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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. 

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 

ES 240 Problem 6 Blog Entry

My name is John Peter Whitney, but I go by Peter.  My parents set it up that way--I don't know why.  This is my answer to Pset 2, problem 6:


* I last took solid mechanics Fall 2001.  This sophomore-level course was taught by Professor Mark Spearing.  We used Crandall, Dahl, and Lardner.  I have forgotten almost everything from that class.

* My undergrad degree is in Physics, and my masters is in aerospace engineering (which I also studied but did not get a degree in as an undergrad).

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