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## ES 240 Problem Set #8, Problem #20 - Green's function of biharmonic operator is not positive definite

Thu, 2007-12-06 23:44 - John Peter WhitneyProfessor Vlassak mentioned that last year every single person did a finite element project. He said he wanted to see more theory projects, so I decided to take him up on that.

I was browsing around one day and happened upon an article that explained that while the Green's function of the laplacian was positive definite, the biharmonic operator's Green's function is not. Physically, this has significance.

## Writings of scientists on doing research

Sat, 2007-12-01 09:32 - Zhigang SuoIn a previous post, Learning to be a PhD advisor, I wrote about learning to do my job from students. Over the years, I have also learned from writings of other scientists on doing research, its dynamics: competition, despair, and exhilaration... Here is a small sample that occurs to me this morning.

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## ES 240 (Fall 2007) Lecture Notes - Viscoelasticity

Fri, 2007-11-30 14:01 - Nanshu Lu
See attachment for ES 240 lecture notes on viscoelasticity.

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## ES 240 (Fall 2007) Homework 29-36

Fri, 2007-11-30 14:00 - Nanshu LuThis problem set is due Friday, Dec.7, 2007.

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## ES 240 (Fall 2007) Lecture Notes - Bending of Plates

Mon, 2007-11-19 11:26 - Nanshu LuES 240 notes for Bending of plates is attached.

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## ES 240 (Fall 2007) Homework 26-28

Fri, 2007-11-16 15:30 - Nanshu LuThis problem set is due Monday, Nov.26, 2007.

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## ES 240 (Fall 2007) Computer Assignment

Sun, 2007-11-04 17:13 - Nanshu LuThis computer assignment is due Friday, Nov. 16, 2007

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## ES 240 (Fall 2007) Lecture Notes - Principle of virtual work and FEM

Mon, 2007-10-29 11:44 - Nanshu LuES 240 notes for Principle of virtual work and FEM. Please see attached.

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## A E Love -Treatise on the Mathematical Theory of Elasticity

Sat, 2007-10-27 23:11 - Cai Shengqiang- Read more about A E Love -Treatise on the Mathematical Theory of Elasticity
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## Stress and Strain: Basic Concepts of Continuum Mechanics for Geologists

Fri, 2007-10-26 11:35 - Eric KiserThis book begins by describing real life examples of mechanical states of different materials. The book next discusses stress. This discussion includes force, mohr circles, tensor components of stress, and stress fields. Next strain is discussed. This ranges from measuring deformation to tensor components of infinite and finite strain. The book concludes by outlining different material behaviors. These include Hookean behavior and Newtonian behavior. This last section also discusses energy consumed in deformation.

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## HW 15

Fri, 2007-10-26 09:23 - Yuhang HuTitle: Theory of Plates and Shells

Author: Stephen P. Tomoshenko and S. Woinowsky-Krieger

Contents:

Chapter 1: Bending of long rectangular plates to a cylindrical surface .

Chapter 2: Pure bending of plates.

Chapter 3: Symmetrical bending of circular plates

Chapter 4: Small deflections of laterally loaded plates

Chapter 5: Simply supported rectangular plates

Chapter 6: Rectangular plates with various edge conditions

Chapter 7: Continuous rectangular plates

Chapter 8: Plates on elastic foundation

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## ES 240 (Fall 2007) Homework 22-25

Thu, 2007-10-25 14:36 - Nanshu LuThis problem set is due on Nov.2, 2007.

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## 15. Recommend a textbook that you think will help students in this course

Wed, 2007-10-24 22:13 - mingguoTheory of Elasticity by Landau and Lifshitz.

http://www.amazon.com/Theory-Elasticity-Third-Theoretical-Physics/dp/075062633X

content:

1 fundamental equations

2 the equilibrium of rods and plates

3 elastic waves

4 dislocations

5 thermal conduction and viscosity in solids

6 mechanics of liquid crystals

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## ES 240 - Sun Min Jung Q15

Wed, 2007-10-24 20:51 - Sun Min JungIf I were to recommend one textbook that will help students in this course it would obviously be the "Theory of Elasticity" by Timoshenko and Goodier. But you could have found that out by simply looking at the course syllabus, so I will also recommend the following books that are helpful in other areas of the course: "Mathematical Phyiscs" by Kusse and Westwig, "Mechanics of Materials" by Beer and Johnson, and "Advanced Engineering Mathematics" by Greenberg.

