Deformation Definition and 207 Threads

Dear all, I have a 3D cube with a nonuniform distribution of temperature. In order to calculate the deformation of the cube using the finite element method, we need nodal forces. How we calculate the nodal force from the temperature distribution? I am aware of a the method based on the...

Hello, I have difficulty interpreting the following fact (I'm reading Cotinuum Mechanics by Spencer). The relative velocity between two nearby points P and Q in the current configuarion is given by: dv_i=D_{ik}dx_k + W_{ik}dx_k where D_{ik}=\frac{d}{dt}e_{ik} is the rate of deformation tensor...

---Quote--- *1. Homework Statement * http://postimg.org/image/yrbu7a0vb/ *2. Homework Equations * e(elongation of a member) = (Force * Length)/(Area * Young's Modulus) *3. The Attempt at a Solution * Is the force P distributed so that the force on each bar is P/3 so that F2...

Dear, I have a task to model the behaviour of certain interphase material. Let's say that functions which describe the change of material parameters are known. i.g. change of the Young's modulus as function of distance from neighbouring material (or (0,0) origin) - PAR=PAR(x)...

Homework Statement Use the principle of deformation of path to deduce \int_0^\infty t^n \textbf{cos}(bt) e^{-at}dt=\frac{n!}{e^{n+1}}\textbf{cos}((n+1)\phi) and \int_0^\infty t^n \textbf{sin}(bt) e^{-at}dt=\frac{n!}{e^{n+1}}\textbf{sin}((n+1)\phi) where a>0, b>0, c=\sqrt{a^2+b^2}, and...

For this problem, my thinking was that since the top of the rod is fixed, then the only part that is elongating is the bottom, so I found the part elongating at AB and said that was the total elongation. I am not sure if this reasoning is sound. I suppose the other possibility would be to add up...

In the tensile test practical for ductile materials, up to the elastic limit, the deformation is recoverable (no line defects). My question is can there be a reduction of area with the elastic deformation? If yes, how it happens? I'm a beginner. Thank you!

Homework Statement A .1in aluminum wire is being pulled from a coil between 2 1in steel rollers. One roller is fixed to the driving motor while the other roller is loaded with a force to provide traction. What is the maximum force that can be applied before the wire is plastically deformed by...

Hi everyone, For current project at work I am looking into possibility of simulating deformation from impact with static force. Here is the input data: A ball of 0.5 kg at speed of 25 km/h crashes into a damping foam which is placed on a rigid wall. Stopping (deformation) distance in the foam...

If a car with no acceleration, only velocity, hits my spring with a spring constant K What will be the deformation in string? How do I calculate the force from impact while acceleration is equal to 0?

For the deformation field given by $$ x_1 = X_1 + \alpha X_2,\quad x_2 = X_2 - \alpha X_1,\quad x_3 = X_3 $$ where ##\alpha## is a constant, determine the matrix form of the tensors ##\mathbf{E}## and ##\mathbf{e}##, and show that the circle of particles ##X_1^2+ X_2^2 = 1## deforms...

A linear elastic strip of natural length a and stiffness k lies between x = 0 and x = a. Each point on the strip is transformed by a differentiable, monotone increasing function f. a) Characterise the change in potential energy. b) Given the boundary conditions f(0) = 0 and f(a) = b, choose f...

Homework Statement I have this question. I need to know the diformation in P direction. Here is the question I use the symmetry and finally with a 1/4 modell I get the following: which is correct according to the instruction. K is the stiffness of the spring. which with symmetry becomes...

Homework Statement What do you understand by the following terms; (i) principal stretch (ii) an anisotropic material (iii) a dilatant deformation, (iv) a Lagrangian description of a deformation, and (v) a pure deformation. Homework Equations Am just trying to find descriptions for...

Could someone please show me how to calculate the deformation of a pad (ideal material with the same elasticity at all directions) under a cylinder ? Thank you very much.

fluid mechanics: defition of "shear flow" [rate of deformation tensor] I'm studying old undergraduate chemical engineering notes for an exam in grad school. Can't recall what this really means, can anyone explain to me what "off-diagonal elements" means and why the trig function velocities...

