Deformation Definition and 207 Threads

Hi, I have two topics: 1) Suppose a propeller is spinning very fast (say it's in a vacuum, no drag) and we arbitrarily lengthen its blades. Eventually the velocity of the tips of the propeller will approach the speed of light. That should be a speed limit, but that implies that the blades of...

From Stress-Strain curves in static loading conditions, we know the stress in force/cross-sectional area that's needed to deform a material. So with a bigger specimen, there's also a bigger cross-sectional area so you need a bigger force to generate the necessary stress. This same concept should...

A cylindrical bag is made from a freely deformable fabric, impermeable for air, which has surface mass density σ; its perimeter L is much less than its length ##l##. If this bag is filled with air, it resembles a sausage. The bag is laid on a horizontal smooth floor (coefficient of friction µ =...

A solid ball of radius R, density ρ, and Young’s modulus Y rests on a hard table. Because of its weight, it deforms slightly, so that the area in contact with the table is a circle of radius r. Estimate r, assuming that it is much smaller than R. I have no issues understanding the...

Was surprised by a study recently where we tested 6 samples for pull-off force at a 10% reduction in clamp Torque and noticed negligible shift in results. Is it possible that at higher torque the clamp is deforming the pipe, reducing the surface contact (friction) between the hose and pipe? The...

Hi, i'm struggling with that problem , i need to find the distance that point N went down.My way of thinking is that the structure is twice not statically determined because of the beam MN and beacuse of the left support which is also unnecessary in order for equilibrium. My 2 equations of...

Summary:: Calculate the deformation on a rod/axle/pipe due to a distributed load. I’m manually trying to calculate the deformation on a rod/axle/pipe due to a distributed load. The rod has an outer diameter of 62mm and an inner diameter of 50, is 170mm long, made from a material with an...

hi guys I have read the other day about how the nuclear quadruple moment descries the deformation of the nucleus, however i can't get my head around how is that!, I am familiar with the multiple expansion in which we can describe the potential of an arbitrary charge distribution by the following...

Sum of forces in the y-direction = 0 and downwards is +ve P + Fab,y = 0 P + Fab (4/5) = 0 Fab = -1.25P ẟ = FL/AE -> ẟab = FabLab/AabE ẟab = (-1.25P*.75)/(pi*(.01)^2*(200*10^3)) = -0.0149P After this step, I am uncertain of how I can relate the vertical elongation with AB's elongation to find...

In the initial position the spring is previously compressed, then the block adds a force, and the spring is again deformed. I think the energy balance is incorrect; the potential energy of the spring is repeated.

What's the derivative of deformation gradient F w.r.t cauchy green tensor C, where C=F'F and ' denotes the transpose?

I'm doing static analysis. I have already set up all the prerequisites, preprocessors such as material addition, sectioning, defining boundary conditions, and displacement. However, I'm not getting the results. Please suggest anything. Kindly find the attachment. regards

In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows: ## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ## and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e. ##...

a)plastic deformation because of permanent deformation b) the other parts that have been destroyed have stored the energy and this saved the passenger compartment. C) the alloy crash barrier is stronger than the car body and and saves more of the energy by deforming shape. I'm not sure about my...

While introducing tensile stress, we're shown a bar fixed at a support being subjected to a force in the axial direction at the opposite end. Then, since the bar is in translational equilibrium, we say that internal forces must balance it out, and this internal resistance per unit area is known...

I would assume that because the samples are made of the same material they would fail at the same stress and so the same strain. However, the data shows that the sample with a greater cross-sectional area fails at a greater strain, and the two are roughly proportional. Does anyone know what...

My guess is that the deformation immediately before would be the sum of elastic and plastic deformation, and the deformation after would be just the plastic deformation, and it therefore would decrease. Is this correct?

Hi. Say you apply a moment on a beam and bend it into an arch. If you take a free body diagram of a section of the beam you would need normal stresses in the radial direction to balance the forces: I have never seen this brought up before though -- is it correct logic? Also, is this sort of...

Hello everyone, in one of my projects I am dealing with the following problem: We have a tank filled of water. If we assumed that a focused ultrasond beam hit the water perpendicularly to the surface. How can I calculate the displacement of the water surface? In particular, I am interested in...

Disclaimer: I am a physics student and I have very little knowledge of topology or differential geometry. I don't necessarily expect a complete answer to this question, but I haven't really found any reference that approaches what I'm trying to ask, so I'd be quite happy to simply be pointed in...

Hello! I am confused about the definition of the quadrupole moment in nuclei. One definition I found, in Wong, says that the quadrupole moment of a nucleus is given (ignoring some numerical constant) by: $$<J,M=J|r^2Y_{20}|J,M=J>$$ so the expectation value of a second order spherical harmonic...

Question is extracted from "Ellad B Tadmor, Ronald E Miller, Ryan S Elliott - Continuum mechanics and thermodynamics From fundamental concepts to governing equations". I just got stuck at part (a). I think if part(a) is solved, I may be able to do the other parts.

Hello: I am looking for a formula that can help me determine the collapse and deformation strengths of plastic tubing. I have been scouring the internet for this information and i have yet to find a satsifactory formula. I have found a formula that seems pretty wide spread ~ however it gives me...

I wrote Newton's equations for the block seen from the non inertial frame. The axis are inclined. ##x) Fe+W_x-f*cos(\alpha)=0## ##y) N-f*sin(\alpha)-W_y=0## Where ##f*## is the pseudo-force and ##Fe## is the elastic force. I set the acceleration as 0 because they are in equilibrium. The thing...

