Introduction To Finite Element Analysis And Design
2nd Edition
ISBN: 9781119078722
Author: Kim, Nam H., Sankar, Bhavani V., KUMAR, Ashok V., Author.
Publisher: John Wiley & Sons,
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Chapter 2, Problem 25E
Consider the tapered bar in problem 21. Use the Rayleigh-Ritz method to solve the same problem. Assume the displacement in the form of
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A 50-mm diameter cylinder is made of a brass for which the stress-strain diagram is as shown. The angle of twist is 5° in a length L =
845 mm. The three points on the nonlinear stress-strain diagram used are (0, 0), (0.0015, 55 MPa), and (0.003, 80 MPa). By fitting the
polynomial T = A + By+ Cy2 through these points, the following approximate relation has been obtained.
T= 46.7 x 10y-6.67 × 10122
Determine the magnitude T of torque applied to the shaft using this relation and the two equations given below.
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Y =
Ty = 2π] ρ?τὰρ
7 (MPa)
100
80
60
40
20
0
0,001 0.002 0.003 Y
d = 50 mm
"K
The magnitude T of torque applied to the shaft is
KN-m.
A²
A 50-mm diameter cylinder is made of a brass for which the stress-strain diagram is as shown. The angle of twist is 5° in a length L =
725 mm. The three points on the nonlinear stress-strain diagram used are (0, 0), (0.0015, 55 MPa), and (0.003, 80 MPa). By fitting the
polynomial T = A + By + Cy² through these points, the following approximate relation has been obtained.
T= 46.7 × 10%y-6.67 × 1012/2
Determine the magnitude Tof torque applied to the shaft using this relation and the two equations given below.
Y
Ty
-
ρφ
T (MPa)
2π ζ ρ?τὰρ
100
80
60
40
20
0
0.001 0.002 0.003 Y
d = 50 mm
L
The magnitude T of torque applied to the shaft is
kN.m.
1) A cylindrical rod of constant shear modulus, G is of length L and located between z=0 and z=L. It has a polar moment of inertia given by J=(Jo)/(1-Z/L) and t=-sin(πZ/2L)where Jo is a constant.The boundary conditions are dΦ(o)/dz =0 AND Φ(L)=0
Find Φ(z) and graph (1/GJo)Φ(Z), and (1/GJo)(dΦ(Z)/dz) ?
Chapter 2 Solutions
Introduction To Finite Element Analysis And Design
Ch. 2 - Answer the following descriptive questions.
a....Ch. 2 - Use the Galerkin method to solve the following...Ch. 2 - Solve the differential equation in problem 2 using...Ch. 2 - Prob. 4ECh. 2 - Using the Galerkin method, solve the following...Ch. 2 - A one-dimensional heat conduction problem can be...Ch. 2 - Solve the one-dimensional heat conduction problem...Ch. 2 - Prob. 8ECh. 2 - Solve the differential equation in problem 8 for...Ch. 2 - Prob. 10E
Ch. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Using the Galerkin method, calculate the...Ch. 2 - The boundary-value problem for a clamped-clamped...Ch. 2 - The boundary-value problem for a cantilevered beam...Ch. 2 - Prob. 16ECh. 2 - Consider a finite element with three nodes, as...Ch. 2 - A vertical rod of elastic material is fixed at...Ch. 2 - A bar in the figure is under the uniformly...Ch. 2 - Prob. 20ECh. 2 - A tapered bar with circular cross section is fixed...Ch. 2 - The stepped bar shown in the figure is subjected...Ch. 2 - A bar shown in the figure is modeled using three...Ch. 2 - Consider the tapered bar in problem 17. Use the...Ch. 2 - Consider the tapered bar in problem 21. Use the...Ch. 2 - Consider the uniform bar in the figure. Axial load...Ch. 2 - Determine shape functions of a bar element shown...Ch. 2 - Consider a finite element with three nodes, as...
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