Chapter 6- PROMAL for Windows Software Package: A User's Guide

Show how to set up PROMAL on a personal computer Show how to use PROMAL for matrix algebra such as multiplication of matrices, solving a set of equations and finding inverse of a matrix, developing and maintaining a database for properties of unidirectional laminas, conducting macromechanics of a lamina, conducting micromechanics of a lamina, conducting macromechanics of a laminate Show by examples how to use each of the above programs



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PROMAL


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What is PROMAL?


PROMAL (Program for Micromechanical and Macromechanical Analysis of Laminates) is an interactive software tool used to complement (not supplement) the senior level course -- Introduction to Mechanics of Composite Materials. The objectives are the following:

First, once students are required and tested in conducting analysis of mechanics of composite materials, the software is then introduced to avoid repetition and tedious calculations.

Second, allow students to carry their own parametric studies to see the effects of variables on the performance of composites.

Third, give a tool to conduct "industrial" type design of structures made of composite materials.
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PROMAL software fits on a single 3.5" disk which is given to each student in the beginning of the semester. It is also available in all the computer laboratories in the College of Engineering.

The software is available in the classroom on a computer connected to a projection system. It is used to conduct parametric studies which are shown both in tabular and graphical form. Many a times students ask "what if" questions and the instructor can now readily answer of those questions now.

Since the present generation is more "hands on" type, the class is held in a computer laboratory once a week. This allows students to carry their own numerical experiments. In the last month of the class, the software is used heavily to do open-ended design problems. The final examination is a take-home real life design problem.

Ten percent of the course grade is reserved for the evaluation of the software collected through E-mail. Feedback includes strengths and weaknesses of the program, and most importantly suggestions to improve the program. The students have given excellent reviews for the program.

Several computational problems are solved using the software. Most problems are open ended and students come up with several answers. Simple designs of pressure vessels and leaf springs do not take more than ten minutes to work out with the PROMAL program, which would otherwise take several hours by using a calculator. The computer program still maintains the student's need to think about the various inputs to the program to get an optimum design. At the end of the exercise, students and Dr. Kaw discuss not only the various design alternatives but also how students think differently.

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Who can buy PROMAL?


CAUTION: This software is distributed only as a THEORETICAL educational tool and is exclusively for the following:
1. University instructors using PROMAL for teaching a course in Mechanics of Composite Materials, or
2. University students using PROMAL to learn a course in Mechanics of Composite Materials, or
3. Continuing education students using PROMAL to learn a formal course in Mechanics of Composite Materials, or
4. Self-study students who are using PROMAL and a text book to learn a course in Mechanics of Composite Materials and have taken a University level course in Strength of Materials.
The software is distributed only for theoretical educational purposes. Any other use is prohibited. DO NOT ANALYZE OR DESIGN physical structures and components using PROMAL.
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How do I Purchase PROMAL?

CAUTION: This software is distributed only as a THEORETICAL educational tool and is exclusively for the following:
1. University instructors using PROMAL for teaching a course in Mechanics of Composite Materials, or
2. University students using PROMAL to learn a course in Mechanics of Composite Materials, or
3. Continuing education students using PROMAL to learn a formal course in Mechanics of Composite Materials, or
4. Self-study students who are using PROMAL and a text book to learn a course in Mechanics of Composite Materials and have taken a University level course in Strength of Materials.
The software is distributed only for theoretical educational purposes. Any other use is prohibited. DO NOT ANALYZE OR DESIGN physical structures and components using PROMAL.

There are three price structures:

Single Copy: Single copies are distributed only with the purchase of the following text book ------- Mechanics of Composite Materials by Autar K. Kaw
Click to find how to order
One person may use it only on one computer.

Course License:$200.00 per year (includes shipping and handling; free updates (only through WWW and ftp, and disks at renewal time) till license is maintained). Instructors and students of one course (including multi-section courses) may use it anywhere on one campus and at home (not at your work place). Send your check to:
Professor Autar K. Kaw
ENB 118
Mechanical Engineering Department
University of South Florida
Tampa, FL 33620-5350. MAKE CHEKCS PAYABLE TO ME USF FOUNDATION
Important: Include your return and e-mail addresses, university or continuing education affiliation, fax and daytime telephone numbers with your check.

