iMechanica - undergraduate education
https://imechanica.org/taxonomy/term/976
enUnderwater Soil Mechanics Problem
https://imechanica.org/node/20159
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/128">education</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1742">discrete element method</a></div><div class="field-item odd"><a href="/taxonomy/term/2051">soil mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/11247">underwater</a></div><div class="field-item odd"><a href="/taxonomy/term/1044">engineering</a></div><div class="field-item even"><a href="/taxonomy/term/976">undergraduate education</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>I am an undergraduate student conducting a research project involving the design of a tool to aid astronauts to perform experiments on lunar surfaces and would like to request some direction about which analytical tools would be best suited for this application (i.e. FEA or DEM software/techniques). The specific scenario of interest is to design a tool that can act as an anchor in a sand-like medium (regolith) on the surface of the moon. Assuming the design implements a method to bury the tool in the sand, the principle goal is to maximize the resistance to a tensile axial load (initial concepts include a sort of helical drill) while buried under the soil. The design will be modelled with the expectation that a future protoype will be tested in an experimental setup consisting of a quantity of lunar regolith simulant submersed in an underwater neutral-buoyancy tank. An advisor has recommended use of EDEM software, and a fellow student is learning about Ansys. Which software would be be suited to underwater soil mechanics problems? Can you recommend introductory learning resources for DEM, soil mechanics, or related concepts? I have consulted standard civil engineering soil mechanics textbooks (i.e. books by Braja M. Das), but the unique underwater scenario makes many sources to be of little use for this project. This is my first post to iMechanica; thank you for your time and attention.</p>
<p> </p>
</div></div></div>Sat, 06 Aug 2016 02:31:23 +0000dphull20159 at https://imechanica.orghttps://imechanica.org/node/20159#commentshttps://imechanica.org/crss/node/20159What would you like for an undergraduate book on QM to explain to you?
https://imechanica.org/node/9791
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/838">quantum mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/976">undergraduate education</a></div><div class="field-item even"><a href="/taxonomy/term/1036">books</a></div><div class="field-item odd"><a href="/taxonomy/term/6006">classical physics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
</p>
<p><strong>1. Background:</strong></p>
<p>A couple of things concerning books happened recently, in the last week or two.</p>
<p>(i) Dr. Biswajit Banerjee announced last week that a new book on metamaterials and waves in composites authored by him is coming out in print within a few months.</p>
<p>(ii) In one of my regular visits to bookshops, I noticed a hardcover copy of Prof. Allan Bower's book on mechanics of solids. Someone (or more likely, some institution) in Pune had ordered it, and the copy happened to be lying near the top of the stack. The book had been online for some time and I had browsed through it already. So, now, when I opened the printed version out of curiosity, I directly went to the Preface part. This is how Prof. Bower opens his Preface:</p>
<p>
</p>
<p> Ronald Rivlin, a pioneer in the field of nonlinear elasticity, was asked once whether he intended to write a treatise on his field. "Why should I write a book?" he replied. "<strong>People write books to learn a subject.</strong> I already know it."</p>
<p>[Emphasis in <strong>bold</strong> is mine.]</p>
<p>
</p>
<p>
<strong>2. "People write books to learn a subject:"</strong></p>
<p>That line really hit me---in two different ways.</p>
<p>Firstly, it has always been a part of the folklore among engineering college teachers that the best way to learn a subject is to teach it. I first heard it in 1984 in the teachers' room in Bharati Vidyapeeth's College of Engineering. I had then realized, first-hand, how true the saying was. And, I had wondered right back then: if it is not possible to teach a course, how about writing a book on it---mainly for learning the subject.</p>
<p>Secondly, it occurred to me now that if I were to pick out just one subject that I wish to understand better, it would undoubtedly have to be Quantum Mechanics. And, so the thought became: why not write a book on QM---in order to learn it. The idea is not so objectionable after all. Especially if you consider that most physicists (and all mainstream physicists) assure all the rest of us (and very probably also to themselves) that nobody understands quantum mechanics.</p>
<p>Actually, I was planning to write 2--3 journal papers that would extend and better explain some of the fundamental features of quantum physics as using my new approach. I had been gathering my thoughts and background material together. Yet, the more I thought about it, the better it began looking to me that perhaps it makes sense to first write a book on QM before writing those articles.</p>
<p>
</p>
<p>
<strong>3. A question for you:</strong></p>
