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Solve Navier type function with Green Function and Fourier Transformation

T.ZENG's picture

I am a freshman in micromechanics area. Many books and papers always say the linear elastic equilibrium equation(Someone also called Navier type function) could be solved with Green Function and Fourier Transformation, but without details. May be the writers think anyone should know these two popular methods in solving the PDE. I have search many books(both mathmatic and mechanics), However, there are little information about solving the navier type function with those two methods. 

If you know any book about this area, please do not hesitate to tell me. Because the question has frustrated me for a long time. Your kind reply will be greate appreciated!!!

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Pradeep Sharma's picture

There are several books that illustrate the use of Green's function and Fourier Transform methods in the context of elasticity---of course most books on PDEs will also provide the basics. A recent book that I see on my shelf is by Asaro and Lubarda. You and find a lot of relevant materials here.

Also,  another (very recent) book by Shaofan Li and Gang Wang on micromechanics is quite useful. This book has several interesting examples. Take a look . I am planning to post a review on this book on iMechanica in a few days.

 

If you want something immediate, you might wish to consult the massive online encylodpeda of all things solid mechanics (by Allan Bower).  

T.ZENG's picture

 

Hi. Pradeep Sharma

Thank you for your kind reply and recommended books.

I think my  puzzlement was due to the lack of mathmatic and mechanics knowledge. Now I am trying my best to improve my abilities. Will you give me some advices on some systermatic book to read, which will be greate help to me.

Best regards! 

 

TAO ZENG

LML,Polytech-Lille

Cite Scientifique
59655 Villeneuve d'Ascq,France

A good starting point for understanding Green's function methods is

Ivar Stakgold's classic books "Boundary Value Problems of Mathematical Physics" or "Green's Functions and Boundary-value Problems".

-- Biswajit 

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