Continuing Education Instructors: Please contact the author directly for prices.


promal@eng.usf.edu

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What are the system requirements?

The program will generally run on any IBM-PC compatible computer running MicroSoft Windows. Specific requirements are: MicroSoft Windows 3.1 or later, MicroSoft MS-DOS version 6.0 or later, 4 MB of available memory, one 3.5 inch high density disk drive and a hard disk with 8 MB available, EGA or higher resolution monitor, MicroSoft mouse. A printer is recommended.
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What programs are in PROMAL?

Master Menu Screen
Matrix Algebra
Lamina Properties Database
Replace Corrupted Lamina Material Database
Macromechanical Analysis of a Lamina
Micromechanical Analysis of a Lamina
Macromechanical Analysis of a Laminate
Master Menu

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The master menu screen with five separate applications from which to choose from.

Promal for Windows-Matrix Algebra

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Matrix Algebra

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The first program conducts multiplication of matrices, solves a set of equations and finds the inverse of a matrix. This program allows you to concentrate on the fundamentals of the course while doing homework problems, rather than spending time conducting lengthy matrix manipulations.



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Lamina Properties Database

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In the second program you can enter the material properties of a composite lamina, update or correct the properties of an existing lamina, and simply review the properties.You can enter properties for up to a maximum of 100 different lamina materials. Properties of three typical composite systems - Graphite/Epoxy, Boron/Epoxy, Glass/Epoxy, and two typical isotropic metals- aluminum and steel are already entered for you in the database.



This program enters fourteen properties- the four elastic moduli, lamina thickness, five strength parameters, two thermal expansion coefficients and two moisture expansion coefficients of a specially orthotropic lamina.

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Replace Corrupted Lamina Material Database

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Somtimes, the material database for the lamina may get corrupted due to power shutdown, computer lockup, accidental rebooting, or other reasons. This option allows you to replace the material database by either:

The database which you had the last time you exited out of the program.

The database which you received with the disk. Note that the database on the disk has only five reserved materials.



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Macromechanical Analysis of a Lamina

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The fourth program conducts the macromechanical analysis of a lamina. The input mechanical properties of a lamina are chosen from the lamina properties database. You can then calculate the stiffness and the compliance matrices, the engineering constants and the strength ratios as a function of the ply angle in tabular or graphical form.




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A Quick Example

Task:
Consider a typical Graphite/Epoxy lamina, find the optimum fiber angle for a load with the following stress components. Use the maximum stress failure criterion for your analysis. Given the following:

LongitudinalStress = 4 KPsi
Transverse Stress = 2 KPsi
Shear Stress = 1 Kpsi

Procedure:
Click on the Macromechanics of a Lamina Button in the Master Menu.
Click on the proper system of units for the input and output.
Click on Select Lamina from Lamina Properties Database Button to select the material properties of the Graphite/Epoxy.
To analyze the lamina for the optimum fiber angle for the given load, select the Graph: Strength Ratios vs. Angle of Ply Button. Enter the components of the stress vector. Once you enter these values, you are presented with the first of four graphs showing the strength ratio as a function of the angle of ply. The second graph shows the results of using the Maximum Stress failure theory.
After inputting the given data, Promal produces the following graphical output



From the graph, the lamina will not fail (SR>1) for fiber angles between 10 and 30 .
Further investigation using Stresses/Strains and Strength Ratios Button shows that 22.5 is the optimum fiber angle as it has a strength ratio of 3.784. So one can apply 3.784 times the stresses given above before the lamina fails.


