A NEW APPROACH TO TEACHING FINITE ELEMENT ANALYSIS FOR LARGE AUDIENCES

Abstract

As a consequence of the introduction of a new 5-year Bachelor-Master degree programme by the Faculty of Aerospace Engineering of the Delft University of Technology the study results for the mandatory Finite Element Analysis course were found to be unsatisfactory and cause a bottleneck in the curriculum. Identifying the underlying problems lead to rejuvenation of the course content and delivery by implementing state-of-the-art software and hardware facilities supported by the Blackboard environment. Study results where spectacularly improved and the bottleneck in the curriculum has successfully been removed. Student response to the improved course are excellent and course content is actively used in later BSc and MSc curriculum components. This paper reports in detail in the changes implemented and new components introduced to attain this result.

Full text

A NEW APPROACH TO TEACHING FINITE ELEMENT
ANALYSIS FOR LARGE AUDIENCES
J.M.A.M. Hol1 , G.N. Saunders-Smits2
1Faculty of Aerospace Engineering, Delft University of Technology,
Kluyverweg 1, 2629 HS Delft, The Netherlands
(J.M.A.M.Hol@tudelft.nl)
2Faculty of Aerospace Engineering, Delft University of Technology,
Kluyverweg 1, 2629 HS Delft, The Netherlands
(G.N.Saunders@tudelft.nl)
Abstract
As a consequence of the introduction of a new 5-year Bachelor-Master degree programme by the
Faculty of Aerospace Engineering of the Delft University of Technology the study results for the
mandatory Finite Element Analysis course were found to be unsatisfactory and cause a bottleneck
in the curriculum. Identifying the underlying problems lead to rejuvenation of the course content
and delivery by implementing state-of-the-art software and hardware facilities supported by the
Blackboard environment. Study results where spectacularly improved and the bottleneck in the
curriculum has successfully been removed. Student response to the improved course are excellent
and course content is actively used in later BSc and MSc curriculum components. This paper
reports in detail in the changes implemented and new components introduced to attain this result.
Keywords: course renewal, improved study results, student response, finite element, electronic
learning environment
1. INTRODUCTION
When the Faculty of Aerospace Engineering [1] designed their new 5 year Bachelor-
Master degree programme in 1995, they took advice from several key aerospace educators
from the United States [2] with a view to facilitate the acquisition of a U.S. accreditation
(ABET). Part of the advice was to introduce a mandatory Finite Element Analysis course
for all third year students as opposed to it just being an advanced course for students
specialising in structures and mechanics. This paper reports on the redesign of a classic
Finite Element Analysis course using current state-of-the-art Finite Element Analysis
Software, Electronic Learning Environment (Blackboard) and its effect it has had on the
motivation of students for Structures and Mechanics, their ability to do Structural Designs
and their study results.
2. HISTORICAL CONTEXT
The existing course has roots dating back to the late 60s and early 70s when Finite Element
Analysis (FEA) reached sufficient maturity to be included in the Aerospace Engineering
curriculum as a generic solution methodology for structural problems. The then-usual

course format consisted of a semester-length series of straight forward classical lectures on
the theory of FEA followed by a 3 hour exam in which students solved small problems
using “FEA-by-hand”.
To improve mobilizing the FEA theory and provide students hands-on experience applying
FEA to engineering problems a stand-alone computer exercise was introduced. Each
student was given an individual exercise concerning a simplified aerospace structure with
loads acting on it. The student was asked to first analyse the structure by hand using
classical and generally accepted mechanics methods to have a “guestimate” of their results,
followed by developing a Finite Element model of their structure for analysis by an input
file driven FEA computer programme. They had to get their model working by debugging
it, correlating and verifying both approaches and finally generating results and a written
report. This was a time-consuming and challenging amount of work done by the students
on an individual basis.
Although the content of the course was modernized over the years, the format of the
lecture series remained unchanged. Similarly the accompanying computer exercise was
updated for new compute platforms and improved FEA computer software but the
problems students worked on where only adapted but never replaced. In 1995 when the
new Bachelor-Master degree programme was introduced the computer exercise employed
“command line” NASTRAN [3] on a multi-user departmental computer environment
accessible by teletype like terminals without graphics facilities. Content wise the computer
exercise was primarily aimed at solving engineering problems as such and by then light on
FEA aspects. Both the course and computer exercise were taught and managed by a single
faculty member.
The yearly enrolment of the course and computer exercise varied from 25 up to 40
students. In general students started course work and stand-alone computer exercise at the
same time. Pass-rates for exams were about 30% and in-line with other mechanics oriented
courses thus forcing students to take multiple attempts at passing the exam. Completing the
computer exercise usually was up to 1 to 2 years after hand-out of the assignments and
often coincided with finishing of the MSc programme. Also disappointing was that
students although having worked with FEA software by choice did not use it in their MSc
course and thesis work.
The introduction of a mandatory course in FEA to all students initially meant nothing more
than moving the existing course and the accompanying computer exercise down into the
third year of the Aerospace Engineering curriculum. However this meant that a small
course of some 30 students had to be expanded overnight to accommodate some 200-250
students. When the first batch of students came through it was quickly realised that the old
traditional set-up was no longer manageable for several reasons e.g.
• Too many students for the staff to manage
• Student-assistants were necessarily introduced to handle the large number of
students
• The set-up of the course was not motivating enough
• The “command-line” set-up of the software was archaic and not state-of-the-art
• The compute environment was unfamiliar to students and difficult to master
• The content of the lecture series and computer exercise where unrelated

