COURSE OUTLINE
AEE 464
APPLICATIONS OF FINITE ELEMENT ANALYSIS IN AEROSPACE STRUCTURES
FALL 2008
OBJECTIVE
This course is intended to introduce the concept of finite element analysis to the fourth year graduating students. It is designed as an application oriented course mixing theory and practice in appropriate proportions that will enable the students to use the method effectively in structural design and analysis.
SUMMARY OF COURSE CONTENT
In the theory part, the underlying principles of finite element analysis is demonstrated through the use of one dimensional bar elements. Program segments that perform critical operations in finite element analysis are introduced. The general methodology of the application of finite element analysis for higher order systems in structural mechanics is introduced with specific easy-to-understand modelling examples using one dimensional elements. The application side introduces a powerful solid modelling and finite element modelling tool MSC Patran/Nastran. Specific structural modelling and finite element analysis examples are given from applications pertaining to aerospace structures. The techniques demonstrated with MSC Patran/Nastran can also be practiced with other commercially available finite element programs.
INSTRUCTOR: Assoc.Prof.Dr. Altan Kayran
Room: 203, Tel: 4274, E-Mail: kayran@ae.metu.edu.tr
TEXTBOOK AND REFERENCE BOOKS:
In the theoretical part, which will cover approximately 2/3 of the course, we will follow the main textbook which will be available in the bookstore. Besides your textbook you can also use the reference books indicated below and/or any textbook on finite element analysis in the library as a guide throughout the theory part.
In the application part there will be class hours specifically designed to introduce you the solid modelling and finite element modelling tool that we will use, together with some application examples of aerospace structures. Supplementary documents on MSC Partan/Nastran will be distributed which will enable students to self-study.
Textbook:
'Concepts and Applications of Finite Element Analysis,' by Robert D. Cook, David S. Malkus, Michael E. Plesha
Third edition
Publisher: John Wiley and Sons
ISBN: 0-471-84788-7
Call Number: TA646 C66 1989
Reference Books and Materials:
COURSE MATERIAL
Class Hours
1- INTRODUCTION 4 hrs
Finite Element Method
Element Characteristic Matrix
Element Assembly and solutions for unknowns
2- ONE DIMENSIONAL ELEMENTS AND 15 hrs
COMPUTATIONAL PROCEDURES
Introduction
Bar Element and Direct Determination of Structure
Stiffness Matrix
Properties of stiffness matrix ---------------------------------------------------- 3 hrs
Element stiffness equation
Bar elements of arbitrary orientation------------------------------------------ (2 hrs)
Assembly of elements
Mechanical and Thermal Loads--------------------------------------------- (4 hrs)
Node numbering and
Application of Boundary conditions-------------------------------------------- (3 hrs)
Solution of equations
Stress computation
Summary example----------------------------------------------------------------- (3 hrs)
3- RAYLEIGH-RITZ METHOD AND INTERPOLATION 9 hrs
Introduction
Principle of stationary potential energy
Problems having many DOF
Potential energy of an elastic body
Classical form of Rayleigh Ritz Method------------------------------------ (4 hrs)
Piecewise polynomial field
Finite element form of the Rayleigh-Ritz method
General derivation of element stiffness matrix (3 hrs)
Interpolation and Shape functions ------------------------------------------ (2 hrs)
4- FINITE ELEMENT PROGRAMS AND THEIR 14 hrs
APPLICATION IN AEROSPACE ENGINEERING
Introduction to MSC Patran/Nastran Element Types,
Application Examples from Aerospace Engineering---------------------------- (1 hrs)
Introduction to MSC Patran Geometric Modelling------------------------------ (4 hrs)
Tutorial Hour #1
General Introduction to MSC Nastran FEM and Applications (1 hr)
Applications on the use of Solid Elements ---------------------------------------- (2 hrs)
Applications on the Use of 2D Elements -------------------------------------- (2 hrs)
Applications on the Use of 1D Elements ----------------------------------------- (2 hrs)
Applications on the Use of Combination of 1D and 2D Elements------------- (2 hrs)
Tutorial Hour #2
GRADING
1 Midterm Examination 20%
Homeworks 12%
HW1: 1.5%
HW2: 3.0%
HW3: 3.5%
HW4: 2.5%
HW5: 1.5%
Project #1 20%
· Code generation for one dimensional truss (or frame) structure
· Structural analysis of a specific example by the use of
the code generated
Project #2 23%
· Structural modelling and analysis of the problem assigned
in Project #1 in MSC Patran/Nastran
· A specific structural design and analysis project to be performed
in MSC Patran/Nastran
Final examination 25%
OVERALL 100%
NOTES
* Detailed explanation and requirements for the projects will be given at the time of a project
assignment
* Project #1 will be prepared individually.
