8.1. Figure P8.1 shows a four-node quadrilateral. The (x, y) coordinates of each node are given...
5.12 Figure (a) shows a four node quadrilateral Ω(e) in R2. Coordinates of the nodes are given. Figure (b) shows a map αξη) of Ω(e) in natural coordinate space ξη. (0,2) (2,2) (p. q) (0, 2) (0,0) (2,0) (0,0) (2,0) (a) e) in x, y space (b) Map Ω(En) of Ω(e) The coordinates of the nodes are also given in the two spaces in Figures (a) and (b) (a) Determine the equations describing the mapping of points in ry and...
4. A four-node quadrilateral element is defined as shown in the figure. a. Find the coordinates in the reference element corresponding to (x, y) = (0, 0.5). b. Calculate the Jacobian matrix as a function of s and t. c. Is the mapping valid? Explain your answer. у л +1 X
3. A two bar truss structure is shown in Figure 1. The coordinates of Points A, C and B are given by (0,0), (0, 10") and (10",0), respectively, in which the x-axis is from A to B and the y-axis is from A to C. Points A and C are fixed. The cross-sectional area of all members in inch?. A vertical point load, P, is applied at the tip of the structure, Point B. Based upon either the Principle of...
Under the standard (x, y)-coordinate system, a grid of points with integer coordinates is given in the picture below. Here, the bottom-left point is the origin (0, 0) and the topright point has coordinate (6, 3). The coordinates of the remaining points can easily be computed accordingly. 2 During the 74th Hunger Game, Katniss and Peeta are separated inside a grid maze. Katniss is currently at the point (0, 0) and Peeta is (badly injured) at the point (x, y)...
y(x,t) = (8.1 mm) sin[kx + (900 rad/s)t + 0] describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y = +2.6 mm and y = -2.6 mm? Number Units
)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...
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proportional to the distance from P to the origin and 8(o, 3,02 15 pts] (0, 1,0)-2/m3 from P to the origin and Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2...
3. Polar Coordinates. (a) Given a rectangular coordinate point (x, y), how do you compute the equivalent polar coordinates: (r, 0)? (b) Given a polar coordinate (r, o), how do you compute the equivalent rectangular coordinate: (x, y)? (c) Consider the drawing in Figure 1. Compute the coordinate of each small circle. (d) What if the circle is centered at the point (cx, cy) (and not the origin). How does the formula change?
In the figure, four point masses are placed as shown. The x and y coordinates of the center of mass are closest to Problem #16 3.0 m 2.0 m 4.0kg 2.0 3.0 m 8.0 kg 6,0 kg阜 3.0 2.0 m 2.0 kg 0 2.0 m 3.0 m A) (2.2 m, 2.6 m). B) (2.2 m, 2.7 m). C) (2.3 m, 2.6 m). D) (2.3 m, 2.7 m). E) (2.3 m, 2.8 m).
3. (2 Points) Let Q be the quadrilateral in the ry-plane with vertices (1, 0), (4,0), (0, 1), (0,4). Consider 1 dA I+y Deda (a) Evaluate the integral using the normal ry-coordinates. (b) Consider the change of coordinates r = u-uv and y= uv. What is the image of Q under this change of coordinates?bi (c) Calculate the integral using the change of coordinates from the previous part. Change of Variables When working integrals, it is wise to choose a...