# solid mechanics

## Question 16

Book Title: Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue (Second Edition, Third Edition released earlier this year)

Author: Norman E. Dowling

The book starts with a general overview and introduction to the mechanics of materials, but later emphasizes deformation, fracture and fatigue of materials. The following is a list of the chapters in the second edition:

(1) Introduction- Discusses types of material failure, design and materials selection, technological challenges, and the economic importance of fracture.

## Vibration

A word file is attached.

Return to the outline of the course.

## “An Introduction to the Mechanics of Solids” by S. H. Crandall, N.C. Dahl, and T. J. Lardner

“An Introduction to the Mechanics of Solids” by S. H. Crandall, N.C. Dahl, and T. J. Lardner

As the title explains, this book shows very basics of the solid mechanics. The book has a good coverage of the concepts of primary elements of mechanics, the three equations, some environmental effect, and examples of torsion, bending, and buckling. This book elaborately explains/proofs several important equations, whose procedures tend to be skipped in many courses due to time limitation. Various case studies/problems accompanied with suitable figures have always helped me to get better senses. It is also easy to find what I am looking for in the book with neatly sorted tables and index. And most importantly, I like this book since the book discusses engineering applications and the limitations of these models.

The materials given in ES240 exceed the range that this book can cover, but this book still is a good resource to go back to when I forget the basics since my sophomore year when I used as our textbook for the materials and structures.

## Solid Mechanics Homework 26-30

26. Stress-strain relations under the plane strain conditions
27. Getting weak: derive weak statements from differential equations
28. Potential energy and Rayleigh -Ritz method
29. Constant strain triangle

Return to the outline of the course.

## Textbook Recommendation

So besides using Timoshenko (which is basically the bible of solid mechanics), I have been using Slaughter's The Linearized Theory of Elasticity which I came across in the Gordon McKay Library.

Unlike some of the other textbooks, there is a big focus put on the theory and the idea behind the examples while still having many worked out problems. The first few chapters give a big refresher course on mathematics and lay the groundwork for what is to be taught later on.

I came across this book in particular for the in depth coverage of Airy Stress Functions.

The book is broken into 11 chapters:

Review of Mechanics of Materials
Mathematical Preliminaries
Kinematics
Forces and Stress
Constitutive Equations
Linearized Elasticity Problems
2D Problems
Torsion of Noncircular Cylinders
3D Problems
Variational Methods
Complex Variable Methods

## Finite Element Method

The notes are attached. Return to the outline of the course.

## Recommend books

If you prefer to learn tensors in solid mechanics, Nye's book is recommended.
The author covers most of the physical properties in various crystal structures. Some handy tables are included in the book. However, he uses ONLY tensors to derive the properties. If you prefer to write down equations one by one, this would not be a suitable book to start.
Timoshenko's book is also recommended too. As a beginner, this book explains not only the problem, also the meaning behind it. It clearly describes the fundamental questions.
Some books

## Plane elasticity problems

A word file is attached.

Return to the outline of the course.

## Solid Mechanics Homework 21-25

21. A fiber in an infinite matrix
22. Anti-plane shear
23. Saint-Venant's principle for orthotropic materials
24. Plane problems with no length scales
25. More scaling relations: a half space filled with a power-law material

Return to the outline of the course.

## Theory of Elasticity by Timoshenko and Goodier

Although I know it is not very original, I am recommending Timoshenko's Theory of Elasticity textbook. I find this book useful because it solves many classical solid mechanics problems without assuming the reader has a strong background in the subject (like me). When I am having difficulty with a homework problem, I turn to the index and it usually directs me to a section of the book directly related to the problem, or sometimes even the solution itself. Many parts of the book complement the course, such as the chapters "Plane Stress and Plane Strain" and "Analysis of Stress and Strain in 3 Dimensions."

The book starts with basic definitions and derivations of stress and strain, then applies these equations to solve problems in different coordinate systems. It also includes chapters on more specific topics, like torsion and thermal stress.

