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From the Euler-Bernoulli beam theory of natural vibrations, using cubic Hermite polynomials approximation, what is the 1^st element of the stiffness matrix?

(a) \(\frac{12EI}{h^3}\)

(b) \(\frac{12EA}{h^3}\)

(c) \(\frac{12EA}{h}\)

(d) \(\frac{12AI}{h^3}\)

This question was posed to me during an internship interview.

Origin of the question is Eigen Value and Time Dependent Problems in chapter Single Variable Problems of Finite Element Method

1 Answer

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Right option is (a) \(\frac{12EI}{h^3}\)

Explanation: In the formulation of the Euler-Bernoulli beam theory, there are two degrees of freedom at a point, w and \(\frac{dw}{dx}\). Typically, the finite element model of this theory uses cubic polynomial. The first element of the stiffness matrix is \(\frac{12EI}{h^3}\), where E is Young’s modulus, I is the area moment of inertia and h is the length of the element.

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