University of Pennsylvania
School of Engineering and
BE & MEAM 455
Dr. Dennis Discher / Dr. Susan Margulies
8-4809 / 8-0882
discher@eniac / margulie@eniac
Lectures: Tu Th 12 - 1:30, 321 Towne Bldg
Recitation: Fri 2 - 3, 309 Towne Bldg
Off Hrs: Margulies TuW 3-4; Discher
(open door 112 Towne)
Laboratory: to begin in Nov and held in LRSM Rm. 13A
FRIDAY RECITATIONS require
Please keep up with regular
Problem Sets and Numerical Problem Sets!
Midterm Exam is Thurs.,
Biological and non-biological
systems are both subject to several basic physical balance laws of broad
Course Description - Lecture,
Fundamental conservation laws are introduced
and illustrated using examples from animate as well as inanimate systems.
include kinematics of deformation, the concept
of stress, conservation of mass, momentum, and energy. Mechanical constitutive
equations for fluids, solids, and intermediate
types of media are described and complemented by hands-on experimental
computational laboratory experiences. Practical
problem-solving using numerical methods will be introduced.
A lecture and topics course
for senior and exceptional junior undergraduate students in Bioengineering
and Mechanical Engineering.
Course enrollment is limited to 30 students.
Prerequisite coursework: Statics,
linear algebra, and differential equations.
YC Fung, A First Course in Continuum
Mechanics, 3rd Ed.Prentice Hall, 1994.
YC Fung, Biomechanics: Mechanical
Properties of Living Tissues 2nd Ed.Springer- Verlag, 1993.
Supplemental Texts (on reserve in Towne
YC Fung, Biomechanics: Motion, Flow
Stress and Growth
YC Fung, Foundations in Solid Mechanics
Atkins and Fox, An Introduction
to the Theory of Elasticity
week 1 - Continuum Notions & Boundary Value Problems;
week 2 - Coordinate Systems and Transformations;
Stress; Equations of Motion
week 3 - Plane stress & Principal Stress;
Thick-walled cylinder (aorta) & Boundary Stress; Failure criteria
week 4 - Deformation & Strain; Strain
Measurement; Principal Strain
week 5 - Examples of Strain; Constitutive
Descriptions: Elasticity via Microscopic Models
EXAM - Stress, Strain, and Tensors
week 6 - More Linear Elasticity; Intro. to Inelastic Phenomena
week 7 - Viscoelasticity, Dissipative Models, Pre-conditioning, Poroelasticity
week 8 - Fluids, Biofluids, & Molecular Ideas; Conservation
of mass, momentum and energy
week 9 - Laboratory: Uniaxial tests chicken skin & muscle,
and synthetic elastomers
week 10 - Differential Eqn. forms of conservation laws; a simple
example with body force integration
week 11 - Practical Intro. to Finite Differences, Methods I, II;
Computational Module I - Elastic Solid
week 12 - Practical Intro. to Finite Elements & Minimiz'n., Method
III; Module II - Soap Film
week 13 - Module III - Fluid Flow; Heart / Thick-walled Sphere
week 14 - Problems in Fluid Mechanics; Remodeling, Growth, &
Final Paper/Exam 30%
Instructors Office Hours:
Prof. Susan Margulies
Prof. Dennis Discher
898 - 0882
898 - 4809
Office Hrs: (tentative) Tu W 3 - 4
T Th 10 - 11
• Notes on CARTESIAN TENSORS:
of Stress Components from Rectangular Cartersian Coordinates to Cylindrical
of a unit square
• Data for pre-lab
• Numerical Methods and Modules
NumPS#1 - 7 as indicated in Numerical Methods Introduction.
A complete listing of the campus public (meaning open to all Penn students)
labs is at
Note the link on that page to College House Computing Labs, which are
located in the residences across campus.
Homework: [generally assigned Tuesdays and due
Thursday of the next week (9 days)]
Problem Set #1
due Thursday Sept. 14
due Thursday, Sept. 21
Problem Set #3
due Thursday, Sept. 28
Problem Set #4
not to be turned in!!
Problem Set #5
due Thursday, Oct. 5
Problem Set #6
due Tuesday, Oct. 17
Problem Supplement due Friday, Dec. 11
Problem Set #7
see Lab Manual; due Thursday, Oct. 27
due Thursday, Nov. 9
Problem Set #9
due Wednesday, Nov. 22
NumPS#1 - 7 as indicated in Numerical Methods Handout.
Can only be found in Towne Library.
They are copyrighted material and cannot be posted on the web.
Exams and Quizzes
Exam 1 is tentatively scheduled Oct. 19
to cover Tensors, Stress, Eqns of Motion, & Strain
University of Pennsylvania
Created: Sept. 1, 1998
Last Update: Nov. 5,1998
All rights reserved; 1998 University of Pennsylvania