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In FEM, what is the name of the shape function of an Euler-Bernoulli beam element?

(a) Hermite cubic interpolation function

(b) Lagrange cubic interpolation function

(c) Consistent element functions

(d) Quadratic interpolation functions

I have been asked this question during an online exam.

Asked question is 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 option is (a) Hermite cubic interpolation function

To explain I would say: Interpolation function of a beam element is continuous with nonzero derivatives up to order two. It is derived by interpolating the displacement polynomial as well as its derivative at the nodes. Such interpolation functions are called as Hermite cubic interpolation (or cubic spline) function. The Lagrange cubic interpolation Functions are derived by interpolating the displacement polynomial but not its derivatives.

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