* Project #2 will be prepared as a group. The groups will be organized before the tutorial
hours. Project#2 will be submitted after the last date of finals, two days before the submittal
of the final grades
* There will be two tutorial hours (17:30 – 20:00) for the hands on modelling and analysis
examples by the students in the computer laboratory. Tutorial hours will be extra hours
not counted in the course material.
Detailed Tentative Schedule:
Sept. 17 : Introduction – 3 hours
Sept. 24 : Introduction – 1 hour
Section 2: Direct determination of stiffness matrix – 1 hour
Assign HW1
Introduction to Patran and Nastran – 1 hour
Distribution of course notes, introduction of Patran GUI, distribution of
Nastran/Patran installation CD for home study
Oct. 8 : Section 2: Properties of stiffness matrices-up to element stiffness eqn. –2 hours
Geometric modeling in Patran – 1 hour
Curve, surface, solid creation, editing, transforming geometirc entities
Oct. 15 : Section 2: Element stiffness equation (end of Part 1) –2 hours
Geometric modeling in Patran – 1 hour
Curve, surface, solid creation, editing, transforming geometric entities continued
Coordinate frames, Assignment of 1st tutorial on geometric modeling
Oct. 22 : Section 2: Assembly of elements (up to concentrated load example)–2 hours
Introduction to meshing – 1 hour
Meshing of parametric and parasolis solids, topological congruency
Workshop 1 (start in class, students are expected to finish this tutorial by next
week)
Substitute day for Oct. 29 : this day will be decided by the class. Preferably this week.
Assembly of elements (continue up to end)–2 hours
Assign HW2
Introduction to meshing – 1 hour
Meshing of surfaces; isomesh vs. paver mesh, topological congruency
Nov. 5 : Section 2: Node numbering and application of displacement boundary conditions
- 3 hours
Nov. 12 : Section 2: Gauss elimination solution of equations (up to end of finding of
support Reactions)- 2 hours
Assign HW3
Meshing of surfaces continued; 1 hour
Associating points, curves to surfaces etc.,
Workshop 2 (start in class, students are expected to finish this tutorial by next
week)
Nov. 19 : Section 2: Solution of equations continued, discussion- 1 hours
Assign HW4
Load and boundary condition application, materials, element properties, result
postprocessing – review and explanation of grouping, – 2 hours
Workshop 15 (start in class, students are expected to finish this tutorial by next
week)
Nov. 26 : Section 3: Principle of stationary potential energy, Classical form of Rayleigh
Ritz Method- 2 hours
Assign Project 1
FEM modeling of 1D elements bars and beams
Introduction of CBAR and CBEAM elements – 1 hour
Dec. 4 : Section 3: Principle of stationary potential energy, Classical form of Rayleigh
Ritz Method- continued- 2 hours
FEM modeling of 1D elements bars and beams-continued– 1 hour
Dec. 17 : Section 3: General derivation of element stiffness matrix, FE form of Rayleigh
Ritz Method- 2 hours
FEM Modeling of stiffeners: introduction of modeling of stiffeners from Patran
library offsets etc.– 1 hour
Dec. 24 : Section 3: General derivation of element stiffness matrix, FE form of Rayleigh
Ritz Method- continued 1 hours
Assign HW5
FEM Modeling of stiffeners: arbitrary shape stiffeners, multi point constraint
elements– 2 hours
Dec. 31 : Section 3: Interpolation and shape functions- 2 hours
FEM Modeling of stiffeners: arbitrary shape stiffeners, multi point constraint
elements– continued 1 hours
Substitute day for Dec. 10 : this day will be decided by the class. Preferably the week of Dec. 29-Jan 2.
FEM application: discussion, items which are not touched upon during the
semester will be introduced. One item is the application of fields. Results post
processing will be elaborated. A selected workshop will be assigned as in-class
tutorial.
Assign Project 2