# students

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

Professor 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.

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

See attachment for ES 240 lecture notes on viscoelasticity.

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

This problem set is due Friday, Dec.7, 2007.

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

ES 240 notes for Bending of plates is attached.

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

This problem set is due Monday, Nov.26, 2007.

## ES 240 (Fall 2007) Computer Assignment

This computer assignment is due Friday, Nov. 16, 2007

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

ES 240 notes for Principle of virtual work and FEM. Please see attached.

## Stress and Strain: Basic Concepts of Continuum Mechanics for Geologists

This 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.

## HW 15

Title: 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

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

This problem set is due on Nov.2, 2007.

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

Theory of Elasticity by Landau and Lifshitz.

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

## ES 240 - Sun Min Jung Q15

If 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.

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

There are a few helpful reviews of this book on amazon.  Here is the link to that page:
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## Mechanics of Materials by F. P Beer, E. R. Johnston, J. T. DeWolf

The hyperlink for reviews on this book on amazon.com is the following:

## Deformable Bodies and Their Material Behavior by HW Haslach and RW Armstrong

Deformable 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.

## Recommended book to accompany ES 240

I recommend the book

“The Linearized Theory of Elasticity” by William S.
Slaughter

Here is a review of it from Amazon:

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

Outline of Content:

## HW 15

I 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 .

## Recruiting PhD students to study Solid Mechanics at Harvard

Each 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.

Faculty 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

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

Here 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