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4. A four-node quadrilateral element is defined as shown in the figure. a. Find the coordinates...
8.1. Figure P8.1 shows a four-node quadrilateral. The (x, y) coordinates of each node are given in the figure. The element displacement vector q is given as q = [0, 0, 0.20, 0, 0.15, 0.10, 0, 0.05]T Find the following: (a) The X-, y-coordinates of a point P whose location in the master element is given by 8 = 0.5 and n = 0.5 (b) The u, v displacements of the point P. 96 116,6) 95 (1,4) 97 94 A...
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...
)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...
Figures 1 (a) and (b) show a linear square plane stress element in st coordinates and its distorted form mapped into quadrilateral in x-y coordinates, respectively. Edge - 1 u (*3. y) (-1,1) 1 1 (1,1) Edge PNJA 5 -Edge s = 1 (XY) 2 (xz. Y2) 2 Edge 1 = -1 (-1,-1) (1, -1) (b) Figure 1 (a) Specify the interpolation functions for the four-node isoparametric quadrilateral element. (4 marks) (b) Discuss how the isoparametric formulation is applied into...
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in X-direction); Py none (in Y-direction); E 30,000 ksi; A 0.2 square inches. The nodal coordinates, the earth-quake displacement/settlement, and members' connectivity information are given aS Applied Load! Earth-Quake MEMBER #1 NODE # X node-i node-j 120.00" 160.00"| 80.00"| Px=-10 Kips none Py- none 120.00" 160.00"0.00"none 120.00"0.00" 0.00" none 0.00" 0.00"0.00" none 0.00" 0.00" 80.00" none none 2 none 4 4 none 4 +2.00" (in...
Finite Element Analysis CVE705 Stiffness Matrix Problem: An eight-node element assemblage shown is used in a finite element analysis. Calculate the diagonal element of the stiffness matrix corresponding to the degree of freedom U100 shown. Use a plane stress case E = 10,000 v = 0.3 t = 1.0 U100
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...
For the truss shown in the figure below, develop element stiffness matrices in the global co-ordinate system. AE 200 [MN] is the same for all members. Use the direct stiffness matrix method to: i. Establish all element stiffness matrices in global coordinates ii.Find the displacements in node 3 ii. Calculate the member stresses 4m 3m 20kN 2 2 Use HELM resources on Moodle to find required determinant and inverse matrix. Answer 9.6x103 [MPa] 0.24mmm u3-0.20mm 0.45mm 16x10-3 MPa σ2-3- 1...
Question 2: For the shaded area shown in the figure a. Find the coordinates of the centroid. b. Calculate the moment of inertia about y-axis. Y to h/2 1m * -- h” h/2 2m Hole * X X 1m 2m 3m 2m 1m 3m 2h/3 t X bh 36 h/3 + X
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...