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## Elasticity: Tensor, Dyadic and Engineering Approaches by P.C. Chou and N. J. Pagano

Wed, 2007-10-24 19:56 - Andrew Seagraves
There are a few helpful reviews of this book on amazon. Here is the link to that page:

Elasticity-Tensor-Dyadic-Engineering-Approaches

http://www.amazon.com/Elasticity-Tensor-Dyadic-Engineering-Approaches/dp...

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## Mechanics of Materials by F. P Beer, E. R. Johnston, J. T. DeWolf

Wed, 2007-10-24 15:51 - Maria Persson GuldaThe hyperlink for reviews on this book on amazon.com is the following:

http://www.amazon.com/gp/product/customer-reviews/0073107956/ref=cm_cr_d...

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## Mechanics of Materials by F. Beer, E. R. Johnston, and J. T. DeWolf

Wed, 2007-10-24 14:35 - Christian Wylonis- Read more about Mechanics of Materials by F. Beer, E. R. Johnston, and J. T. DeWolf
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## Crystallography and Crystal Defects by A. Kelly and G. W. Groves

Wed, 2007-10-24 14:07 - Kathleen W. DiSanto- Read more about Crystallography and Crystal Defects by A. Kelly and G. W. Groves
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## Deformable Bodies and Their Material Behavior by HW Haslach and RW Armstrong

Wed, 2007-10-24 14:01 - Nathan ThielenDeformable Bodies and Their Material Behavior by HW Haslach and RW Armstrong is a great reference book for solid mechanics. This text discusses a wide variety of materials, the relationships between applied stresses, displacements and material properties, the mathematical approximations to predict mechanical behaviors, and the practical uses for the theory. The text helps to understand how the theory can be applied to practical problems. The text has many worked examples to common problems.

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## Recommended book to accompany ES 240

Wed, 2007-10-24 13:15 - Sunny WicksI recommend the book

“The Linearized Theory of Elasticity” by William S.

Slaughter

Here is a review of it from Amazon:

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## Solid Mechanics: An Introduction (Solid Mechanics and Its Applications) by J. Ward

Wed, 2007-10-24 08:51 - Stephen Steiner
**Review Online:** http://www.amazon.com/Solid-Mechanics-Introduction-Its-Applications/dp/0792319494

**Outline of Content:**

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## HW 15

Tue, 2007-10-23 10:51 - Lei QiaoI find the book , An Introduction to the mechanics of solids , is very helpful to me.

It is written by Stephen H. Crandall and Thomas Lardner .

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## Homework question 15: Linear Algebra by S. Lipshutz and M Lipson

Mon, 2007-10-22 21:04 - Alex EpsteinAmazon review link:

http://www.amazon.com/Schaums-Outline-Algebra-Seymour-Lipschutz/dp/00713...

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## Recruiting PhD students to study Solid Mechanics at Harvard

Sun, 2007-10-21 16:11 - Zhigang SuoEach year, several new students begin their studies of Solid Mechanics for PhD degrees at Harvard School of Engineering and Applied Sciences. The students come from all over the world. We have no constraint on where they come from.

**Facu****lty members in Solid Mechanics**. The School of Engineering and Applied Sciences is not divided into departments, but faculty do assemble into programs. Faculty members directly responsible for the program of Solid Mechanics are

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## Foundations of Solid Mechanics by Y. C. Fung

Fri, 2007-10-19 14:51 - John Peter WhitneyHere are the chapter names:

1) Prototypes of the theory of elasticity and viscoelasticity

2) Tensor analysis

3) Stress tensor

4) Analysis of strain

5) Conservation Laws

6) Elastic and plastic behavior of materials

7) Linear elasticity

8) Solutions of problems in elasticity by potentials

9) Two-dimensional problems in elasticity

10) Variational Calculus, energy theorems, saint-venant's principle

11) Hamilton's principle, wave propagation, applications of generalized coordinates

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