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What is the displacement function for one-dimensional, two noded linear elements in terms of its shape functions N1 and N2?

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+1 vote
in Finite Element Method by (110k points)
What is the displacement function for one-dimensional, two noded linear elements in terms of its shape functions N1 and N2?

(a) N1u1+N2u2

(b) N1u2+N2u1

(c) N1u1-N2u2

(d) N1u2-N2u1

I had been asked this question in examination.

This intriguing question comes from Library of Elements and Interpolation Functions topic in division Interpolation Functions, Numerical Integration and Modelling Considerations of Finite Element Method

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The correct choice is (a) N1u1+N2u2

The explanation: For a linear element, the displacement function is a linear polynomial of nodal displacements. A one-dimensional, two noded linear elements have two nodes with corresponding displacements u1, u2 and corresponding shape functions N1, N2. The displacement function is given by N1u1+N2u2.

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