAQUS. In-class training sessions will focus on ABAQUS and ANSYS. Students will also have access to a trial ABAQUS copy with the text book. Otherwise procurement of software is the responsibility of the student.
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