## Office Hour Change for Oct. 19

Office hour for tomorrow (Oct. 19 Thursday) will be rescheduled as 4:00pm to 4:30pm.

## Textbook Recommendation

It's a bit hard to recommend a text, when I have yet to find one that I really love. Currently I am working from Advanced Strength and Applied Elasticity by A.C. Ugural & S.K. Fenster. It contains all of the relevant information, though I find the explanations of the concepts a bit slim. So far is has covered all of topics we covered in class. The first four chapters seem the most relevent. These are titled Analysis of Stress; Strain and Stress-Strain Relations; Two-Dimensional Problems in Elasticity; and Failure Criteria. The rest of the text deals with more specific topics (torsion, bending, plastic behavior, etc.).

Here is a link to the Amazon page, where the book gets mediocore reviews.

## Solid Mechanics Homework 16-20

• 16. Recommend a textbook that you think will help students in this course.  See recommendations from students who took this course before.
• 17. Disclination (the cut-and-weld problem)
• 18. Design a rotating disk to avert plastic deformation
• 19. A half space of an elastic material subject to a periodic traction on the surface
• 20. Orthotropy rescaling

Return to the outline of the course.

Hey, people often call me Mads which circumvents the ordeal of pronouncing my "real" name correctly which can be tricky. I'm a first year PhD student in applied mathematics. I am currently trying to balance doing courses and research with Michael Brenner, L. Mahadevan and Howard Stone.
My undergraduate and first masters are from Cambridge University, England, during which I studied Pure maths, Applied maths, statistics, mechanics (primarily fluid and some solid) and theoretical pysics.
My interests are primarily in mechanics (fluid, solid and bio). Apart from fluid mechanics I find problems in elasticity and viscoelasticty theory very curious and interesting (currently I am looking at friction in elastomers). I also like looking at biological systems where "structure reveals function". Even though I am primarily a theorist I really enjoy conducting table-top, so called cheap experiments, and talking to experimentalists in any area.

## Namiko Yamamoto for ES240 Problem6

I am a first year PhD student in Aeronautics and Astronautics department at MIT. I also have obtained B.S. and M.S. from the same department. I have taken one Solid Mechanics (graduate level) course at MIT, but since it did not cover waves/vibration or nonlinear plate theory, I look forward to these new topics later in the course very much. My most research work has been done at Technology Laboratory for Advanced Materials and Composites at MIT. My M.S. thesis topic was on micro solid oxide fuel cell. The goal was to design and fabricate thin film tri-layer fuel cell structure that is thermomechanically stable at high operation temperature. We started with mechanical testing to acquire properties, and designed membranes with von Karman plate theory. My PhD topic is nano-engineered composites with carbon nanotubes (CNTs). Solid mechanics is very directly related to these structural tasks including stiffness testing. Generally, having better sense of mechanics behind and having many analysis tools will be greatly helpful. So far I have been having much fun coming to Harvard, taking a little break from MIT (I have been there more than enough, although I still love it there). I hope to learn as much as possible from this course.

## Hi :)

Hi everyone, I am Roxanne, a G-2 student in applied physics.  My major was chemical engineering when I was an undergraduate student in Taiwan.  I had no background on mechanics then.  When I was a G-1, I took AP 293 (Deformation of Solids).  This course gave me some ideas on the plastic flow, elastic properties, and dislocations of materials. Math, like partial differential equation and tensors are pretty challenging to me…always.

Currently, I am working with Frans, and my research focus is on studying the creep phenomena in metals.

http://deas.harvard.edu/matsci/

## Xuanhe Zhao

My name is Xuanhe Zhao, and I'm a first year student in DEAS. Before joining Harvard, I got my Master Degree in Materials Engineering from University of British Columbia, Canand. I have took one course on Computational Mechanics, and read a couple of books on theory of elasticity.

The major goal for me taking ES 240 is to learn how to understand and solve engineering problems, both familiar and unfamiliar, in a intuitive way. In addition, I will further consolidate my background in solid mechanics.