The large groups of students some of whom had little interest in structures meant self-
motivation was no longer implicitly present. At the same time pass-rates for examinations
started deteriorating and the time students took to complete their computer exercise
increased. A significant number of students postponed taking the course or never handed
in their reports for the exercise. As a result the course became unpopular with students thus
creating a bottleneck in the Aerospace Engineering curriculum and an unmanageable
situation. Based on these findings it was realised that in its existing set-up this course could
not be sustained.
At the same time one of the leading FEA software manufacturers active in Aerospace,
MSC.Software [3] offered low-cost access to state-of-the-art Windows-based pre- and post
processors to accompany their existing FEA software. Also the analysis software which
traditionally required high-end compute resources could effectively be used on common
Personal Computers. This made a complete professional state-of-the-art FEA software
environment accessible to large groups of students.
A simultaneous University initiative [4] to enhance the computer based environment
offered to students introduced the electronic learning environment Blackboard [5]. Using
funds from this initiative a state-of-the-art computer laboratory was installed to be used
specifically for course related computer-based training and exercises.
Combining the worrisome results of the course and computer exercise with the availability
of contemporary hardware and software facilities created an opportunity to overhaul this
component of the Aerospace Engineering curriculum.
3. COURSE RENEWAL
Based on the findings presented in the previous section both the course and computer
exercise needed to be revised. Typical requirements identified for the re-development of
both course and computer exercise were
l integrate the course and the computer exercise
l focus of the course and the computer exercise is on FEA aspects
l the computer exercise content is to parallel the course content
l example problems (content) are contemporary engineering problems
l the computer exercise to be done with the new hardware and software facilities
l where applicable use the electronic Blackboard environment
l the course and the computer exercise run in parallel for 7 weeks
l students are required to take course and computer exercise in parallel
l the computer exercise is graded based on individual performance
l the course is graded by means of an exam
l final grade is weighted average of the course and the computer exercise grades
l personnel should be limited to one faculty member supported by student assistants
Based on these requirements and limited human-resources available the initial effort was
devoted to developing a new computer exercise which was seen as the most effective
strategy to improve the overall course results. At the same time a new 80-seat computer
laboratory and the professional state-of-the-art FEA software MSC/Patran and
MSC/Nastran [3] became available early which enabled early implementation of the new
computer exercise. Any remaining development capacity was to be used to implement a
best-effort improvement of the course.

3.1 Computer exercise
As the old computer exercise were unsuited, a completely new series of hands-on computer
exercises was developed into 7 weekly sessions of 4 hours using the new software and
compute facilities. Each session was designed in such a fashion that what was covered in
the lectures was immediately put into practice at the next session while fully utilizing the
state-of-the-art graphical software environment to account to the needs of the more visually
oriented current student generation. This was done by creating weekly work packages
consisting of tutorials, instructions, exercises and problems. For a given work package
the tutorials and instructions effectively are on the job training for both the compute
environment and topic related examples of the course material introduced in the lectures.
The exercises and problems themselves integrate the tutorials and instructions with the
course material. The exercises and problems are set up to be done independently by the
students with workouts to be handed in at the end of each session. Individual tailoring of
exercises enables individual grading of computer exercises and students.
By design the work packages enable and stimulate students to vary the different variables
in the Finite Element models they developed for each work package. This challenges
students to focus on studying the effects of parametric variations of their models.
Anchoring the exercises in actual engineering problems provides students a good
grounding in learning to critically interpret results obtained from these models.
Scheduled practical sessions in the 80-seat computer laboratory are run by one member of
staff and 3-4 teaching assistants. Accommodating a larger number of students is done by
scheduling multiple sessions per week with smaller equal size groups and number of
teaching assistants.
3.2 Course
The development of a completely new series of hands-on computer exercises combined
with limited staff resources implied only marginal capacity was available to update the
course content. Being aware of active learning concepts [6] the existing course content
used in the lectures was first reorganised into manageable small pieces using learning
objectives. This offered an opportunity to remove outdated topics from the course content,
introduce a limited number of existing but unused content topics and reorganize the overall
order of presentation of the course topics. This resulted in the course being up-to-date
content-wise while offering the lecturer more flexibility in adapting the course delivery to
the current student generation even in the context of a classical lecture series.
Earlier research done by University educational services [?] has shown that in general the
classical lecture centric method of teaching courses, results in students putting off their
self-study time to master the course content as far into the future as possible. This
effectively crams a high-intensity effort into the final days before an exam with multiple
exams usually scheduled nearly simultaneously. While such a high-intensity effort may be
enough to pass the exam it is not very effective in mastering and exercising the course
content nor does it help to promote usage of course content to later courses and exercises.
To address these issues an optional set of weekly homework exercises was offered. As
homework exercises stimulate studying the lecture material its intended purpose is to
spread the study load over the lecture period thus evening out the study load. Similar to the
computer exercises the individually tailored sets of homework exercises were designed to
run parallel to the 7-week course cycle and cover the same material. Homework is offered

