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,
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Chapter 2, Problem 15E

The boundary-value problem for a cantilevered beam can be written as

d 4 w d x 4 p ( x ) = 0 , 0 x 1 w ( 0 ) = d w d x ( 0 ) = 0 , d 2 w d x 2 ( 1 ) = 1 , d 3 w d x 3 ( 1 ) = 1

Assume p ( x ) = x . Assuming the approximate deflection in the form of w ˜ ( x ) = c 1 ϕ 1 ( x ) + c 2 ϕ 2 ( x ) = c 1 x 2 + c 2 x 3 . Solve for the boundary-value problem using the Galerkin method. Compare the approximate solution to the exact solution by plotting the solutions on a graph.

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