Introduction To Finite Element Analysis And Design
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,
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 2, Problem 9E

Solve the differential equation in problem 8 for the following boundary conditions using the Galerkin method: u ( 0 ) = 1 , u ( 1 ) = 2 .

Assume the approximate solution as: u ˜ ( x ) = ϕ 0 ( x ) + c 1 ϕ ( x ) , where ϕ 0 ( x ) is a function that satisfies the essential boundary conditions, and ϕ 2 ( x ) is the weight function that satisfies the homogeneous part of the essential boundary conditions, that is. ϕ 1 ( 0 ) = ϕ 1 ( 1 ) = 0 . Hence, assume the functions as follows: ϕ 0 ( x ) = 1 + x , ϕ 1 ( x ) = x ( 1 x ) .

Compare the approximate solution with the exact solution by plotting their graphs. The exact solution can be derived as: u ( x ) = 2.9231 sin x + cos x x .

Blurred answer
Students have asked these similar questions
5.112 A mounting bracket for electronic components is formed from sheet metal with a uniform thickness. Locate the center of gravity of the bracket. 0.75 in. 3 in. ༧ Fig. P5.112 1.25 in. 0.75 in. y r = 0.625 in. 2.5 in. 1 in. 6 in. x
4-105. Replace the force system acting on the beam by an equivalent resultant force and couple moment at point B. A 30 in. 4 in. 12 in. 16 in. B 30% 3 in. 10 in. 250 lb 260 lb 13 5 12 300 lb
Sketch and Describe a hatch coaming and show how the hatch coamings are framed in to ships strucure?
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Thermodynamics: Maxwell relations proofs 1 (from ; Author: lseinjr1;https://www.youtube.com/watch?v=MNusZ2C3VFw;License: Standard Youtube License