Prof Krishna's Finite Element Page

"Finite Elements for the Practising Engineer",

IES Journal, Institution of Engineers, Singapore, June 1983, p.57-74.

     I wrote this IES Journal paper on finite element analysis (FEA) 23 years ago this month (July, 2006).
     I read it again, and  wondered what I would change if I wrote it today.
     Nothing much!
     The size, speed, and power of the computer hardware have increased millions-fold. (Remember, I started with the very first paper of civil engineering application of finite elements by Clough, Martin, and Topper, working on second generation mainframes, with punched paper tape input, blinking lights and no monitors, and a two-inch wide paper strip alphanumeric output -- see if you can guess the year!) Finite element analysis software has kept pace, with an awesome array of elements, automatic mesh generation, and instant 3D-colour-animated-graphics output.
     But concept and philosophy remain the same.
Good FEA is still as much an art as a science.
     On the other hand, dangers of misuse and abuse of FEA have actually increased, because the new generations of users take the basis of the method for granted, and many come to depend on the automatic "wizards" of the computer packages they use ... even letting the machines think for them!
     It was more fun when we had to do the grid and type in all the data ourselves, and try to squeeze the elephant through the eye of a needle; and then, when the reams of paper with the zillions of numbers spewed forth, try to make sense -- credible, usable sense -- out of it all.
     I will try to share with you some of my early experiences as time goes along.
     But, for now, read (and, if you wish, download) the 1983 article ...
     Click HERE

"Finite Element Analysis in Implant Dentistry",
© HongKong Tranfor Publishing Co., Ltd., 2006

     I am a co-author of this book on finite element analysis in implant dentistry.
     What is a Civil Engineer like me doing in a book on Dentistry?

     Well, when I was in the USA, I was lucky  to be in on the beginnings of applications of the finite element method (FEM) -- with the second generation of computers! [See above.]
     It was also the norm for a faculty member to collaborate with other professionals -- not just across departments, but across disciplines -- with overlapping interests but different skill sets, for mutual benefit.             
     That was how I got involved with a dentist to analyse a tooth by FEM to find out if and how a cavity filling would fall out when one took a scoop of ice-cream after sipping hot coffee.
     The work got published in a dental journal, in 1983.
     Years later, when I was teaching a post-graduate course in FEM at the National University of Singapore, in 2000 I believe, Dr. J.P. Geng, a visitng dentist from China auditing my course asked me if I would write up the finite element method part for his book.
     And that was how I ended up co-authoring a book on Implant Dentistry!
     [Secretly, I believe that what I have written will be useful to non-dentists too!]  

      For more details on the book, and a free copy of my part of the  book, click

"Three Dimensional Finite Element Analysis of Thick-Walled Pipe-Nozzle Junctions with Curved Transitions"

"Three Dimensional Finite Element Analysis of Thick-Walled Pipe-Nozzle Junctions with Curved Transitions", Preprints of the First International Conference on 'STRUCTURAL MECHANICS IN REACTOR TECHNOLOGY', (Ed. Thomas A. Jaeger), Berlin, Germany, 20-24 September 1971, Vol. 3, Reactor Pressure Vessels, Part G, Steel Pressure Vessels, G-2/7(22p)
Click on
THUMBNAIL at left to read (and, if you wish, download) the full text.

There was an exciting climax to my prsentation of this paper at the Conference in Berlin:

During the question session that followed, a burly American stood up, introduced himself (as Dr. Miller, if I remember right) and said that the summer after I had done the analysis at Oak Ridge National Laboratory in 1968, he did the testing ot the specimen which had been designed to the specifications I had checked out with the finite element analysis.

He concluded with the dramatic statement: "Guess what the stress concentration factor was, Dr. Krishna?", paused three seconds for effect, and said, "3.01"!

That felt Gooood! You see, I had come up with 2.98.