Analysis of Euler-Bernoulli Beam with Piecewise Quadratic Hermite Finite Elements

Cong Ying Li; Han Jie Zhang; Dong Dong Wang

doi:10.4028/www.scientific.net/AMM.444-445.163

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 444-445Analysis of Euler-Bernoulli Beam with Piecewise...

Analysis of Euler-Bernoulli Beam with Piecewise Quadratic Hermite Finite Elements

Abstract:

The piecewise quadratic Hermite polynomials are employed in the finite element context to analyze the static and free vibration behaviors of Euler-Bernoulli beam. The desirable C1 continuity is achieved for the piecewise quadratic Hermite element that is required for the numerical solution of the Galerkin weak form of Euler-Bernoulli beam. In contrast to the classical cubic Hermite element, the piecewise quadratic Hermite element has a piecewise constant curvature representation within each element and thus the integration of the stiffness matrix is trivial. Several benchmark problems are shown to demonstrate the convergence properties of the piecewise quadratic Hermite element. The frequency error of the beam free vibration with this quadratic Hermite element is derived as well. Numerical examples consistently verify the analytical convergence rates.

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Periodical:

Applied Mechanics and Materials (Volumes 444-445)

Pages:

163-167

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.444-445.163

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Online since:

October 2013

Authors:

Cong Ying Li, Han Jie Zhang, Dong Dong Wang

Keywords:

Euler-Bernoulli Beam, Piecewise Quadratic Hermite Element, Static Analysis, Vibration Analysis

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