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Complex variable methods
- What types of PDEs can be solved using complex variable methods
- Anti-plane shear
- Elements of a function of a complex variable (contour integral, analytic continuation, conformal mapping)
- Line force
- Screw dislocation
- Crack
- Circular hole
- Elliptic hole
- Plemelj formulas
- Riemann-Hilbert problem
- Crack interacting with a point singularity
- In-plane deformation
- Dundurs parameters
- Interfacial cracks
- Anisotropic materials. Stroh formalism
Return to the outline of ES 421 Advanced Elasticity
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 complex variable methods 2009 02 21.pdf | 325.67 KB |
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Valuable resource
Dear Zhigang,
I'm very much enjoying your lecture notes. Especially, this note on complex variable methods summarizes key aspects of fracture and elasticity problems. I'm very happy to have a chance to read it. Thank you so much for your enthusiasm and effort.
Jay
Mechanics: accumulative and infinitely extensible
Dear Jay: Good to hear from you! Thank you so much for your kindness. I'm sorry that you had to return to Korea early in the semester. I've just given the last lecture of ES 241 Advanced Elasticity yesterday. Most other sit-in people stayed with me till the end.
This is a second-year graduate course in solid mechanics. The students have all taken ES 240 Solid Mechanics, so that I can assume that they have some adult experience of the subject. In addition, we have separate courses on fracture mechanics, plasticity, mechanical behavior of materials, and kinetics. They are all taught at advanced levels.
There is no other constraint on what I have to cover. From very beginning, I knew I would not be able to cover everything that I'd love to cover. Instead of trying to cover everything, I have tried to uncover a few things that are interesting to me and that seem to have lasting value. The notes are rather terse and contain typos and, I'm sure, errors and bad judgments. Often I would go over two pages of the notes in a 90-minute lecture. Many students made perceptive comments in class.
This was the first time that I taught the course. It was both an exhilarating and exhausting experience. I have tried to build ideas from scratch, and tried to trivialize them (i.e., making them transparent in hind sight). I was constantly delighted by the insights and ingenuities of great mechanicians of the past. It was humbling, too. I had to admit in class so many times that I could not have discovered this or that even if I were there!
But that is precisely the beauty of our subject: great depth and breadth. All we are hopeful is to learn great ideas of the past, make a few interesting applications, and add a few new ideas that will make a future professor say, "Ah, that is clever. I wouldn't be able to come up with this even if I were there."
Our subject is accumulative and, I believe, infinitely extensible.
assigning angles on two sides of a branch cut
I thank Hicheme for alerting me of an error in the notes. I have updated the notes on p.6 and p.13. On p.6, I also inserted a short parapgraph on assigning angles on two sides of a branch cut.
I hope to work through the notes again later this semester, when I teach the topic again.
Complex variable methods in linear (plane) elasticity
Dear Mr Zhigang,
I would be grateful if you sent me some information (notes, ebooks, etc) about the application of the complex variable method in elasticity problems, especially for the cases in which conformal mapping is involved.
Best regards,
George Papazafeiropoulos
Re: Complex variable methods in linear (plane) elasticity
Here are my notes. I don't know of any other notes on the subject online. A short book on the subject is
A.H. England, Complex variable methods in elasticity.