## Megan McCain

I am a first year grad student in bioengineering working in Dr. Parker's Disesase Biophysics Group (http://www.deas.harvard.edu/diseasebiophysics/). I attended Washington University in St. Louis for undergrad, where I double majored in biomedical engineering and biology and minored in chemistry. The only courses I have taken related to solid mechanics are Biomechanics and Transport Phenomena, both of which covered basic mechanics. As an undergrad, I worked in a research lab that focused on cardiac electrophysiology. The lab I am in now is interested in how the mechanical and electrical behaviors of cardiac cells are related, so I need to gain a stronger background in mechanics to match my background in electrophysiology. I hope that this class will help me develop an intuition about the mechanical behavior of objects, which I can apply to the mechanics of cellular events.

## Michael Petralia

I completed my undergraduate degree in Mechanical Engineering at The Cooper Union for the Advancement of Science and Art, in New York City. At the undergraduate level, I have taken two courses related to solid mechanics: Solid Mechanics and Stress & Applied Elasticity. Though these courses covered most of the same topics, the focus was not on working with developing the equations for different situations. The majority of the work was in knowing when to apply the equations and coming up with quantitative solutions. Thus my weaknesses will be related to coming up with equations to model various stress situations.

Concerning my research, I am working with Prof. Robert Wood in the microrobotics laboratory. My focus will be on aquatic robots on the order of several centimeters in length. Because of the restrictions inherent in working at this scale, it will be important not to over-design the systems. From studying solid mechanics, I hope to gain the ability to analyze the states of stress and strain in materials such that I can effectively develop efficient systems for microrobotics.

My name is Will Adams and I am a first year grad student in BME. I have no previous courses in solid mechanics or strength of materials but I have taken two fluid mechanics courses, ES220 and ES123, as an undergrad which contain many of the same lines of thinking. Hopefully the math formalisms of these classes will help in ES240 but having no solids background leaves me with little intuition about experimental results. Hopefully I can acquire this here. I was a BME major as an undergrad here in DEAS.

My name is Adrian Podpirka and I am a first year grad student studying applied physics. I came to Harvard after finishing my Bachelors in Material Science and Engineering at Columbia University. As an undergraduate I took Mechanics of Solids with Professor Xi Chen and Mechanical Properties of Materials with Professor Noyan.

Related to this course, my main weakness is the mathematics involved since it has been more then 3 years since I took differential equations. Also, both my undergraduate courses were not tensor based. My main strength in this course would be my understanding of material properties and the phenomenas involved.

My likely research direction will probably be in the field of fuel cell membranes with Professor Ramanathan.

## Solid Mechanics Homework 11-15

This set of homework relies on a few elementary facts of the algebra of vectors and tensors.  If you are vague about these facts, see some old notes I wrote when I taught ES 240 in 2006:

11. Positive-definite elastic energy density
12. The coefficient of thermal expansion (CTE) is a second-rank tensor.
13. Hooke's law for anisotropic, linearly elastic solids
14. Invariants of a tensor
15. A "derivation" of the Mises (1913) yield criterion

## Solid Mechanics Homework 6-10

6. Post an entry in iMechanica to explain to your teaching staff and classmates why you take this class.

7. Residual stress around an inclusion
8. Lame Solution in Cylindrical Shape
9. Stress Concentration around a Circular Hole
10. Back-of-Envelope Calculation

Return to the outline of the course.

## Office Hour for ES 240

Zhigang Suo: Wed. 3pm Pierce 309

Nanshu Lu: Thur. 4~6pm Pierce 403

Valid for every week except special notification is published.

## Solid Mechanics Homework 1-5

Due 26 September 2008 in class

1. Nothing Is Continuum, but...
2. Hooke's law in various forms
3. Compatibility: the strain-displacement relations
4. Traction vector on a plane
5. Turbine blade: centrifugal force and creep

Return to the outline of the course.