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Micromechanical Analysis of a Lamina

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The fifth program conducts the micromechanical analysis of a lamina using formulas from the strength of materials approach. You enter the elastic moduli, coefficients of thermal and moisture expansion of the fiber and the matrix from the keyboard. You can then calculate the elastic moduli, thermal and moisture expansion coefficients of a unidirectional lamina for a particular fiber volume fraction. The program also displays these properties in a tabular/graphical form as a function of the fiber volume fraction.




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A Quick Example

Task
The following are the mechanical properties of the constituents of a Glass/Epoxy lamina:

Fiber Young's modulus = 70 GPa
Matrix Young's modulus = 3.5 GPa
Fiber Poisson's ratio = 0.2
Matrix Poisson's ratio = 0.35
Fiber coefficient of thermal expansion = 0.5E-05 m/m/°C
Matrix coefficient of thermal expansion = 6.0E-05 m/m/°C

Find the fiber volume fraction for which the thermal expansion coefficient perpendicular to the fibers is a maximum.

Procedure:
Click on Input Elastic Moduli of Fiber and Matrix Button to enter the elastic moduli of the fiber and the matrix.
Click on Input CTE for Fiber and Matrix Button to enter the coefficient of thermal expansion for fiber and matrix. Note your units!
Click on the Graph: CTEs vs. FVF Button.

From the graph, as shown in above Figure, we see that the maximum transverse thermal expansion coefficient occurs when the fiber volume fraction is between 0.05 and 0.1. Next, using these values as the upper and lower limits, iteratively use the CTEs of Unidirectional Lamina Button to find the fiber volume fraction for which the thermal expansion coefficient is a maximum. Following this method, a fiber volume fraction of 0.071 is found to produce the maximum transverse coefficient of thermal expansion.


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Macromechanical Analysis of a Laminate

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The sixth program conducts the macromechanical analysis of a laminate. The laminate can consist of a single type of lamina, hybrids, and sandwich panels. The material properties for the lamina are selected from the material database of the second program. Next you enter the orientation of the plies and the corresponding material number of each ply in the laminate. You can also read laminate stacking sequences from a data file. Now you can display the orientation and ply properties, the stiffness and the compliance matrices, and the equivalent plate properties of the laminate. Enter the mechanical and hygrothermal loads to calculate the global and local stresses and strains, strength ratios at the top, middle and bottom surface of each ply in the laminate.




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A Quick Example

Task:
Determine the uniaxial stress you can apply in the x-direction to a (0/45/60/90) Graphite Epoxy laminate. The x-direction is parallel to the fibers in the 0° ply. Use the maximum stress criterion as a basis for your answer. Use the properties of unidirectional Graphite/Epoxy from the lamina properties database.

Procedure:
Click on the Macromechanics of a Laminate Button in the Master Menu.
Click on the Load/Make a New Stacking Sequence File Button to make a new laminate stacking sequence. Since the subscript "s" on the laminate stacking sequence denotes a symmetric laminate, enter eight for the number of plies. Choose the options of a single material and a symmetric laminate. Double click on Graphite/Epoxy in the Material ListBox to flood the material number column in the laminate stacking sequence grid or enter the material number manually in the grid. Enter the angle of the top four plies from top to bottom. Click on Save/Return to Main Menu Button to save the data file.
The task is to find the maximum uniaxial load you can apply in the X-Direction based on the Maximum Stress failure theory.
Click on Applied Mechanical and Hygrothermal Loads Button to enter a unit force per unit length in the X-direction, that is, Nx=1 lb/in. Click on Strength Ratios Button to view the table of strength ratios and are given below.


Minimum obtained value of strength ratio
= 1.298x10³ (90^o ply)
Maximum value of uniaxial load Nx
= Load x Strength Ratio
= 1.298x10³ lb/in.
Thickness of the laminate
= Number of plies x Thickness of one ply
= 0.039368 inches.
Maximum allowable uniaxial stress in X-direction
= Maximum value of load/ Thickness of laminate
= 1.298x103/0.039368
= 32.971 Ksi.
Minimum obtained value of strength ratio
= 1.298x10³ (90^o ply)
Maximum value of uniaxial load Nx
= Load x Strength Ratio
= 1.298x10³ lb/in.
Thickness of the laminate
= Number of plies x Thickness of one ply
= 0.039368 inches.
Maximum allowable uniaxial stress in X-direction
= Maximum value of load/Thickness of laminate
= 1.298x10³/0.039368
= 32.971 Ksi.