Hi all, I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor). I have attached the specifics of the question in a attached photo. Ultimately, there comes a point...

I am trying to do a problem on Material Non-linearity , to model steel for large deformation , beyond yield point , I have tensile testing data for the steel ( in form of Engineering stress vs Engineering strain). for defining the model , I chose Multilinear Isotropic hardening now there...

Homework Statement Hello guys! Now this is not a homework question, but it may sound like one. If a uniform sized and massed sphere was spinning in space away from any source of forces that could affect it, wouldn't the only forces that act on it are the centripetal and centrifugal? And if this...

Homework Statement Hello guys! Now this is not a homework question, but it may sound like one. If a uniform sized and massed sphere was spinning in space away from any source of forces that could affect it, wouldn't the only forces that act on it are the centripetal and centrifugal? And if...

I am posting this from a friend's account since I've been unable to register for a while. Brace yourselves for this is going to be a long post. ----------------------- TLDR: I am trying to figure out the reason for AlSi's lower than expected from atomic misfit solid solution hardening...

Hi all, I have a question regarding deformation analysis. For materials with non-zero Poisson's ration, when is it justified to use plane strain analysis rather than three-dimensional? Perhaps one case is when we are going to analyze a thin sheet. Are there other cases too? Thanks, Hassan

Hello, When we use slope deflection method in frames we neglect axial deformation in order to get the same delta when the frame is sway,(that what i understood) So i have two questions 1. Neglecting axial deformation means ignoring axial force??Or what?? 2. How to neglect axial...

I'm trying to give an answer to the following problem, I hope someone could come in help! Consider a smooth n-dimensional manifold M with smooth (nonempty) boundary \partial M, and suppose given a function f: M\setminus \partial M \to \mathbb{R} (which one can assume to be differentiable)...

Hello Forum, I was reading a book about the physics of sports. It talks about karate and deformation energy that gets transferred to a target when a punch hits it... The formula for the deformation energy contains the coefficient of restitution and say that a small coefficient belongs to...

Let RP2 denote the real projective plane (it can be obtained from glueing a Mobius band and a disk whose boundary is the same as the boundary of the Mobius band). I know if one punches a hole off RP2 then the punched RP2 is homotopy equivalent to a Mobius band which is in turn deformable to a...

Structural Analysis-"small deformation" Hi all, Assume a cantilever beam fixed to a wall. We let the beam bend under its own weight. In practice the bending could be significant and as the bar bends, the distance between the tip of the bar and the wall decreases. Now my question are...

For a day and a half now we have been trying to calculate a self-assigned problem. However, this has not turned out to be easy and build-up frustration has lead us to this forum. Our challenge was to calculate what under pressure a food packing company needs in it's jars to make sure the lid...

Imagine a circle lying on xy plane and initially at rest w.r.t. frame S. Then S' comes and gets the circle and moves it with velocity v along x axis. The radius which is along x axis,should be contracted but not other radii and this means that the circle becomes an ellipse and because its sth...

Hello, I was wondering if anyone can help me with my FEA approach. I want to check that my boundary conditions for a simple quarter torus (representing a section of a helical spring) are correct. I'm neglecting the helical angle at this stage. I have fixed one end in all axes, and applied...

I have a little question about waves. Waves deform its medium elastically. For example: sound waves will propagtae through air because of local compression and decompression of the air. Is it possible for a material to get ductile deformation by means of a wave. Can I deform a material...

Dear all, I am Levy , I am glade to take part into physics Forums, I hope I can share my know with everybody and study from you, Thank You! I test the PET of creep deformation recent days, who has some reference about this aspect. Thank you

I do not really understand this as you can probably tell, but What is the difference bewteen Linear and Cubic displacement deformation functions in beam bending? For example why would one be used over another to model or calculate beam bending? or how does either type effect what bending...

