COURSE OUTLINE
AEE 464
APPLICATIONS OF FINITE ELEMENT ANALYSIS IN AEROSPACE
STRUCTURES,
FALL 2014
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:

'Finite Element Modeling for Stress Analysis,' by Robert D. Cook, ISBN:0-471-10774-3,
Call Number: TA347 F5 C665

'An Introduction to the Finite Element Method,' by J.N. Reddy, ISBN: 0-07-051355-4, Call
Number: TA347 F5 R4

‘MSC.Nastran Primer for Linear Analysis, 2nd Edition, by Harry G. Schaeffer, ISBN: 158524-011-7, Call Number: TA647 S27 2001

MSC Patran Course Notes and Tutorials

MSC Patran On line documentation

'Structural Dynamics; An Introduction to Computer Methods,' by Roy R. Craig, Jr., Call
Number: TA654 C72
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
APPLICATION IN AEROSPACE ENGINEERING
Distribution of course notes, introduction of Patran GUI, distribution of
Nastran/Patran installation CD for home study
Introduction to MSC Patran/Nastran Element Types,
Application Examples from Aerospace Engineering
Introduction to MSC Patran Geometric Modelling
General Introduction to MSC Nastran FEM and Applications
Applications on the use of Solid Elements
Applications on the Use of 2D Elements
Applications on the Use of 1D Elements
Applications on the Use of Combination of 1D and 2D Elements
28 hrs
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
OVERALL
25%
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
* Application section is 2 hours per week. Therefore, every other two weeks there will be an
in-class tutorial for geometric modelling/finite element modelling, analysis and postprocessing.
Detailed Tentative Schedule:
Introduction
Introduction to Patran and Nastran
Distribution of course notes, introduction of Patran GUI, distribution of
Nastran/Patran installation CD for home study
Introduction
Section 2: Direct determination of stiffness matrix
Assign HW1
Geometric modeling in Patran
Curve, surface, solid creation, editing, transforming geometirc entities
Section 2: Properties of stiffness matrices-up to element stiffness eqn.
Geometric modeling in Patran
Curve, surface, solid creation, editing, transforming geometric entities continued
Coordinate frames, Assignment of 1st tutorial on geometric modeling
Section 2: Element stiffness equation (end of Part 1)
Introduction to meshing
Meshing of parametric and parasolis solids, topological congruency
Workshop 1 (start in class, students are expected to finish this tutorial by next
week)
Section 2: Assembly of elements (up to concentrated load example
Introduction to meshing – 1 hour
Meshing of surfaces; isomesh vs. paver mesh, topological congruency
Assembly of elements (continue up to end
Assign HW2
Meshing of surfaces continued;
Associating points, curves to surfaces etc.,
Workshop 2 (start in class, students are expected to finish this tutorial by next
week)
Section 2: Node numbering and application of displacement boundary conditions
Load and boundary condition application, materials, element properties, result
postprocessing – review and explanation of grouping,
Workshop 15 (start in class, students are expected to finish this tutorial by next
week)
Section 2: Node numbering and application of displacement boundary conditions
Gauss elimination solution of equations (up to end of finding of support Reactions)
Assign HW3
FEM modeling of 1D elements bars and beams
Introduction of CBAR and CBEAM elements
Section 2: Solution of equations continued, discussion
Assign HW4
FEM modeling of 1D elements bars and beams-continued
FEM Modeling of stiffeners: introduction of modeling of stiffeners from Patran library offsets
etc.– 1 hour
Section 3: Principle of stationary potential energy, Classical form of Rayleigh Ritz Method
Assign Project 1
FEM Modeling of stiffeners: arbitrary shape stiffeners, multi point constraint elements
Section 3: Principle of stationary potential energy, Classical form of Rayleigh Ritz Methodcontinued
FEM Modeling of stiffeners: arbitrary shape stiffeners, multi point constraint elements–
continued
Section 3: General derivation of element stiffness matrix, FE form of Rayleigh Ritz Method
Self study, tutorial, completing missing parts
Section 3: General derivation of element stiffness matrix, FE form of Rayleigh
Ritz Method- continued
Assign HW5
Section 3: Interpolation and shape functions- 2 hours
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.
General review, Assign Project 2