<p>So, with those thoughts in mind, I would like to raise the title question to you:</p>
<p><strong>What would you like an undergraduate book on QM to explain to you?</strong> Or, better still (because it makes it more personal): <strong>What do you want me to explain to you, concerning the introductory topics of QM?</strong></p>
<p>By introductory topics, I mean the topics covered in (roughly in the order of increasing depth or complexity): Eisberg and Resnick, Hameka, Phillips, Scherrer, Liboff, Gasiorowicz, etc. Also, many other books falling within this same range, e.g.: Griffiths, Zettilli, etc.</p>
<p>If you have any points to raise in this regard, feel free to do so. I will keep this particular post open for comments until I finish writing the book (whenever I come to do that).</p>
<p>Any one may write me. However, a word about the intended audience and the nature of treatment is in order.</p>
<p>
</p>
<p>
<strong>4. The intended audience and the intended treatment of the book:</strong></p>
<p>The primary intended audience is: 3rd/4th year undergraduate students in engineering and applied sciences. Especially, those who did not have a course on electromagnetic fields beforehand (such as those majoring in mechanical, materials, chemical, aeronautical, etc. areas).</p>
<p>The treatment will follow the historical order of developments. I will begin with a summary of the pre-requisites, including very rapid (and perhaps rather conceptual) surveys (done from my own viewpoint, sort of "an engineer's viewpoint") of such topics as: Newton's laws; partial differential equations; The beginning of the energy- and fields-based reformulation of Newton's mechanics by Leibniz; complex numbers and Euler's identity; Lagrangian reformulation of Newtonian mechanics; relevant matrix theory; Fourier theory; relevant probability theory; Hamilotonian reformulation of Newtonian mechanics; electromagnetic field theory from say Coulomb to Maxwell and Hertz; the eigenvalue problem in classical physics; cavity radiation; special relativity (taken as highlighting certain features of the classical electrodynamics).</p>
<p>The QM proper will begin with Planck, of course, and will closely follow the historical sequence, though the notation might be modern---however, I wish to emphasize that I will not introduce Dirac's notation until he introduces it, so to say. Similarly, I will introduce Heisenberg's matrix mechanics before Schrodinger's wave mechanics. I intend to leave the reader at about 1935, though an appendix or two on entanglement is possible.</p>
<p>I will try to keep the length at about 300 pages at the most. I would love to see if it can be done within 250 pages, but doing so seems not easily possible. I will leave out many conceptual explanations, esp. of the prior theories, primarily because that burden has already been relieved for me in the form of Manjit Kumar's book. In a way, I do see my intended book as being complementary to Kumar's book.</p>
<p>I will cover neither Feynman's reformulation nor Bohm's ideas.</p>
<p>The book will also not be a vehicle to introduce my own approach. However, it is impossible for any author to keep aside his viewpoint, while thinking or writing. In this case, I will try to restrict myself to highlighting the wonderful series of ridiculous conclusions to which the earlier theories lead (often isolated and put forth by the formulators of those theories themselves), and providing some explicit hints for getting out of them. However, in the planned book, I will not go beyond providing hints alone. ... Yes, I will be willing to give out some of the material or thoughts that, properly, should have come in the research articles first. However, as far as journal articles go, frankly, I do not care!</p>
<p>The book <strong>will </strong>carry mathematics. (It won't be addressed to the layman.) It will carry derivations too, but only in simple and essential terms. (By simple, I do not mean: devoting inordinate time to one-dimensional and time-independent cases. Adopting this policy may mean that the book ends up being suitable only to the beginning graduate students of engineering. If so, that would be OK by me.)</p>
<p>Further, I would often provide the derivations in an order other than what is found in the usual treatments. For instance, the prerequisites part itself will cover spherical harmonics---right in the context of classical physics. Also, the angular momentum of the EM field. (Yes, the prerequisites part will be a major part in this book, perhaps 40% of the total material.) The prerequisites part will also point out the issue of the instantaneous action-at-a-distance, right in the PDE section.</p>
<p>In short, it will almost be a university text-book. Except that I don't expect any university to adopt it for their classroom usage! Therefore, there won't be any routine kind of chapter-end exercises, nor a section at the beginning of the chapter motivating the student. However, some pointers for further thought might be provided via notes at the end of the book.</p>