and graded in a tight weekly cycle to stay synchronous with the lecture series. As
homework is not a customary component of our teaching methods by definition the
homework had to be an optional component of the course in which students were free to
participate. To provide some incentive to students to enrol in this homework system grade-
bonus points could be earned.
The homework problems offered are similar to the questions asked during the concluding
exam. The original exam remained but the link between course material and the exam was
now clearer to the students.
The course content used in the lectures, the homework assignments and final workouts plus
an unmoderated non-anonymous discussion forum for this course are available via our
electronic Blackboard environment. The Blackboard environment enables fast updating
and distribution of lecture material. It also provides students with 24/7 worldwide access
to the teaching material. Adding the unmoderated non-anonymous discussion forum gave
students peer support whenever they encountered problems or had questions regarding
course material. It offers staff members an opportunity to monitor and act on students
reactions to the course material.
3.3 Initial results
The development of a completely new series of hands-on computer exercises,
reorganisation of the course material, introduction of the homework system and
Blackboard environment for the course were all implemented during one lecture year.
Although being a momentous effort we succeeded in timely completing all associated
tasks.
The new elements in the course delivery i.e. new computer laboratory environment and
Blackboard were received well. To our surprise he optional homework offered was
voluntarily picked up by more than 80% of enrolled students thus showing their
willingness to try new avenues of learning. The effect of the sets of homework exercises
are obvious in the exam results as their is a distinctly better mean grade for those students
taking the homework exercises. When bonus grade-points are factored in this improvement
is even stronger. The final and most stunning result was that pass-rates of the course
improved spectacular and exceeded 70% .
As the computer exercises are run in parallel to the lecture series students who passed the
exam first-time have completed their FEA course in one semester. This off-course
alleviates the earlier identified bottleneck in the Aerospace Engineering curriculum.
Overall student response to the rejuvenated course and computer exercise was excellent.
Both the University run sensor inquiries as well as the student body organised lecture
response groups returned positive results. During the third year Design Exercise [?] and
subsequent MSc course and thesis work which follows the FEA course, students
increasingly on their own initiative use our state-of-the-art FEA environment as an
engineering tool.
The only currently drawback identified is the need for more staff involvement and
introduction of additional student assistants. Balanced against the strong improvement in
pass-rates this

4. CONCLUSIONS AND RECOMMENDATIONS
Redesigning the course as a reaction to the identified problems with the original course and
taking into account the needs of the more visually orientated students, has resulted in
spectacularly improved results. Pass rates of the exam which were traditionally no more
than 30% soared to 75 % and up. Staff work pressure came down and the overall teaching
of the course became far more pleasant. The use of state-of-the-art Finite Element Analysis
software as a design and analysis tool in the third year Design Exercise is now a
widespread phenomenon, improving the quality of the design and enhancing the
understanding of structural design of the students. As an added bonus, the enrolment in the
structures and mechanics group for Master’s thesis also went up.
REFERENCES
[1] Faculty of Aerospace Engineering website: http://www.lr.tudelft.nl
[2] Covert, Eugene E.: Engineering Education in the ‘90s: Back to basics, Aerospace
America, April 1992 pages, 20-23 & 46.
[3] NASTRAN website: http://www.mscsoftware.com
[4] Delft University of Technology ICT in Education website: http://
www_en.icto.tudelft.nl
[5] Blackboard website: http://www.blackboard.com
[6] Graaf, E. de: Research and practice of active learning in engineering education, Pallas
Publications, Amsterdam, 2005
Curriculum Vitae
Jan M.A.M. Hol
In 1983 Jan M.A.M. Hol obtained his MSc in Design and Analysis of Aerospace Structures
from the Faculty of Aerospace Engineering at Delft University of Technology. After
working several years at the Energy Research Centre of The Netherlands as an application
consultant specializing in Finite Element Analysis he returned to work on the development
of DISDECO. From 1988 onwards he teaches Finite Element Analysis and does research
in collapse behavior of imperfect thin-walled shell structures. He currently is involved in
the development of a new BSc Curriculum for the Faculty of Aerospace Engineering.
Gillian N. Saunders-Smits
Gillian N. Saunders-Smits obtained a MSc. in Aerospace Structures and Computational
Mechanics from the Faculty of Aerospace Engineering at Delft University of Technology
in 1998. After a short period in industry, she returned to the Faculty of Aerospace
Engineering in 1999 as an assistant professor. Since 2000 she is the faculty's project
education coordinator. She also teaches Mechanics and is currently doing a PhD in
engineering education.