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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Textbook Question

Chapter 2, Problem 24E

Consider the tapered bar in problem 17. Use the Rayleigh-Ritz method to solve the same problem. Assume the displacement in the form of u ( x ) = a 0 + a 1 x + a 2 x 2 . Compare the solutions for u ( x ) and P ( x ) with the exact solution given below by plotting them. u ( x ) = F x π E r ( 0 ) r ( x ) , P ( x ) = E A ( x ) d u d x = F

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Chapter 2, Problem 23E

Chapter 2, Problem 25E

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Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 = 19kN. a W1 L/2 W2 Multiple Choice Answers Multiple Choice Answer: Axial force at point A (kN, tension positive): a. 3.31 b. 31.97 c. 37.33 d. 31 Multiple Choice Answer: Displacement at point B (mm, positive to right): a. 0.0061 b. 0.0395 c. 0.0193 d. 0.0261 Axial force at point A (kN, tension positive): Displacement at point B (mm, positive to right): L/2 P1 P2 (type in your multiple choice answer, e.g. a, b, c or d) (type in your multiple choice answer, e.g. a, b, c or d)

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.

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. P4 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

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. 4E Ch. 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. 8E Ch. 2 - Solve the differential equation in problem 8 for...Ch. 2 - Prob. 10E

Ch. 2 - Prob. 11E Ch. 2 - Prob. 12E Ch. 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. 16E Ch. 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. 20E Ch. 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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Solution Summary: The author explains how to find displacement and axial force using the Rayleigh-Ritz method of given tapered bar system matrix of the given problem.

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