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Give an example of a design problem solved with PROMAL?

An electronic device uses an aluminum plate of cross-section 4"x4" to take a pure bending moment of 13,000 lb-in. The factor of safety is two. Using the properties of aluminum given in Table 3.4, find the thickness of the plate. The designer wants to at least halve the thickness of the plate to make room for additional hardware on the electronic device. The choices include unidirectional laminates of Graphite/ Epoxy, Glass/Epoxy or their combination (hybrid laminates). The ply thickness is 0.125 mm (0.0049213"). Design a plate with the lowest cost if the manufacturing cost per ply of Graphite/Epoxy and Glass/Epoxy is 10 and 4 units, respectively.

SOLUTION:
The maximum normal stress in a plate under bending is given by

Stress = M t/(2 I)
where
M = bending moment (lb-in)
t = thickness of plate (in)
I = second moment of area (in^4)

For a rectangular cross-section, the second moment of area is
I = b t^3/12
where
b = width of plate (in).

Using a factor of safety, F = 2 and given b = 4 inches, then the thickness of the plate using the Maximum Stress criterion is
t= 0.9871 in

Now the designer wants to replace the 0.9871 inches thick aluminum plate by a plate of maximum thickness 0.4935 inches (half that of aluminum) made of laminated composites. The bending moment per unit width is 3,250 lb-in.

Using the factor of safety of two, the plate is designed to take a bending moment per unit width of 6250 lb.

The simplest choices are to replace the aluminum plate by an all Graphite/Epoxy laminate or an all Glass/Epoxy laminate. Using PROMAL program, the strength ratio for a single 0 degree ply for the above load for Glass/Epoxy ply is

SR = 5.4942 E-5

Since the bending moment per unit width is inversely proportional to the square of the thickness of the plate, the minimum number of plies required would be 135 which gives the thickness of the all Glass/epoxy laminate as

t = 135 x 0.0049213
= 0.664 in.

The thickness of an all Glass/Epoxy laminate is more than 0.4935 inches and is hence not acceptable. Similarly for an all Graphite/Epoxy a laminate, the minimum number of plies required would be
n = 87 plies
which gives the thickness of the plate as
t = 87 x 0.0049213
= 0.42815 in.
The thickness of an all Graphite/Epoxy laminate is less than 0.4935 inches and is hence acceptable.

Even if an all graphite/epoxy laminate is acceptable, Graphite/Epoxy is 2.5 times costlier than a Glass/Epoxy, one would suggest the use of a hybrid laminate. The question which arises now is in what sequence the plies should be stacked. In a plate under a bending moment, the magnitude of ply stresses is maximum on the top and bottom face. Since the longitudinal tensile and compressive strengths are larger in the Graphite/Epoxy ply then in a Glass/Epoxy ply, one would put them as the facing material and the Glass/Epoxy in the core.

The maximum number of plies allowed in the hybrid laminate is
= 0.4936/0.0049213
= 100 plies

Several combinations of 100 ply symmetric hybrid laminates were subjected to the applied bending moment. Minimum strength ratios in each laminate stacking sequence were found. If the strength ratios are greater than one, the cost of the stacking sequence was determined. The hybrid laminate with the lowest cost is [16 plies of Graphite/Epoxy, 68 plies of Glass/Epoxy and 16 plies of Graphite/Epoxy].

The above example dictated the use of unidirectional laminates. How will the design change if there were multiple loads? Examples of multiple loads include a leaf spring subjected to bending moment as well as torsion, a thin pressure vessel subjected to an internal pressure to yield a biaxial state of stress. In such cases, one may have a choice not only of material systems or their combination but that of orientation of plies as well. Since there can be infinite combinations of angle plies, attention may be focussed on angle plies of 0, 90, 45 and -45 angle plies and their combination thereof. This reduces the possibilities to a finite number for a limited number of material systems, but still the number can be quite large to handle.



