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 8E
To determine
Theunknown coefficients for the given differential equation using Galerkin’s method
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Find the solution set of each of the following
equation/inequality.
+18
4
2(x-1)
5
VI
8-3x
20
Consider the following vectors:
• F = 10 @ 0°
• G = 5 @ 180°
What is the solution to F+G?
O -10 @ 0°
10
5 @ 180°
7.5 @ 45°
O 10 @ 0°
-15
5 @ 0°
-5
O 15
O -10
Question (4): Let f(x) = 2x2 +1. Use the limit definition of the derivative to find f'(x).
(3 Marks)
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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- find a real general solution: * y + 4y' + 5y =x +2arrow_forward- The projection of the vector i+3j+7k on the vector 2î + 6j+3k is: a: 41 41 b: 7V59 41 c: V59 d: 4arrow_forwardConsider the following vectors: • F= 10 @ 0° • H=7 @ 90° What is the solution to F+H? 12.21 @ 34.99° 17.00 @ 45.00° 10 70 @ 45.00° O 12.21 @ 0.6107° 7 34.99 @ 191.4° 10 @ -11.72° O 12.21 O 70 O -5 @ 135.6° 10 @ 34.99° 7 @ 34.99°arrow_forward
- The general solution of the differential equation tan(0) y" +y' = sec(0) is:arrow_forwardConsider the following vector: • J= 17 @ 195° What is the x component of J? 17 @ 195° 16.42 @ 90° 17 @ 15° O 17 @ 180° (10, 16.42) O -16.42 @ 180° (0,17) 16.42 @ 180° 16.42 @ 0° 16.42 @ 195° 16.42 @ 15° O (17,0)arrow_forwardUsing an appropriate method, find the general solution for the following differential equation, dy +2= cos 2x . dxarrow_forward
- Question no 3: let f(x) = v1 + ax² in the interval [1, 4] with n=6 and a= (last three digits in the form 0.88) 4 X 1 f(x) Evaluate the integral of f (x) using trapezoidal and Simpson's rule Answer:arrow_forwardDetermine if the infinite series is convergent or divergent. n+1 n =0 n+3arrow_forwardConsider the following. y = x2 y= 12 - x 16 14 12 10 8 10 12 Find the area of the region by integrating with respect to x. (b) Find the area of the region by integrating with respect to y.arrow_forward
- Let f be any non-zero real valued function in x and y and R be a closed bounded region above the x-axis. Then the double integral of f over R is always positive * False Truearrow_forwardThe direction of the resultant approximately is * For the figure below, the resultant is.: * -42 CSumFy: * -20 20 N 75 N 35 165.22 N 45° -45 220.12 N 50 N 150 N 20 156.3 N 42 161.65 N 80 N -35 45 160 N 200 N Other: -134.45 N 242.17 N 300.15 N 170 N 325.25 N CSumFx= * 350,54 N 170. 56 N 150.32 N 210.76 N Other: -120.16 N 198.34 N -180.33 N -160.54 N O O OOOOarrow_forwardQ1: * Q1 Calculate The Inverse Of The Matrix: [4 A= 2 -2 11 4 4 3 1 Add file Q2: * Using Green's theorem, evaluate the line integral (y- a)dr- (x +y°)dy, where the contour C encloses the sector of the circle with radius a lying in the first quadrant 0 = 1/2 R >-0 aarrow_forward
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