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Ajit R. Jadhav's blog

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FEM Is Not a Local Method (and It Isn't Global Either)

In the literature, FEM has sometimes been characterized as a local approach, but IMO this needs to be corrected.

The piecewise continuous trial-functions of FEM can be looked at from two different viewpoints:

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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.

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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


It shows a frictionless glass tube lying on a horizontal desktop. The tube is smoothly bent at a couple of places as shown in the figure.

Suppose that a small steel ball (say, one taken from a ball-bearing) enters the tube at the point A, with an initial velocity of v.

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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.

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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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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.

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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:

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

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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.

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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.

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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?

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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.)

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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?

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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: 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:

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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?

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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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