A displacement field is given by u-0.01y2 in, v-0.03yz in, and w-0.01 x (4 + 6x2)...
The components of a velocity field are given by u = x + y, and v = xy3 + 81 and w = 0. Determine the location of the stagnation point (V = 0) in the flow field where y is positive
Q2 For the displacement field given below, obtain the strain energy and kinetic energy based on a plane stress problem. Ow(x, y,0) Ow(x, y, t) U(x,y,2,t) = u(x, y,t) - 2 12; V(x, y, 2, 1) = v(x,y,t) -2- 62; V(x,y,z, t) = w(x,y,t) дх
1). It is found that the displacements in a component are described by x} + v(x* – x3) VX, X2 XX3 u, (x), X2, X3) u, (x7, X2,x;) uz(X, X2, X3) = 2a where a and v are constants. Determine the strain components in the component. = a a 2). The strain tensor at a material point in a steel component is obtained from an FEA as -180 -242 0 E = -242 -3500 x 10-6 0 0 0 Assuming...
Q1. [15 Marks] The stress field in a thin flat structural member can be described by the following equations: Ox 20x + 30xy2 + 20y Oy = 30x2 – 50xy + 20 Txy = 20x – 100y? 02 = Txz = Tyz = 0 where (x, y, z) are in metres and the stress components are in MPa. a) Determine the body forces required to support the structural member in equilibrium; [2 marks] b) Draw a 2D stress element at...
The temperature field function is given by T(x, y) = 6x2 + 3y2 – 4xy – y – 3x Determine the minimum for the given temperature field with fminsearch. (Round the final answer to four decimal places.) The minimum for the given temperature field is___.
3. For the infinitesimal deformation defined by the following displacement field: u; = a*(X, + X3) Uz = a?(X2 + x3) Uz = -a(X,X2) a) Given that a is a small constant, find the normal strain at point (0.2.-1) along the 18:-1:43 direction b) Find the change in the right angle between infinitesimal material fibers at point (0.2.-1) lying along the directions (8:-1:43 and 4:4-7)
Let V be a vector space over a field F, and let U and W be finite dimensional subspaces of V. Consider the four subspaces X1 = U, X2 = W, X3 = U+W, X4 = UnW. Determine if dim X; <dim X, or dim X, dim X, or neither, must hold for every choice of i, j = 1,2,3,4. Prove your answers.
1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix), ) Is the state of stress a possible equilibrium stress field? Neglect body forces. 10 point 2. The assemblv shown in 1. Consider the following displacement field in an isotropic linearly elastic solid descri terms of the Young's modulus E and Poisson's ratio v: (a) Determine the stress tensor (matrix), )...
)Given a 4-node element in x-y plane as shown here: Node X 3 3 1 8 a) Using the shape functions in u-v plane, determine an expression for mapped points from u-v to x-y, i.e. x- x(u, v) and y -y(u, v), for points within the 4-node element in u-v plane. Then, determine value of x and y for a point with (u, v)-(0.3,0.3). (10 points) b) Determine the value of Jacobian matrix, [J], and its determinant for such mapping...
[1] In parallelogram WXYZ, if u joins X to Y and v joins X to W, which connection forms a vector equal to u + v? v + u? u-v? V-u? A. W to Y B. Y to W C. X to Z D. Z to X W z Y [2] A linear combination of vectors is given. Determine the resultant vector using the tip- to-tail method for adding vectors geometrically. (9,-6) + (-12, -1) - (3, -15) + 5(2,...