<p>Most readers here at iMechanica (and many of the readers of my personal blog) come from engineering and applied sciences background. They are likely to have run into QM as a part of their courses on modern physics, solid physics, nanomaterials, etc. They might have had run into issues concerning the real QM. I would love it if I can provide answers to their questions. And, it goes without saying that students of "pure" sciences---physics, chemistry, etc.---would be as welcome as those of engineering sciences. This book would be directed at them, not at the layman---or at the philosophers.</p>
<p>Of course, as far as raising the questions go, any one may feel free to submit his query via a comment. (I may not reply every comment at iMechanica; I do not moderate anything here.)</p>
<p>All in all, it would be a book written by an engineer, and primarily for engineering/applied science undergraduates/beginning postgraduate students. There already is an excellent book in this space: Prof. Leon van Dommelen's online book. I really like it, but thought that I would have approached many things differently, and so, thought of writing my book. Most important difference, to my mind, is that I would stick to the historical approach throughout. But, yes, as far as undertaking this huge an effort goes, Prof. van Dommelen's book would remain a kind of an inspiration for me.</p>
<p>
</p>
<p>
<strong>5. One final point: Sample questions:</strong></p>
<p>Some time ago, I had written a list of questions that I thought UG students should ask their professors. However, there were also other topics in that post. For ease of direct referencing, here I am copy-pasting those questions below (with a bit of editing). Go through them and see if you have any other questions you wish to raise:</p>
<p>
</p>
<ol><li>
Why are quantum-mechanical forces conservative?</li>
<li>Does the usual time-dependent Schrodinger’s equation (TDSE) apply to propagation of photons? If yes, why does no textbook ever illustrate TDSE involving photons? If not, what principle goes against applicability of TDSE to photons?</li>
<li>What kind of physics would result if the QM wavefunction were not to be complex-valued but real (scalar)-valued? What if the wavefunction were to be deterministic rather than probabilistic? What contradictions would result in each case?</li>
<li>Does QM at all need an interpretation? If yes, why? Why is it that no other theory of physics seems to need special efforts at interpreting it but only QM does, esp. so if all physics theories ultimately describe the same reality? If QM does not need an interpretation, why do people talk about the phrase: “interpretation of QM”? What do they mean by that phrase?</li>
<li>What, precisely, is the physical meaning of an operator? Please don’t simply repeat for us its definition. Instead, please give us the physical meaning of the concept. Or is it the case that no physical meaning is possible for this concept and that it is doomed to remain an exclusively mathematical concept? If yes, why use it in the postulates of a physical theory—without ever taking the care to define its physical correspondents?</li>
<li>Are all quantum-theoretical operators Hermitian? If yes, why? What physical fact does this property indicate/highlight/underscore? What if they are not Hermitian?</li>
<li>Give one example of an important eigenvalue problem from classical mechanics in which the differential equation formalism is very clearly shown to be equivalent to the matrix formalism.</li>
<li>Does the QM theory necessarily require the concept of a wavepacket when it comes to detailing what a QM particle is? If yes, why? What would happen if it were not a packet of waves but instead just a monochromatic wave? If the theory does not necessarily require packets of waves, then can you suggest us any alternative treatment—if there is one?</li>
<li>In every differential equation we have studied thus far, the primary unknown always carried some or the other physical units/dimensions. For example, for mechanical waves, the primary variable would be the displacement from the equilibrium position. But the QM wavefunction seems to be a dimensionless quantity; at least, textbooks don’t seem to note down any units for it. Is it a dimensionless quantity? Why? What important things does this tell us about the nature of theorization followed in QM?</li>
<li>Is QM an action-at-a-distance theory?</li>
<li>How, precisely, does QM relate to the classical EM? Is the term V(x,y,z,t) in Schrodinger’s equation to be understood in the classical sense? If yes, why do people say that between the two, QM is more basic to EM?</li>
<li>Explain precisely how the Newtonian mechanics is implied by QM.</li>
<li>And, one question I raised yesterday, via a tweet: In the mainstream interpretation---taught to all undergraduates world-wide---it is not meaningful to speak of emission of particles. Particles are never emitted, only absorbed---because only absorption can be "observed." The whole world is a series of absorptions, so to speak. True or false? (Hint: In Keynesian economics, there are only consumers, no producers!)
</li>
</ol><p>
<br />
Those were the questions I thought of, some time ago. ... I am sure you can do better.
</p>
<p>
I now look forward to hearing from you.
</p>
<p>
</p>
<p>
--Ajit
</p>
<p>
Also posted at my personal blog [<a href="http://ajitjadhav.wordpress.com/2011/02/12/what-would-you-like-an-undergraduate-book-on-qm-to-explain-to-you/" target="_blank">^</a>].
