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 28E

Consider a finite element with three nodes, as shown in the figure. When the solution is approximated using u ( x ) = N 1 ( x ) u 1 + N 2 ( x ) u 2 + N 3 ( x ) u 3 .

a. calculate the interpolation functions N 1 ( x ) , N 2 ( x ) , and N 3 ( x ) , if it is intended to obtain the displacement field in the following form: u ( x ) = c 0 + c 1 x + c 2 x ; and

b. when the nodal displacements are given as: u 1 = 0 , u 2 = 0.5 , and u 3 = 1 , sketch the function u ( x ) .

Chapter 2, Problem 28E, Consider a finite element with three nodes, as shown in the figure. When the solution is

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