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How do I register the software?


Register by e-mail with the subject as "Registration" and body with name, university/continuing education affiliation, postal address, e-mail address, telephone number and how you obtained a copy of the software- a personal copy/ site license/ continuing education course.
promal@eng.usf.edu

OR
Register by mailing a post card with name, university/continuing education affiliation, postal address, e-mail address, telephone number and how you obtained a copy of the software- a personal copy/ site license/ continuing education course to:

Autar K. Kaw
ENB 118
Mechanical Engineering Department
University of South Florida
Tampa, FL 33620-5350
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How do I get technical support?

Before getting technical support, check your manual and this page. For a response to your technical needs, send your questions and comments by e-mail to:
promal@eng.usf.edu

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What are the commonly asked questions?


Question: When I run/setup PROMAL, I get an error - Use Graphics Server 2.1 or higher. How do I solve this problem?
Answer: Copy gsw.exe and graph.vbx from the PROMAL directory to your Windows/system directory. You may have older file versions of these two files. Be sure to make a backup of the older files of gsw.exe and graph.vbx in a separate directory as you may need these if you have programming languages such as Visual Basic VB 3.0 on your machine.
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What updates to PROMAL are available?

Check this page periodically for downloading latest promal.exe file. You cannot run PROMAL just with the promal.exe file. Downloading is only for registered users.

PROMAL.EXE Updated Files
Promal.zip file- Original promal.exe.
Same as in sales before Nov. 30, 1996
Make a backup of the current promal.exe file on a disk for safekeeping. Download the promal.zip file by clicking here. Unzip it and call it promal.exe. Then copy it over the current promal.exe file in your promal directory.


Promal1.zip file- Updated promal.exe.
Same as in the book on "Mechanics of Composites" and sales after Nov. 30, 1996
Make a backup of the current promal.exe file on a disk for safekeeping. Download the promal1.zip file by clicking here. Unzip it and call it promal.exe. Then copy it over the current promal.exe file in your promal directory.


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Are help files to PROMAL available?

Help files to PROMAL will be available in May 1997 via ftp and www at this page.

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Tell me something about the author?


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Dr. Kaw is a full Professor of Mechanical Engineering at the University of South Florida, Tampa, FL. He graduated from Clemson University with a Pd.D. degree in Engineering Mechanics in 1987. He also received his M.S. degree from Clemson University in 1984. He obtained his B.E. (Hons) degree from Birla Institute of Technology and Science in 1981. He joined University of South Florida as an Assistant Professor in 1987 and was tenured and promoted to Associate Professor in 1992. He was then promoted to Full Professor in 1996. Professor Kaw's main scholarly interests are in the fracture mechanics of composite materials and development of instructional software for engineering education. His research has been funded by Air Force Office of Scientific Research, Research and Development Laboratories, Wright Patterson Air Force Base, and Montogomery Tank Lines. He is a member of the American Society of Mechanical Engineers (ASME), American Society of Engineering Education (ASEE) and the American Academy of Mechanics (AAM). He has written more than 25 journal papers and developed several software instructional programs for courses such as Mechanics of Composites and Numerical Methods. Professor Kaw received the following awards
• Southeast Section American Society of Engineering Education (ASEE) Outstanding Contributions in Research Award in 1996,
• State of Florida Teaching Incentive Program Award in 1994, 1996
• American Society of Engineering Education (ASEE) New Mechanics Educator Award in 1992,
• Society of Automotive Engineers (SAE) Ralph Teetor Award in 1991.
• At the University of South Florida, he received University Outstanding Undergraduate Teaching Award (1990 and 1996), Faculty Honor Guard and the College of Engineering Teaching Excellence Award (1990 and 1996).
  
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  How is Mechanics of Composites taught at USF?