Homework Statement Compute the angle of twist of the free end relative to the fixed end of the steel bar: 200 N*m, 80 x 10^9 GPa (shear modulus of elasticity) (Length 1: 1.2 m, dia of .040 m on left, length of .4 m dia of .020 m, on right) Homework Equations angle =...

Hi, I got confused thinking about cause and effect. If force is applied to a car due to collision, it deforms car. The longer is the time of a collision, the smaller is average force applied. Longer time is achieved by crumple zone deformation, which is affected by force. I find here circular...

I am not sure which formula to apply, can anyone help me out? Homework Statement 28. A square copper bar experiences only elastic deformation if it is stressed less than 95MPa. To support a load of 1340kg without exceeding this stress, the minimum square cross-section ( i.e. width of one...

I understand the concept behind continuous deformations. Say we have two curves ζ1 and ζ2 from A to B on some domain D and say that Pdx + Qdy is closed. Say we can show n points A=c1,c2,...,cn=B and A=d1,d2,d3,...,dn=B, so that we can first say follow the curve ζ1 from A to c1 then over to...

I am a forensic engineer trying to find the solution to a physics / metallurgy problem. No one in my office seems to know how to approach the problem. I was hoping I could get an answer from the folks in the forum. Please help. A 440C steel ball having a diameter of 1.0” is propelled...

Homework Statement Force exerted on a car by a crash barrier as the barrier crushes is F=-(4.5+140s) kN where s is the distance in metres from the initial contact. If a car of mass 2000 kg is traveling at 100 km/h when it hits the barrier the barrier deformation required to bring the car to...

Homework Statement Homework Equations \delta = PL/AE The Attempt at a Solution As you can see I know that F_{cd} is related to F_{be} and a second relationship can be found by the geometry of the deformations. I end up with F_{cd} = 11.9^{kN} but the answer is supposed to be...

I don't really know why, but I'm having trouble actually building deformation retractions, although I understand the concepts behind homotopies, etc.For example, when constructing a deformation retraction for \mathbb{R}^n-\{0\} to S^{n-1}, I found that you could define the mapping F(x,t) =...

The deformation process involves different stages. I was wondering how do you call the process where the materials return to their orginial state? Just as given in the bold text. And, moreover, what is the formula which calculates the time it returns back to the orginal state for a random...

Homework Statement A soccer ball with radius R = 11 cm is inflated to a gauge pressure of 9×104 Pa. The ball is dropped onto and bounces elastically off of a hard smooth floor. Find approximate expressions for the surface area of the ball in contact with the floor, the amount of time the ball...

Hi! I'm working in a laboratory and been assigned to the task of verifying on of our machines calculations. The machine calculates the deformationenergy needed to test a sample that's been moulded in a brass form. Its this value I need to validate. The information I have at this point...

Hello, I am developing an analytical approach to determine the creep constants of a constitutive model for nickel-base superalloys. I require creep strain versus time data to valid my approach. I've searched through literature and have found very little usable data. I need creep...

Homework Statement A square plate of edge length L = 1 m, thickness t = 5 cm, is fixed on two edges. The other two edges are free. A load of F = 10 kN is applied at the corner opposite that where the fixed edges intersect. Use shell elements to compute the deflection at the loaded corner...

I have to calculate the elongation of a pencil under a load. I know I have to use deflection = PL/AE but since the pencil has 2 materials in it I have to modify that equation. I know that both materials extend by the same amount. Could anyone explain to me how to get that equation?

Homework Statement A cylindrical sample of soft tissue, with diameter = 8 mm, height = 6 mm, is firmly glued to two steel compression plates. Using axisymmetric elements, find the force needed to compress the sample by 0.5 mm. For the purpose of this problem you may assume that E = 1 kPa, ν =...

Hii all :smile: What is Fuzzy manifold ? and what is deformation ? thank u >>

deformation and forging! (URGENT!) A mechanical press is powered by a 22.4 kW motor and operates at 40 strokes per minute. It uses a flywheel, so that the rotational speed of the crankshaft does not vary appreciably during the stroke. (a) If the stroke length is 15.24 cm, what is the maximum...