</p>
<p>
[E&OE]
</p>
<p>
</p>
</div></div></div>Sat, 12 Feb 2011 09:54:34 +0000Ajit R. Jadhav9791 at https://imechanica.orghttps://imechanica.org/node/9791#commentshttps://imechanica.org/crss/node/9791UG Course on Solid Mechanics
https://imechanica.org/node/1424
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/179">solid mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/975">strength of materials</a></div><div class="field-item even"><a href="/taxonomy/term/976">undergraduate education</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
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.
</p>
<p>
<strong>0. Note: </strong>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.
</p>
<p>
<strong>1. Introduction:</strong>
</p>
<p>
The range of (stress/strain/displacement analysis) problems to address.
</p>
<p>
Qualitative and empirical characterization of materials response under tension, compression, shear, fatigue, creep, impact, etc.
</p>
<p>
Engineering choices and the need to make precise the notions of strength, deflection, deformation etc. under different loadings.
</p>
<p>
What quantities must be formulated to meet the above objective? The static case as the simplest.
</p>
<p>
Revision of the simplest 1D case (covered earlier in high-school physics): strain, stress, Hooke's law and Young's modulus.
</p>
<p>
The notion of stress as internal resistive state. The notion of strain as something to do with (relative) displacement. Highlight that stress-strain can be induced out of temperature and EM fields imposed on a constrained body. Highlight Strains --> Stress.
</p>
<p>
Arouse curiosity: What would stress and strain look like in 2D? In 3D?
</p>
<p>
<br /><strong>2. Strain: </strong>
</p>
<p>
The displacement undergone by a rigid body (particle). The vector *fields* of relative displacement and deformation.
</p>
<p>
Identifying the components of the deformation field.
</p>
<p>
Isolation of the strain and rotation tensor fields starting from the displacement vector field. Simple (non-rigorous) demonstration that both are tensor fields.
</p>
<p>
Introduction of the notion of compatibility. Making it mathematically precise using the differential strain-displacement relations. (May be, a demonstration using a finite differences based model that the compatibility relations indeed ensure compatibility. Touch upon sufficiency.)
</p>
<p>
Strain as an essentially geometric concept.
</p>
<p>
Simple examples (e.g. Shames)
</p>
<p>
<strong>3. Stress:</strong>
</p>
<p>
Internal resistance to external loading--why the notion matters. Historical evolution. The idea of the mathematical cut and the resistive traction vector.
</p>
<p>
Introduction of the idea of a stress field. Taylor's series expansion and equilibrium equations (i.e. divergences of the three traction vectors).
</p>
<p>
Simple (non-rigorous) demonstration that stress is a tensor field.
</p>
<p>
Point out the similarity with the kinematical (geometric) characterization of strain.
</p>
<p>
Point out how the complementary property of shear corresponds with dropping the rotational part from the definition of strain.
</p>
<p>
Introduce the linear stress-strain constitutive relations--first for components, and then, the interrelations.
</p>
<p>
Simple examples (e.g. Shames)
</p>
<p>
<br /><strong>4. 2D and 3D Fields: General considerations</strong>
</p>
<p>
The geometrical definition of the principal quantities. Why have them: simplified presentation or "visualization" of tensor fields. The mathematical jugglary and Mohr's circle.
</p>
<p>
The plane stress and the plane strain conditions: Why have the condition. Where it applies. The pitfalls.
</p>
<p>
Analysis of some typical examples.
</p>
<p>
The tri-axial state of stress. Some typical examples. How and why the complexity increases. Why such a loading is adverse. How and why 2D analysis is not enough or can be misleading.
</p>
<p>
<br /><strong>5. The Structure of the Theory:</strong>
</p>
<p>
Bring out the structure of the subject matter:
</p>
<p>
Relative Displacement <--> Deformation <-> Strain <-> Stress <-> Traction <-> Loads.
</p>
<p>
Apply the structure to the static case: three laws (in Shames): compatibility, constitutive law, equilibrium relations.
</p>
<p>
Demonstration (physical arguments) that a vector field cannot take the place of the tensor stress field. Ditto, for stress field.
</p>
<p>
Stress analysis as a BV problem. Introduce the effect of size (even if typical analytical models are always for infinite domains).
</p>
<p>
<br /><strong>6. The Application Specifics:</strong>
</p>
<p>
Point out the typical combinations of member geometry+loading (to be studied next).
</p>
<p>
Spend some time to establish the relations of 3D stress/strain tensor concepts and the analysis in question for each of these combinations.