  Taught first in 1988, a conventional lecture course on Introduction to Composite Materials is now a model course in the College of Engineering. The course now has the following multidimensional components with a strong philosophy on using technology only to "complement" the course content.

  The course starts with a one month long introduction to composites, although the main emphasis of the course is on teaching the mechanics of composites. Aspects covered include applications, mechanical properties, manufacturing, advantages and drawbacks of various types of composites. These aspects are covered by using professional videos such as "New Materials," "Composites Manufacturing," etc. Also, a request letter sent by Professor Kaw to 300 companies associated with manufacturing, applications and testing of composites in United States generated several promotional videos ranging from filament winding to pultrusion, brochures, testing procedures, specifications and design guidelines. Professor Kaw shows the videos in a classroom with a TV and video recorder setup, and the videos are also available for check out by students from the University Media Center.

  Since composites are such a vast field, Professor Kaw teaches the introductory chapter in the Introduction to Composites course using a newspaper question-answer style. Although many were skeptical of this "USA-Today" approach, students have shown great appreciation for this style. They learn faster and like the progressive style of questions. This format also makes it a prime candidate for browsing on the WWW pages. Many questions are based on queries by students in the classroom. New questions can easily be added and answers can be updated at appropriate places.

  A comprehensive WINDOWS-based software package called PROMAL has been written at USF to complement the classroom instruction. Professor Kaw and several Independent Study students have written this software package. This combined effort has generated a quality product that caters to needs of both students as well as the instructor. Since the national publication of PROMAL (DOS-version of PROMAL) in 1990, Professor Kaw and students have continually updated it several times into the present form.

  Students using PROMAL can instantly conduct pragmatic parametric studies, compare failure theories, and have the information available in tables and graphs instantaneously. The availability of the software allows Professor Kaw to answer many questions instantaneously. PROMAL is more than a black box because it shows intermediate results as well.

  The students can use PROMAL anywhere on campus or home since it is stored on a single 3.5" disk and can be set up in a couple of minutes. Several universities in the nation are using this program. These include Florida State University and Texas A & M. The software was also introduced in the Annual Summer Faculty Development Program held jointly by NSF (National Science Foundation) /ASEE (American Society of Engineering Education) to train faculty members in new areas of engineering.

  Out of three classes per week, Professor Kaw holds one of these classes per week in a computer laboratory where each student has a computer and a video output connected to the instructor's computer. This allows the student to first see an example done by the instructor and then conduct his own numerical experiments.

  The availability of the computer for each student becomes especially important at the end of the semester where students design laminated composite structures. Most problems are open ended and students come up with several answers. Simple designs of pressure vessels and leaf springs do not take more than ten minutes to work out with the PROMAL program, which would otherwise take several hours by using a calculator. The computer program still maintains the student's need to think about the various inputs to the program to get an optimum design. At the end of the exercise, students and Professor Kaw discuss not only the various design alternatives but also how students think differently.

  Even with the use of new technology, the emphasis on teaching and testing the student's knowledge about fundamentals has not changed. All tests are closed book type and only nonprogrammable (but scientific) calculators are allowed in the test. Only the final examination is a take-home design project where the student designs a laminated composite structure using any available tools. These include handbooks, material databases, mathematical packages such as MATHCAD and the PROMAL software.

  In the middle of the course, students get to visit companies that make composite materials products. They see the development of the product from beginning to finish. The timing of the visits works very well since it reinforces the fundamentals learned in the classroom but also gets them to be enthusiastic about the designing of composites.

  This course, which is a popular technical elective for Mechanical Engineering students, has been taught every Spring Semester since 1988 with 15 to 20 students enrolled each time. The course is currently attracting about 30 students. The positive impact has been the placement of students in companies such as Boeing, General Dynamics, Pratt & Whitney, etc., and the fostering of interest in graduate education in the Mechanics of Composites field.

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  What is the course handout for Mechanics of Composite Materials at USF?

