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Briefly describe the importance of shape functions. If a truss element has the end node displacements...
answer it or leave it for another expert 2 LI2 A three-node bar element shown below...
answer it or leave it for another expert
2 LI2 A three-node bar element shown below is uniform and is allowed only axial displacement u. Its degrees of freedoms are us, U and us The shape functions for this bar are given by 2x-1x N L-31x+2x and N 4(Lx-x b.Using the properties of shape a function, determine which of the above shape functions are N, N2 and Na
2 LI2
A three-node bar element shown below is uniform and is...
Finite Element Method 5.17 Displacements of the three-member truss shown are confined to the plane of...
Finite Element Method
5.17 Displacements of the three-member truss shown are confined to the plane of the figure, and points 1, 2 and 3 are fixed to the stationary rim. All members have the same A, E, and L a) Obtain the 2x2 stiffness matrix that operates on the horizontal and vertical degrees of freedom of the central node. b) Obtain the corresponding global force vector c) Solve for the displacements and for axial stress in member (2-4), when the...
Problem 2 (3 points) 1m 1m For the planar truss below, determine the nodal oay displacements in t...
Problem 2 (3 points) 1m 1m For the planar truss below, determine the nodal oay displacements in the Global Coordinate system using the finite element direct method Global y Node 2 Node 1 Global x Element 1Element 2 2m Assume all the truss members are of the same Young's modulus E-65x 109 Nm. Element 1 and element 2 have the same cross-sectional area of 0.01 m and the cross-sectional area of element 3 is 0.02 m2. Do not rename the...
)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...
)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...
Solve the following truss problem. All truss members are ANSI 2x2x0.25 hollow square tubes (with rounded...
Solve the following truss problem. All truss members are ANSI 2x2x0.25 hollow square tubes (with rounded corners) for which the cross-section area is A-1.5891 in2. The material has a modulus of E-29E6 psi. Length of element 1 and 5 is L-20 inches, and length of element 3 and 6 is 2L 40 inches. 7 5 6 P-1000 lb 2. 1. Solve in an Excel spreadsheet using the truss element. Note that there are only four different element stiffness matrices (look...
finaite element 3. Consider the beam-bending problem shown below. Using one element and assuming that the...
finaite element
3. Consider the beam-bending problem shown below. Using one element and assuming that the beam length is , modulus of elasticity E, area A, and moment of inertial: a) Solve for unknown displacements. b) Find the displacement at x = 1/2 4. For problem 3 above assume that these is no truss axial effect or D.O.F Compute components of the element stiffness matrix using shape functions. K22 k23 k24 k33 k34 K44
Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry...
Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3 marks) (b) Imman F FIGURE Q2b: 3 Springs (0) Derive an expression for the Total Potential Energy of the structure shown above in Q2b. (5 marks) (1) Apply the minimum potential energy method to derive the...
1. Find displacements at each node and forces in each element for the series of spring...
1. Find displacements at each node and forces in each element for the series of spring shown below. (20 points) 3 4 3 100 K k1 k4 u2 k3 из U4 k1 50 k/in k2- 20 k/in k3-40 k/in k4-50 k/in 2. For the following truss structure, all the members has the same elastic modulus E and cross section area A. (10 points) 2 4000 lb 10.000 lb 3 3 4 30 in. 30 in. 30 in Find the structural...
finite elemtns 1. Consider the element and the coordinate systems x and y in centimeters shown...
finite elemtns
1. Consider the element and the coordinate systems x and y in centimeters shown in figure below 1(0,0), 3(15,0), M(15,10), N(0,10) cm for coordinates. Unity Umx=Umy=-3 cm Unx=Uny=0 cm Dix-Diy= 0, Uje – Ujya 0.1 cm Umy Um U hu U iy U: Uix JY U; a) Compute the finite element shape (interpolation) functions values at x=y=5 cm using natural coordinate system. b) Verify that the shape functions obtained satisfy all the three Lagrangian properties.
For the 3-D indeterminate (4-member) TRUSS structure shown in Figure 2A. Given that Px 10K (in...
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...
answer it or leave it for another expert
2 LI2 A three-node bar element shown below is uniform and is allowed only axial displacement u. Its degrees of freedoms are us, U and us The shape functions for this bar are given by 2x-1x N L-31x+2x and N 4(Lx-x b.Using the properties of shape a function, determine which of the above shape functions are N, N2 and Na
2 LI2
A three-node bar element shown below is uniform and is...
Finite Element Method
5.17 Displacements of the three-member truss shown are confined to the plane of the figure, and points 1, 2 and 3 are fixed to the stationary rim. All members have the same A, E, and L a) Obtain the 2x2 stiffness matrix that operates on the horizontal and vertical degrees of freedom of the central node. b) Obtain the corresponding global force vector c) Solve for the displacements and for axial stress in member (2-4), when the...
Problem 2 (3 points) 1m 1m For the planar truss below, determine the nodal oay displacements in the Global Coordinate system using the finite element direct method Global y Node 2 Node 1 Global x Element 1Element 2 2m Assume all the truss members are of the same Young's modulus E-65x 109 Nm. Element 1 and element 2 have the same cross-sectional area of 0.01 m and the cross-sectional area of element 3 is 0.02 m2. Do not rename the...
)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...
Solve the following truss problem. All truss members are ANSI 2x2x0.25 hollow square tubes (with rounded corners) for which the cross-section area is A-1.5891 in2. The material has a modulus of E-29E6 psi. Length of element 1 and 5 is L-20 inches, and length of element 3 and 6 is 2L 40 inches. 7 5 6 P-1000 lb 2. 1. Solve in an Excel spreadsheet using the truss element. Note that there are only four different element stiffness matrices (look...
finaite element
3. Consider the beam-bending problem shown below. Using one element and assuming that the beam length is , modulus of elasticity E, area A, and moment of inertial: a) Solve for unknown displacements. b) Find the displacement at x = 1/2 4. For problem 3 above assume that these is no truss axial effect or D.O.F Compute components of the element stiffness matrix using shape functions. K22 k23 k24 k33 k34 K44
Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3 marks) (b) Imman F FIGURE Q2b: 3 Springs (0) Derive an expression for the Total Potential Energy of the structure shown above in Q2b. (5 marks) (1) Apply the minimum potential energy method to derive the...
1. Find displacements at each node and forces in each element for the series of spring shown below. (20 points) 3 4 3 100 K k1 k4 u2 k3 из U4 k1 50 k/in k2- 20 k/in k3-40 k/in k4-50 k/in 2. For the following truss structure, all the members has the same elastic modulus E and cross section area A. (10 points) 2 4000 lb 10.000 lb 3 3 4 30 in. 30 in. 30 in Find the structural...
finite elemtns
1. Consider the element and the coordinate systems x and y in centimeters shown in figure below 1(0,0), 3(15,0), M(15,10), N(0,10) cm for coordinates. Unity Umx=Umy=-3 cm Unx=Uny=0 cm Dix-Diy= 0, Uje – Ujya 0.1 cm Umy Um U hu U iy U: Uix JY U; a) Compute the finite element shape (interpolation) functions values at x=y=5 cm using natural coordinate system. b) Verify that the shape functions obtained satisfy all the three Lagrangian properties.
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...
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