Consider a velocity field given by: Axi 2 a) Find the strain rate and rotation rate...
Consider a two-dimensional ?ow with velocity
components
.Find expressions for the
vorticity and the strain rate tensor.
V1 = CT1, 12 = -CT2
4. Consider a viscoplastic stress versus strain rate relationship of the form ơi,-CijklDk1 where where λ and μ are constants. (a) Express σ as a function of λ and μ. (b) S (3A+ 2a) Dkk and σ;,-2μ0% where σ0 and Dij are the deviatoric how that ơi : parts of the Cauchy stress and rate of deformation tensors, respectively.
4. Consider a viscoplastic stress versus strain rate relationship of the form ơi,-CijklDk1 where where λ and μ are constants. (a)...
In some region of space, the electric field is given by E = Axi + By2j. Find the electric potential difference between points whose positions are (xi, yi) = (a, 0) and (xf, yf) = (0, b). The constants A, B, a, and b have the appropriate SI units. (Use the following as necessary: A, B, a, and b.)
Consider a steady, two-dimensional, incompressible flow field in the x-y plane. The linear strain rate in the x-direction is 1.8 s−1. Calculate the linear strain rate in the y-direction. The linear strain rate in the y-direction is
(30p) Consider a two-dimensional strain state defined by 612 = € and all normal strains zero. Write the strain and the stress tensors in this coordinate system (use Hooke's law). The shear modulus is G. Find the principal strains and the principal directions of strain. Write the stress and strain tensors in these principal directions. Are these also the principal directions of stress? You don't need to solve the eigenvalue problem for stress to answer this question. Find the effective...
Consider a steady, two-dimensional, incompressible flow field in the x-y plane. The linear strain rate in the x-direction is 1.65 s−1. Calculate the linear strain rate in the y-direction. The linear strain rate in the y-direction is s−1
IV Analysis 1. Given the rotation velocity of link 1, to obtain the velocity of link 2. (10 Marks) 3 P23 2 Pis
IV Analysis 1. Given the rotation velocity of link 1, to obtain the velocity of link 2. (10 Marks) 3 P23 2 Pis
3. (25pts) An idealized velocity field is given by the formula V = 4txi – 2t2 yj + 4xzk a) Is this flow steady or unsteady? b) Is this flow 1D, 2D or 3D? c) Compute the acceleration vector a = axi + ayj + a_k d) Compute the acceleration vector at (1,1,1)
1) What is the equation for the volumetric strain rate? (Hint: Uses dot product). incompressible flow be determined from the volumetric strain rate? Given the velocity field V= (u, v) (0.75+1.2x) +(2.25-1.2y ), determine if the flow is incompressible or compressible. (20 pts) How can 2) What is the equation for vorticity? (Hint: Uses cross product). How can irrotational flow be determined from vorticity? Given the velocity field V = (u, v) (0.75+ 1.2x)t+ (2.25 1.2y), determine if the flow...
6Show that the Eulerian strain rate is given by 147 and [see Eq. (3.5.10) for the definition of al e D. 3.5.3 Infinitesimal Rotation Tensor The displacement gradient tensor can be expressed as the sum of tensor and a skew symmetric tensor. We have of a symmetric where the symmetric part is similar to the infinitesimal strain tensor (and when l▽u| ~ |▽oul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor lelilt lh the...