Analytical Finite Element Formulation of Non-uniform Euler-Bernoulli Beam - Sulaeman, Erwin; Kapania, Rakesh (2011)

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Structural beam element is widely used for many applications. To satisfy some requirements, it is not uncommon that the beam has to posses a non-uniform distribution of its cross section along the span. A common approach to analyze such a structure is by using a variational principle to develop the element stiffness matrix. In the present paper, an analytical formulation for a stiffness matrix of a non-uniform beam with arbitrary polynomial variation of EI along its span is investigated. The present stiffness matrix is composed using a structural flexibility approach by direct integration of Euler- Bernoulli differential equation. In addition to polynomial function, the proposed stiffness matrix contains logarithmic function which is not found in the formulation based on standard variational principle. Validation of the present formulation is performed by comparing to exact analytical solution and NASTRAN structural analysis software.