  INTRODUCTION TO COMPOSITE MATERIALS

  EML 4562/ EML 5930

  ROOM ENG 309 (M W F 8:00-8:50)

  INTRODUCTION: "Do not give them any more straw to make bricks with, as your custom has been; let them go and find straw for themselves" (Exodus 5). Although man-made composites have existed for thousands of years, the high technology of advanced composites has been used in the aerospace industry only for the last thirty years. The applications are becoming diverse ranging from aircraft structures and missile canisters to tennis racquets and fishing rods. The objective of this course is to analyze and design fiber reinforced composite materials.

  OBJECTIVES: Introduce to advanced composite materials and their applications. Develop fundamental relationships for predicting the mechanical and hygrothermal response of multi-layered materials and structures. Study micromechanical and macromechanical relationships for lamina and laminated materials with emphasis on continuous filament. Introduce material, structural and strength optimization to design laminated composite materials using user friendly software.

  PRE-REQUISITES: Machine Design and Analysis I, EML 3500 or equivalent.

  TEXTBOOK: Mechanics of Composite Materials by Autar K. Kaw

  E-MAIL :

  kaw@eng.usf.edu

  OFFICE HOURS: MWF 10-11 AM. Any other time by appointment 974-5626.

  HOMEWORK: All students should maintain a file of solved homework problems. Homework problems include those assigned in the course handout as well as in the class. Bring this file to class everyday. Start each problem on a fresh page and write on only one side of the paper. All homework problems are due next week on the same day of the week. I will ask you to submit a particular assigned problem(s) in class at least 6 times during the semester. Due to the nature of the submission requirements, no late homework will be accepted. The lowest homework grade will be dropped.

  GRADING POLICY: EML 4562 Grade A - 80-100 Grade B - 70- 79 Grade C - 60- 69 Grade D - 50-59 Grade F - 0-49. Your final grade will be rounded off as follows at the end of the course. For example,

  84.000001-85.000000 will be rounded off as 85, and 84-84.000000999999999 will be rounded off as 84. EML 5930 Grade A - 90-100 Grade B - 80- 89 Grade C - 70- 79 Grade D - 60-69 Grade F - 0-59. Your final grade will be rounded off as follows at the end of the course. For example, 84.000001-85.000000 will be rounded off as 85, and 84-84.000000999999999 will be rounded off as 84.

  COURSE SCHEDULE

  CHAPTER 1 ------ Introduction to Composite Materials
  CHAPTER 2 ------ Macromechanical Behavior of a Lamina
  CHAPTER 3 ------ Micromechanical Behavior of a Lamina
  CHAPTER 4 ------ Macromechanical Behavior of a Laminate
  CHAPTER 5 ------ Design and Failure of a Laminate
  

  All the examinations and tests stated above will be closed book and closed notes. A formula sheet made by the instructor may be allowed to be used in an examination. Course grades will be evaluated on the above percentages and a letter grade will be assigned to you as outlined in the University catalog for undergraduate students (1996-97).

  MAKE-UP TEST POLICY: NO make-up tests will be given. However, in the event of a serious illness (physician's statement documenting severity of illness required), death in the family or other legitimate, documented, verifiable emergency resulting in the absence from a schedule test, a student may be given the same grade for the missed test as the score on the final examination. Notification of absence must be given prior to the commencement of the scheduled examination or test to me. Do not presume that your reasons for missing an examination or test are acceptable unless authorization is given to you.

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  TEXT BOOK
  Purchase Text Book| Objective| Table of Contents | Chapter Objectives

  PROMAL SOFTWARE
  PROMAL | Restrictions PROMAL| Purchase PROMAL |
  System Requirements | Programs | Design Example
  Registration | Commonly Asked Questions Updates | Help files

  
  GENERAL QUESTIONS
  About the Author | Course at USF | Course Handout

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  Links to composite material sites with educational value
  Carbon-Carbon Composites
  Local Composite Company - Advanced Technology and Research
  Composite Companies Listing and Links
  Carbon-Carbon brake pads
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  This home page was developed by Autar Kaw and Andrew Pappas
  Copyright © 1997; Autar Kaw and Andrew Pappas