Ajit R. Jadhav's blog

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The Fundamental Physical Bases of the WR Approach (and, Consequently, of FEM) in General

It has been quite some time (more than 1.5 years) that I had touched upon the topic of the physical bases of FEM in general, and of the general weighted residual (WR) approach in particular, at iMechanica (see here).

The position I then took was that there is no known physical basis at all for the WR approach---despite its loving portrayals in mathematical terms, or its popularity.

Further, I had also expressed (here and elsewhere) that a basis in physical principles existed for FEM only in a rather limited sense: wherever the energy interpretation was available for the model. (Note, this too is already at variance with what some of the authors have written in books.)

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A (really) small problem

Here's a quick one.

Refer to the accompanying figure.

Figure to accompany a really small problem


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53rd Congress of ISTAM (2008)


The 53rd Congress of the Indian Society of Theoretical and Applied Mechanics (an International Meet) is slated to be held during last week of December 2008, in Hyderabad, India. The last date for sending in both the abstracts and the full-length papers is 30th September, 2008.

People from outside India are especially encouraged to participate. Hyderabad is well connected by flights. Usually, the ISTAM conferences are low on budget but high on enthusiasm. The ISTAM conferences typically cover a broad range of topics.

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M Tech/ME and B Tech/BE Projects Available in Pune (Mech., CS, etc.)

I have quite a few ideas for MTech/ME/BTech/BE degree projects. The projects may be suitable in many different branches, including Mechanical, Computer Science, Metallurgical, Aerospace, Civil, etc. (In a few cases, MSc/M Phil students of departments like Physics or Computer Modeling and Simulation would be suitable too.)

All these projects are available for the new academic year (2008-09), at Pune, India.

Students from COEP and IIT Bombay are encouraged to apply. Others, please go through the document available here before getting in touch with me. In any case, there are no stipends/assistantships to go with these.

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I have quite a few things to tell...

My PhD defence at the University of Pune is already over.

I have also received post-doc offers, one from a group at MIT Boston, as well as another one from the University of California, Berkeley. The two offers followed within hours of each other. The jobs are in the computational sciences/engineering areas; the people were impressed by what I did in my PhD as well as my iMechanica writings.

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I got an email

This was n-th time that while being right in the process of posting, my work was not saved, but got automatically wiped out. I will write as much as I can, from my recollection. (Invariably, such things begin to happen when the India-USA Nuclear Deal or some other issue of international importance reaches a critical phase. It is funny that in no such time do I get job---even if the Indians in the billionnaires lists, including Ambanis (Hindu) and Premji (Muslim) keep multiplying their accumulated money. (Hope that at least some of the bad attention that I always get at such times now goes their way, too!))

Anyway, let me recover as much of my thoughts as possible.

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FEM: How should it be taught?

I am designing a new course on FEM, to be offered privately in India. It will emphasize fundamentals, and try to supply (or bring out) the physical interpretations behind the mathematical formalisms.

More details: It probably will be directed to the working engineer who has already used existing commercial package(s). The initial idea is to split it up over about 6 week-ends, 4 hours per day of the week-end (say Saturday and Sunday each). However, minor details like that may change. I just wanted to give an idea of the length of the course, the time available for class-room interaction, that's all. Please see the attached brochure. (A typo in the test is now corrected in the version 0.7).

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An interesting question...

See the following site:


And then, think: If you had to answer the same question, what would your answer be?


(BTW, I know I have quite a few comments to reply here, but somehow have not been able to find time to do so.... I will, soon enough... Anyway, in the meanwhile, wish you all a happy new year... And oh yes, I think it would  be great if mechanicians could share their answers to the above referred question too.)

-- Ajit

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A Note on Stereology

The best place to start is Wikipedia: http://en.wikipedia.org/wiki/Stereology.

Most active research in stereology is done in medical and biological community.

In engineering, in USA, Prof. Rhines and Prof. de Hoff, both of the University of Florida at Gainesville did a lot of pioneering work. The stereological researchers active in engineering in USA are mostly limited to the "progenies" of the Florida school. These include (and I quote off-hand): Prof. Arun Gokhale of GeogiaTech and Prof. Burton Patterson of the University of Alabama at Birmingham (who was my guide at my first attempt at PhD). 

