Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
Questions tagged [continuum-mechanics]
875 questions
203
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8 answers
Why do we bend a book to keep it straight?
I noticed that I have been bending my book all along, when I was reading it with one hand.
This also works for plane flexible sheets of any material.
Illustration using an A4 sheet
Without bending the sheet:
With a bend along perpendicular…
AlphaLife
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votes
2 answers
Why aren't the lengths of the bars on a toy glockenspiel proportional to the wavelengths?
As you might already know, frequency of musical notes is arranged in a such a way that if, for example, an A note has frequency of $x$, another A note which is placed one octave higher would produce frequency of $2x$.
So here's my childhood toy…
Moctava Farzán
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How can transverse waves on a string carry longitudinal momentum?
In general, if a wave carries energy density $u$ with velocity $v$, it also carries momentum density $u/v$. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves.
However, I'm having trouble seeing how the momentum…
knzhou
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Why does the curve of a hanging chain not minimize the area below it?
If we have a chain of fixed length hanging from two points we know that it will form a curve that minimizes the chain's potential energy.
If we imagine the chain as having many small segments, then the potential energy of each segment is $E_p =…
jan
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Why is the stress on a body not a vector?
In my textbook, Physics, Part II—Textbook for Class XI, there's a line which talks about why stress is not a vector:
Stress is not a vector quantity since, unlike a force, stress cannot be assigned a specific direction. Force acting on the portion…
archie
- 395
21
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4 answers
Why can't a piece of paper (of non-zero thickness) be folded more than $N$ times?
Updated:
In order to fold anything in half, it must be $\pi$ times longer than its thickness, and that depending on how something is folded, the amount its length decreases with each fold differs. – Britney Gallivan, the person who determined that…
iamsid
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8 answers
Shape of a rotating rope with one free-end
One end of a uniform rope (with total mass $M$) is fixed on the edge of a cylinder. The cylinder has a radius $R$ and rotates with angular velocity $\omega$. The axis is vertical in a gravitational field. Air drag is neglected. What is the shape of…
shinotakatoshi
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19
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1 answer
Bell-curve formed by sliding paper
If you take a piece of paper, keep a finger on its edges and slide both the edges towards the centre, the shape that the side facing you makes looks kind of like a bell-curve. Is it possible to prove that it actually is a bell-curve? If it isn't is…
Supernerd411
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19
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4 answers
Conservation Vs Non-conservation Forms of conservation Equations
I understand mathematically how one can obtain the conservation equations in both the conservative
$${\partial\rho\over\partial t}+\nabla\cdot(\rho \textbf{u})=0$$
$${\partial\rho{\textbf{u}}\over\partial t}+\nabla\cdot(\rho…
user2536125
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In wave motion of a string both kinetic energy and potential energy are minimum at $y=y_\text{max}$ then why does the string come down again?
In wave motion of a string both kinetic energy and potential energy are minimum at $y=y_\text{max}$ then why does the string come down again?
As everything in nature tries to attain the lowest energy possible, what brings that string element back to…
mathemather
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Similarity between Schrodinger and Euler-Bernoulli equations - any possible physical meaning?
I noticed a long time ago the similarity between Schrodinger equation and Euler-Bernoulli beam equation. Namely, Euler-Bernoulli equation is equivalent to the system of Schrodinger equation for a free particle and its complex…
Yuriy S
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15
votes
3 answers
Continuum limit for solid mechanics
Is there a rigorous derivation of the limits for continuum properties in solid mechanics? For instance, the stress-strain relationship may be linear for large samples (the slope being the Young's Modulus) but at what limit does that break down?…
tpg2114
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Why is the (non-relativistic) stress tensor linear and symmetric?
From Wikipedia:
"[...] the stress vector $T$ across a surface will always be a linear function of the surface's normal vector $n$, the unit-length vector that is perpendicular to it. [...] The linear relation between $T$ and $n$ follows from the…
R S
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15
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Rotate a long bar in space and get close to (or even beyond) the speed of light $c$
Imagine a bar
spinning like a helicopter propeller,
At $\omega$ rad/s because the extremes of the bar goes at speed
$$V = \omega * r$$
then we can reach near $c$ (speed of light)
applying some finite amount of energy
just doing
$$\omega = V /…
Hernan Eche
15
votes
2 answers
How can I adapt classical continuum mechanics equations in order to agree with general relativity?
I come from a continuum mechanics background, and I make numerical simulations of fluids/solids using the Finite Element Method. The basic equation we solve then is Newton's law of motion, written in terms of relevant vectors and tensors. Using a…
BrouH
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