Hello all, I hope this post is in the appropriate thread. Would anyone have any insight on a method to quantify deformation of a shape? For example, I attached two images of a white shape of interest at the center (one deformed and one undeformed). I'm trying to develop a metric/parameter...

Hey guys, so I have to give a 10 minute presentation for my class. I am absolutely terrible at memorizing stuff. Its pretty bad. If I can find an interesting or cool topic I would be able to remember material better. It needs to be about deformation or fracture of a material in terms of micro...

This is highly speculative, and I very much doubt that it is actually correct. If anybody knows of a correct equation for time-dependent axial deformation, or at least how to go about deriving a more correct equation, I would greatly appreciate any feedback.

Summary: In terms of stress, strain & deformation, what is better for a given component. 1) low stress or high stress 2) less strain or large strain 3) less deformation or large deformation? Some dimensional changes were made in an existing component to study how these changes effect the...

This question is about 2-d surfaces embedded inR3It's easy to find information on how the metric tensor changes when $$x_{\mu}\rightarrow x_{\mu}+\varepsilon\xi(x)$$ So, what about the variation of the second fundamental form, the Gauss and the mean curvature? how they change? I found some...

Could I please get a hint on how I should start this question/how I should parameterize these variables? I'm going to head to sleep as I am from the eastern time zone. I apologize ahead of time for my delayed reply.

Hi, Starting with an example to clarify what I am looking for. Assume an extension force applied on a distance from the centroid/neutral axis of a body: see attached, please. As result, bending force besides the tensile force will be generated in that body as presented in section A-A in the...

If we have two points P and Q in undeformed material and after deformation they become P' and Q'. The deformation tensor is the derivative of the displacement. What is the displacement? vector PP'? or the change from PQ to P'Q'? is the second question is the strain "change in length". Why the...

Consider a spring balance with no initial deflection. Let an object of mass 'm' be attached to it. We allow the spring to come into equlibrium, and 'd' is the deflection at this eqb position. We add another object of mass 'M', while m is also present, so that the final position is x, and hence...

Homework Statement An elastic membrane in the x1x2-plane with boundary circle x1^2 + x2^2 = 1 is stretched so that point P(x1,x2) goes over into point Q(y1,y2) such that y = Ax with A = 3/2* [2 1 ; 1 2] find the principal directions and the corresponding factors of extension or contraction of...

Homework Statement Stretch forming[/B] A 38.1 cm-long sheet with a cross sectional area of 3.2258 cm2 is stretched with a force, F, until alpha = 0.35 rad. The tip of the force is fixed to the strip by some means, thus maintaining the lateral position of the force. (The left portion of the...

Hello! I read from ansys element reference that for solid 65 the key option (1) is used to include or suppress extra deformation shapes. I would like to ask what extra deformation shape mean.

If a gravitational wave passes an elastic body it will be deformed. The source of the work done on it comes from the energy of the gravitational wave. In curved spacetime e.g. an accelerated expanding FRW- or static Schwarzschild-spacetime an elastic body will be deformed too. What is the...

I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?

Let us look at short segment of a rod with its length dx. Due to longitudinal wave, left endpoint moves for s in the direction of x-axis and the right endpoint moves in the same direction for s+ds. Because I want to calculate the elastic energy of the wave motion, I need the extension of dx so...

Homework Statement Homework Equations deformation=(force*length)/(elastic moduli*area) The Attempt at a Solution and since most of the variable are constants it seemed like a simple plug in problem, however it seems that my use of the forces is incorrect. unfortunately we had no examples...

In this video, a man applies an angular acceleration to the base of a rod. While the rod rotates, it bends. Why? What force is there that causes the bending, aside from rod's own weight? It seems to me to be the work of a fictitious inertial force. I was always taught that those forces don't...

Hi initially I am aware that large deformation in solid mechanics requires non linear strain theory in the lieu of infinitesmall strain theory. But I wonder that if we can approximate large deformation of material using infinitesmall strain of small elements employing and summing linear strains...

Hello, I have a fairly simple question but I guess I am having a hard time trying to understand it. I have a plastic connection of two different geometries (see attachment). When I hold end of the front portion (of the uniform diameter) and apply torque at the bigger cylinder geometry, there...

Is there any relation between power law exponent of of P-h curve and strain hardening exponent of stress-strain curve?

I have a problem to do with my project in college. I'm creating a hanging fire pit, basically made of 3 lengths of square steel bar connected to a plate at the top and on hinges. The 3 legs of the frame move in slots and when in the open position would be at 45 degrees. The actual fire pit is...

Homework Statement The 40 ft long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap in inches so that the rails just touch one another when the temperature is increased from -20 F to 90 F. The cross sectional...

Homework Statement Refer to image attached. Lets say I have a deformable solid that is being accelerated by a force that is equally distributed along the back face of the Main Body that is drawn in the picture. Attached to this Main Body is a Wing. At high accelerations, there will be inertial...

Hi everyone, i am currently doing a rotor analysis with "modal analysis" on Ansys and even though my rotor's specs are L=145mm D=10mm and the rotating velocity is 10000rpm i get a deformation of 100mm at most of the modes. I have read that this might be cause of a mass-normalized value but i am...

Hi all, I have a doubt that I would like to solve with oyu help. Basically I want to calculate forces on a solenoid due to the magnetic field it produces and than calculate deformation. I consider 2 cases: 1/ Static I did analytic calculation for force calculation, and i made FEM simulation...

As I understand it, in order to compute a contour integral one can deform the contour of integration, such that it doesn't pass through any poles of the integrand, and the result is identical to that found using the original contour of integration considered. However, I have seen applications...