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The efficiency of turbines

Hello students (and also others) at iMechanica,

Last weekend, while channel browsing on TV, I happened to notice a documentary on the Hoover dam (in the US). It showed a number of jets of water, huge ones, forcefully springing forth out of the rock faces just downstream of the dam. These were the water jets coming off the electricity generation plant of the dam, *after* their job of generating electricity was already over.

Watching these fascinating water streams reminded me of a brain teaser. Might as well share it here. (It might look like high-school physics, but you can use it to understand higher courses in engineering as well.)

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Some loud (and crazy) thinking on automobiles...

At iMechanica, almost none talks about topics from structural dynamics and design, theory of machines, automotive mechanics, space mechanics, etc.

Let me help correct this situation by raising two questions below. Well-thought answers from any individual are welcome.

First, some background for the questions.

Most Indian cities were not deliberately designed in modern times but have evolved over centuries. Therefore, the in-city roads are, typically, very narrow, with very sharp turns in the bylanes. Parking space is almost a dream. (BTW, many European cities too carry narrow roads, I have heard, though not as much of traffic congestion.)

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Naming the SI Unit for Fracture Toughness (KIC)

To: Engineers, Fracture Analysts, Mechanicians, Physicists...

In science and engineering, we have an excellent tradition: naming a physical unit using the name of a prominent personality from the concerned field. For example, in SI system, we measure force in newton, work in joule, power in watt...

But the unit of fracture toughness, i.e. KIC, is too lengthy to pronounce: (mega) pascal-underoot-meter. Further, it has also been in use for something like half a century by now, perhaps more. So, how do you like the idea of giving a name to this unit?

As far as I can see, the possible choices are:

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Jobs: advertised and applied for

In this thread, I intend to create a record of all the job applications related to CAE (teaching, research or application engineering) and/or software development for the same (research or application engineering) that I have made, and responses, if at all any, that I have got. (Jobs involving a component of management are included.)

This blog entry is unusual in that I intend to reply back myself, one reply per job application I have made (sometimes going back as far back as 4 years or more). I have a lot of "data" as I have gone without a job for 6 years out of the last 6.5 years.

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Comparative Computational Mechanics / Engineering Science

If you had to design a course of the title: "Comparative Computational Mechanics" or "Comparative Methods of Computational Engineering Science and/or Mechanics", what would its contents be like?

Feel free to assume an appropriate level of preparation on the part of the course students (e.g. undergraduate/graduate/training of experienced engineers). Feel free to give concrete details (points to be taught) or a general outline as you wish. Feel free to note down what methods of computational mechanics, in your opinion, should be given more weightage in the overall course. If you can think of good illustrative examples that may better help the cause of a *comparative* analysis, please note down the same too.

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Why lionize mathematics in science/engineering?

This has reference to (only) the *last paragraph* in Prof. Harry Lewis' recent post, found at: http://www.imechanica.org/node/1423#comment-2880.

The reason I write the present post is because I always seem to have had a view of inventing, learning, or teaching mathematics that is remarkably at odds with what Prof. Lewis' last paragraph *seems* to imply.

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UG Course on Solid Mechanics

Given below is a sequence that might properly address the question of what to teach in the first (and the only) UG couse on strength of materials or solid mechanics.

0. Note: It's a mistake to believe that the contents for such a course can be covered in a linear fashion. Apply the spiral theory of knowledge and revisit certain concepts again and again: e.g., the concepts of stress, strain, fields, BV problems, theoretical structure, etc.

1. Introduction:

The range of (stress/strain/displacement analysis) problems to address.

Qualitative and empirical characterization of materials response under tension, compression, shear, fatigue, creep, impact, etc.

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Stress or strain: which one is more fundamental?

In between stress and strain, which one is the more fundamental physical quantity? Or is it the case that each is defined independent of the other and so nothing can be said about their order? Is this the case?

To begin with these questions, consider the fact that first we have to apply a force to an object and it is only then that the object is observed to have been deformed or strained. Accordingly, one may say that forces produce strains, and therefore, it seems that stress has to be more fundamental. If so, how come stress cannot be measured directly? This is the paradox I would like to address here.

Of course, to begin with, my position is that you can never directly measure stress.

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Systematization Schemes for Mechanics and Concept Maps

1. Introductory

Recently, there has been some active discussion on topics like:
-- Open-source textbooks
-- Comparing lecture notes
-- Unification of mechanics
-- Wikipedia and Citizendium

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