</p>
<p>
Spend less time than is usual on discussing the usual strength of materials kind of analyses (or their proofs). Spend up to half or even less time if they are not civil engineering majors. (Comments: Popov's book, in particular, spends inordinately long time on beams alone. Not necessary for non-civil engineers. Most teachers spend such a long time on these topics and emphasize them on exams primarily because the teachers themselves have come from the civil engg. depts!)
</p>
<p>
Always trace principal stresses/strains (or pure shear ones) for each and every case of stress analysis that ever gets discussed in the class. Always show Mohr's circles. (No book does this--and I doubt if any teacher does it either.)
</p>
<p>
The cases to be covered are the usual ones: beams, columns, torsion
</p>
<p>
Beams: Forces, stresses and displacements of beams.
</p>
<p>
Torsion: The usual topics.
</p>
<p>
Columns: The usual topic.
</p>
<p>
To reiterate: Cover the topics in a way that it is the understanding of stress/strain *tensor* field concepts that gets reinforced, not a reverence for the particular approximations in analysis.
</p>
<p>
<br /><strong>7. Failure and Fracture:</strong>
</p>
<p>
-- Distinguish between failure and fracture. (e.g., stiffness as the design criterion.)
</p>
<p>
-- Failure criteria. Do point out their relevance to design. Point out the physical meanings of each criterion--don't leave anything (in this topic or otherwise) just mathematically dangling abstractly, connecting nowhere to physical reality.
</p>
<p>
-- Introduction to elastic stability. Do point out how we *begin* by assuming instability in the analysis. Highlight how the simple analysis of column instability is just a begnning.
</p>
<p>
-- Stress concentration and fracture toughness. (Introduction). Do mention size effect.
</p>
<p>
<br /><strong>9. Miscellaneous topics:</strong>
</p>
<p>
Some of them, optional; others, better handled in an accompanying laboratory course.
</p>
<p>
-- Study of an array of the typical components of machines and structures. (Charts showing stress distributions in such components.)
</p>
<p>
-- Energy theorems. This is good inasmuch as physics is being tied to. Unfortunately, this also means calculus of variations (CoV). The new movement is towards towards explaining everything as an application of (CoV)--from optics and QM to mechanics of solids. This is very unfortunate. Actually, CoV is just an optional way of viewing physics and often-times not at all at the core of the physics of the specific situations. So, spend time wisely.
</p>
<p>
-- Introduction to elasticity. If the audience is talented enough, introduce the use of potentials in some simple 2D problems. (Do not emphasize complex number manipulations by themselves--and always remember, the entire theory is only linear elastic and 2D. Mathematical pleasure apart, it has severe restrictions as a theory of engineering.)
</p>
<p>
-- Introduction to the kind of analysis that is involved in tackling topics like plasticity, metal forming, rheology, etc.
</p>
<p>
-- A study of the parallels in the theoretical structure of solid and fluid mechanics
</p>
<p>
-- Stress waves.
</p>
<p>
-- Impact loading.
</p>
<p>
-- NDT
</p>
<p>
-- Experimental stress analysis: Photo-elasticity, brittle coatings.
</p>
<p>
<br /><strong>General Comments:</strong>
</p>
<p>
(i) Introduce the field concept as early as possible.
</p>
<p>
(ii) Discuss each pedagogical (or illustrative) example from all points of view: analytical solution, principal stress contours, computer simulation, photoelasticity results.
</p>
<p>
(Note, here, analytical solutions have been distinguished from principal stresses. This is not a redundancy. The point is, often times, analytical solutions are expressed in terms that are convenient to analysis, but which may not bring out the principal (or pure) quantities.)
</p>
<p>
Always discuss variations in boundary conditions and their impact on solution.
</p>
<p>
(iii) Do not emphasize and do not reward the facility in sheer mathematical manipulations--such a facility can be rather easily developed via sheer pattern-matching, without having developed any real physical understanding.
</p>
<p>
(iv) For the same reason, do not assign many small programs in C/C++/Java/VB etc. that take away mental energy in simply another kind of drill tasks. Instead, give away working programs to students and ask them to try out some variations.
</p>
<p>
(Note: This post will probably undergo several revisions.)
</p>
<p>
</p>
</div></div></div>Sat, 19 May 2007 15:16:09 +0000Ajit R. Jadhav1424 at https://imechanica.orghttps://imechanica.org/node/1424#commentshttps://imechanica.org/crss/node/1424Error | iMechanica